Position Dependent Control (PDC) of plant production Hannu E. S. Haapala Department ofAgricultural Engineering and Household Technology, RO. Box 27, FIN-00014 University ofHelsinki, Finland ACADEMIC DISSERTATION To be presented, with the permission of the Faculty ofAgriculture and Forestry of the University ofHelsinki, for public criticism in Auditorium XII, Aleksanterinkatu 5, Helsinki, on July 25th, 1995, at 12 noon. AGRICULTURAL SCIENCE IN FINLAND https://www.c-info.fi/en/info/?token=6JYV46hB6XHrwxcz.gNrmSSaE_kR1hbE-bd0_uQ.h2FhXByKJPr5yc7Z7IdOcBgNAxl54n1VLQ1uHpqeuw67T6rHt-aSoETMl1ymvM3OFxr6inwkBSQNi_QyUd1S3opMXEzFKU439FbQ7isof-eOgkQCil6FdgDgo34BcXnhY_F0RZCh81u4e6164biU2bwdtMJNg0Ys72nPMrrmhyuIKEH8t0h23QWLy2u5jgEyUCiruxyefzmTF98Bij2mB2CJMDx8nanH1G-bAVT_hU7lIf7L3knjEzX4q1K5-tnSMusTPYwJdS0rdg AGRICULTURAL SCIENCE IN FINLAND Preface As the work is now done it is my pleasure to thank all the people who have made it possible and, moreover, pleasant for me to study the subject. The years of research and reporting have brought me much joy and many moments of satisfaction to be remembered. The financial support of the Academy ofFinland has been essential for this work. Without it this project would never have seen the sunlight. As a junior fellow of the Academy I sincerely thank themfor the opportunity offered. I hope that the results will speak for themselves and that the invest- ment will be found worthwhile! In the beginning the Board of Agriculture and Forestry was also financing the research, and I express my gratitude for that, too. The English manuscript was revised by Ms. Viola Frilund, DK, and edited by Ms. Sari Torkko, M.Sc.; I greatly appreciate their collabo- ration. I would also like to thank theBoard ofAgricultural Science in Finland for including this work in their journal. The people at my Department at the University of Helsinki have provided me with an inspir- ing scientific society to work in. During the years the Department has changed its name and given proof of its ability to make dynamic changes withinresearch. The current Department of Agricultur- al Engineering and Household Technology is a growing center of multidisciplinary knowledge and know-how. The agricultural and household sectors work together with different emphasis of the ac- tivity but utilize the same basic sciences. The much talked-about synergy effect is operating in prac- tise. The nicest thing is that the spirit of the Department is fine. Prof. Aarne Pehkonen has given me valuable advice during my work. The technical staff and my researcher colleagues have helped me in many turns. Thank you all very much for your support! My research groupof Position Dependent Control, the “Star Group” in everyday speech at the Department, has established a new culture at the Department. We are a true multidisciplinary re- search team, with special responsibilities for everyone involved. I thank you all - Antti, Kalle, Liisa, Markku, Tero, and the short-time workers as well - for a remarkable co-operation. 1 have really had a good timecarrying out this project with you. I wish you all the best for the future, both in research and in “real” life. This study is concentrated on positioning and therefore my special thanks go to Mr. Markku Hirvenoja, M.Sc., who has conducted many of the practical positioning tests, and to Mr. Kalle Lindell, student in engineering, who has been working on the GPS technology. Thank you for a first-class job! My family - Kaarina, Liinamaija, Sinihannele and Annieveliina have supported me in this stressing phase of life. Your loving patience has been tried many times. I could not express my feelings better than to say, “I love you”. This phase is now over and maybe we will find more time for each other in the future. My parents Arvo and Sirkku have always emphasized the value of good work. May this work be a gift to you to show how much I appreciate the agricultural background I have there in Kiikoinen. Viikki, April 15th, 1995 Hannu E. S. Haapala AGRICULTURAL SCIENCE IN FINLAND List of important acronyms (in the order of appearance) * Defined in this study *PDC Postilion Dependent Control. A control system in which all the used information is position- fixed. The position-fixed information is used to manipulate the inputs to the target position. The target position is called the Production Location (PL). PDC can be utilized in all posi- tion-fixed operations. In this study the target PL is an areally limited location in an agricul- tural field. *PL Production Location. The target position of Position Dependent Control (PDC). The size of a PL is application-specific. The production process and the output required determine the largest area that can be treated as an individual PL. In practise, the incomplete adjustability of ma- chines sets the smallest achievable PL size. *EC Effect Curve. A graphical representation of the effect of a production task, usually performed by an implement. In plant production the production task is a production operation such as ferti- lising, plant protection, tillage, etc. Thus the EC describes the evenness of spread or tillage in both cross and length direction. The cross EC is scaled so that the target effect level will be 1.0. There are some basic cross EC types some of which are used in this study. *ES Effect Sum. A graphical representation of the sum of Effect Curves (ECs). As production loca- tions are treated there will always be some overlapping if optimum working widths (Wopts) are used. Thus the ECs are allways summed to the Production Locations (PLs). An ES curve shows the effect in the target PLs when ECs are summed. Positioning errors in PDC cause inaccurate targeting of the ECs and degrade the quality of resulting ES. *Wopt Optimum working width. The working widthof an implement that produces the best available Effect Sum (ES) of parallell ECs. Wopt can be calculated if the Effect Curve (EC) of the implement is known. In practical work the Wopt changes dynamically. The typical (tested) ES of the implement is used when Wopt is determined. *CVmax Maximum Coefficient of Variation allowed. A limit value for the CV of the Effect Sum (ES) curve. The CVmax sets a quality limit for the implement's work. The suitable CVmax for each position dependent task must be separately derived from the actual production process. Therefore an alternative definition includes the transfer functions from the ES curve to the production output. The CVmax is calculated for the production output instead of the ES. The last option is more valid because it includes the actual production process. *Werr Cross targeting error. The deviation of the location of the implement from the required loca- tion in cross direction of travel. *Werrmax Maximum cross targeting error. The maximum allowed deviation of the location of the implement from the required location in cross direction of travel. Werrmax is calculated by setting a maximum Coefficient of Variation (CVmax) for the Effect Sum (ES) curve. *Lerr Length targeting error. The deviation of the location of the implement from the required loca- tion in direction of travel. *Lerrmax Maximum length targeting error. The maximum allowed deviation of the location of the implement from the required location in direction of travel. Lerrmax can be calculated by setting a maximum Coefficient of Variation (CVmax) for the Effect Sum (ES) curve. In this AGRICULTURAL SCIENCE IN FINLAND study Lerrmax was set by the reaction of the production process to nitrogen input. Lodging was set as the trigger for poor length targeting. DR Dead Reckoning. A vector navigation system that uses distance and heading information to cal- culate positions. Different sensors can be used to get the required parameters. The system is sensitive to accumulated error because each new position is based on the previous ones. The best devices can achieve an accuracy of 1.3% of the distance travelled. DR is frequently used as a backup for other methods, i.e. GPS. (Hakala 1992, Krakiwsky 1994) GPS GlobalPositioning System. A satellite navigation system that gives positioning information 24 hours a day all over the world. The GPS system that is based on a network of 24 geosynchro- nised satellites is managed by the U.S. Department of Defence (DoD) and in the future by the Department of Transport (DoT) as well. Positioning accuracy levels available range from the standard Coarse/Acquisition (C/A) to Precise (P) service level. The best accuracy is not avail- able for civilian users and the signals are intentionally degraded (S/A, Selective Availability in C/A, and encryption of the P-code). The standard GPS gives an accuracy level of ±lOO meters (95%, typical values are c. ±20..30 m). The most accurate systems for geodetic measure- ments are accurate down to below one centimeter (95%). There are receivers that use the digital codes transmitted by the satellites (Code Receivers) and those that use the carrier wave instead (Codeless Receivers). The C/A service can be enhanced to the level of approx, one meter by differential corrections (DGPS). The differential corrections can be achieved by purchasing extra equipment or they can be received from commercial sources. The stand- ard positioning service is free of charge. (Toft 1987, Tyler 1993, Van Dierendonck 1995) DGPS Differential Global Positioning System. The GPS system with a correction system that in- cludes a fixed reference station the coordinates of which are accurately known. The differen- tial corrections are calculated in three basic ways. The first option is to calculate the position of the fixed receiver and correct the moving receiver's position with the calculated error. The second way is to correct the satellite ranges. The third option is to send the needed raw data to the receiver that calculates the corrections locally. The corrections can be done by post- processing or in (near) real time. The real-time corrections require a data link between the receivers. The reference station can be in quite a high distance (200..300 km) from the mov- ing receiver without considerable degradation of the accuracy. It must, however, see all the same satellites than the moving receiver to be able to make the corrections accurately. (Toft 1987, Bäckström 1990, Tyler 1993, Van Dierendonck 1995) RTKGPS Real-Time Kinematic Global Positioning System. The GPS system that uses the carrier phase and On-The-Fly ambiquity resolution (OTF) technics. An RTKGPS. also called RTS- (ReaI-Time Survey) GPS calculates the number of carrier cycles between the receiver and the satellites and keeps track of the phase continuously. In case of carrier slip the OTF tech- nique ensures a rapid solution of the unknown number of cycles (the ambiquites). The OTF can be assisted with code receiving to limit the probable search space of the lost cycle. The RTKGPS requires a nearby (<10..20 km) reference station. (Tyler 1993,Abidin 1994, Van Dierendonck 1995) AGRICULTURAL SCIENCE IN FINLAND Contents Abstract 1 Introduction 248 1.1 Sustainable agricultural engineering and the need for accurate control of field operations 248 1.2 Production Location and Position Dependent Control 250 1.3 Position Dependent Control in crop production 251 1.4Earlier work on locational control 252 1.4.1 Off-line and on-line measurements 252 1.4.2 Earlier international work on locational control 254 1.4.3 Earlier work at the Department ofAgricultural Engineering and Household Technology 255 1.5 Contents of this study 256 2 Position dependent adaptive crop production 257 2.1 Need for Position Dependent Control 257 2.2 Size of the Production Location 259 2.3 Possibilities ofrealizing adaptive Position Dependent Control 260 2.3.1 System knowledge 261 2.3.2 Controllability of the crop production system 262 2.3.3 Technical possibilities 263 2.3.4 Economy and markets ofPosition Dependent Control 267 2.4 Effect of targeting accuracy - simulationwith mathematical models and empirical data 269 2.4.1 Accuracy in working width - simulation with the ECs 272 2.4.1.1 Discussion of the simulations with Effect Curves 280 2.4.1.2 Conclusions of the simulations with Effect Curves 281 2.4.2 Accuracy in direction of travel - a simulation model for effects ofnitrogen targeting accuracy... 281 2.4.2.1 Discussion of the simulations in direction of travel 287 2,4.2.2 Conclusions of the simulations in direction of travel 287 2.4.3 Accuracy in space for PDC - conclusions based on simulations of cross- and length targeting accuracy 288 3 The Keimola survey 289 3.1 Soil fertility and yield variation of spring wheat 289 3.1.1 Soil variation 290 3.1.2 Yield variation 293 3.2 Extracting Production Locations from the Keimola data 295 3.2.1 Linewise Production Locations 295 3.2.2 Yield-based Production Locations 296 3.2.2.1 Simulation ofyield level selection 297 3.2.2.2 Choosing sampling methods for extracting Production Locations from yield data 297 3.2.2.3 Local regressions for Production Locations that are selected on the basis ofyield levels 299 3.2,3 Fixed-length Production Locations 300 3.3 Discussion of the Keimola tests 300 3.4 Conclusions of the Keimola tests 302 4 Positioning 303 4.1 Coordinate systems 303 4.2 Positioning, orientation and navigation 306 4.3 The map in Position Dependent Control 306 4.3.1 The digital map 307 4.3.2 The map in Position Dependent Control of field operations 308 4.4 Classification ofpositioning systems 309 AGRICULTURAL SCIENCE IN FINLAND 4.4.1 Autonomic vehicle sensor systems 310 4.4.2 Transmitter/receiver systems 311 4.4.2.1 Short and medium distance systems 311 4.4.2.2 Long distance systems 313 Enhanced satellite navigation 315 4.5 Positioning methods for Position Dependent Control in agriculture 318 4.5.1 Earlier applications of positioning in agriculture 318 4.5.2 Choosing the method for further tests: Why GPS? 320 4.6 Positioning tests at Viikki Experimental Farm 322 4.6.1 The test route 323 4.6.2 Tests with post-processed DGPS 324 4.6.3 Tests with real-time DGPS 324 4.6.4 Positioning accuracy in the test route 326 4.6.5 Positioning accuracy in road tests 330 4.6.6 Positioning accuracy in field work 330 4.6.7 Discussion of the positioning tests 332 4.6.8 Conclusions of the positioning tests 333 5 Examination of the results and conclusions 334 5.1 Potentialities of Position Dependent Control in field crop production 336 5.2 Requirements for the methods for attaching field crop information to a coordinate system 337 5.2.1 Requirements based on yield and soil parameter variation 337 5.2.2 Simulated requirements 338 5.3 Possible solutions 339 5.4 Future developments 340 References 343 Selostus 350 Appendices 1-12 Citations in the text are made according to the technical system. This system is not normally used in Agricultural Science in Finland. AGRICULTURAL SCIENCE IN FINLAND AGRICULTURAL SCIENCE IN FINLAND Position Dependent Control (PDC) of plant production Hannu E. S. Haapala Department ofAgricultural Engineering and Household Technology, P.O. Box 27, FIN-00014 University of Helsinki, Finland The aims of this work were to get answers to the following three questions: (1) What are the potenti- alities of coordinate-based field crop production? (2) What are the requirements for the method of attaching field crop information to a coordinate system? (3) What are the possible solutions? The work was focused on the effects of positioning quality. In PDC (Position Dependent Control) positioning is needed to target the inputs and to relate inputs and outputs accurately to each other. Systems analysis was used to accomplish a mathematical model of the position dependent control system. The model developed describes a system which consists of models for the positioning meth- od and the target. An accuracy requirement of ±5 meters for N-fertilization was set with the devel- oped model. The results from Keimola gave information on the variability of soil and wheat yield. Regres- sions for individual input variables and multiple regressions calculated for whole sample lines (ä 50 m) were low (r2 <0.11 and r2 <0.15). Attachment of the variation information to coordinate gave re- gression estimates with r 2 's up to 0.99. Positioning tests in Viikki show adequate accuracy (uncer- tainty ellipse <25 m 2 @95%) ofDGPS (Differential Global Positioning System) satellite positioning. DGPS was tested both in an accurately measured test route and field tests during drilling. Road tests in covered locations were also made. PDC of plant production gives accurate control over the position fixed production process. The enhanced controllability can be used to adjust the production to meet environmental or economical criteria. The variable requirements for positioning can be set with simulation. The simulations need valid models for the production in the target area. GPS satellite navigation together with a GIS (Ge- ographical Information System) database is a potential technics for the realization of this local con- trol. Key words', site-specific control, spatially variable field operations, GPS, GIS, simulation © Agricultural Science inFinland 247 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Introduction 1.1 Sustainable agricultural engi- neering and the need for accu- rate control of field operations Sustainability is a widely used term but it also has variable meanings. Sustainability can be de- fined by various criteria of production, econo- my or environment. In engineering, sustainabil- ity is commonly accepted to include environmen- tally and economically sound technologies which utilize their inputs efficiently. This means, in other words, technologies which use renewable resources and have high efficiency coefficients. In other contexts, sustainability is considered to be a philosophy or a set of rules used to select production methods. Furthermore, it can be a synonyme for organic production or economi- cally maximized production. It is widely agreed that nonrenewableresources should not be used. The time span of sustainability is subject of con- stant argument. Current practises can be sustain- able for us but not for the future generations. (Francis and Youngberg 1990, Heinonen 1993, Azelvandre 1994) As a result of a large literature review Fran- cis and Youngberg (1990) conclude:“Sustainable agriculture is a philosophy based on human goals and on understanding the long-term impact of our activities on the environment and on other species. Use of this philosophy guides our ap- plication of prior experience and the latest sci- entific advances to create integrated, resource- conserving, equitable farming systems. These systems reduce environmental degradation, maintain agricultural productivity, promote eco- nomic viability in both the short and long term, and maintain stable rural communitiesand qual- ity of life.” Azelvandre (1994) summarizes sustainabili- ty criteria as follows: 1. Does a technology cause environmental damage and/or resource depletion in its creation or manufacture? 2. Does a technology cause environmental damage in its use or implementation? 3. Does the technology promote and encour- age direct democracy when feasible? 4. Does it foster community self-reliance on a local, regional, national level? 5. Does it encourage human growth and ful- fillment? 6. Does it encourage equitable distribution of material wealth? (Does the community which utilizes and benefits from a tech- nology own it?) 7. Does it contribute to community stabili- ty? 8. Does it adequately reflect human values and aesthetics? 9. Does it not have negative effects on hu- man health? (Closely related to criteria 1 and 2 above.) Two additional criteria: 10. Technical efficacy: Does it do the re- quired task efficiently on top of all the above criteria? 11. Context dependency: The Appropriate- ness of a technology will depend on the particular context. There is no universally correct technology. As shown in the examples above, sustaina- bility criteria are many. International attempts have been made to decide which criteria should be used. Sustainable development has been viewed in e.g. the so called Brundtland Comis- sion (Harris 1988, EC 1992). Regional authori- ties have made their own decisions. In Finland the Academy of Finland has a Research Pro- gram for Sustainable Development (Väyrynen et al. 1990) and a Research Program for Sustaina- ble Agricultural Engineering (Elonen et al. 1991). In the latter program sustainable agricul- tural engineering is defined as the technology that operates with a high efficiency coefficient and that does not cause environmental degrada- tion. (comp. Francis and Youngberg 1990 and 248 Haapala, H. E. S.: Position Dependent Control ofplantproduction AGRICULTURAL SCIENCE IN FINLAND Azelvandre 1994 above) Plant production is very important in the de- terminination of sustainability because it is a primary part of production. Thus plant produc- tion technology plays an important role in the efficiency of the whole agricultural production system. It determinesto what extent we get pri- mary products and byproducts that can not be used or that have negative effects on the envi- ronment. (Elonen et al. 1991, Fig. 1) The Research Program for Sustainable Agri- cultural Engineering focuses on the following (Elonen et al. 1991): 1. Development of calculation methods and information systems. 2. Development of adaptive control technol- ogy. 3. Development of operating principles and construction of agricultural machinery. 4. Development of cropping systems that keep the soil covered as much of the time as possible. 5. Future research in agricultural engineer- ing. 6. Improvement of soil structure and the use of minimized tillage to maintain soil health, to get low production costs and to minimize soil and nutrient losses. 7. Better utilization of machine capacity and reducing energy consumption. 8. Possibilities of renewable energy use in agriculture. 9. Developing methods for keeping the seta- side easily accessible for continued food production. 10. Developing systems for mutual manage- ment of water, gas, temperature and nutri- ent balance in the soil and plants. 11. Technology of alternative plant protec- tion. The program states that multidisciplinary knowledge is needed in the development of sus- tainable technics. This kind ofknowledge is scat- tered, so that we need information systems such as knowledge based systems to manage it. We also need sophisticated methods to identify tech- nologies that stress the environment. Adaptive control is needed in almost all of the listed tasks, i.e. we need technology that adapts its perform- ance to animal and crop variation. To achieve this, it is inevitable to develop agricultural ma- chines and implements to meet more accurate control requirements. Future research is needed because particularly strategic but also operative decision making needs knowledge of future trends. Improvement of soil structure is possi- ble with light-weight transport technics and pro- duction methods that do not compact the soil. We should use more integrated solutions that take into account all factors of the plant's surround- ings. (Elonen et al. 1991) Technology Assessment (TA) is nowadays a central part of major decision making in many countries and international organizations. This is because it is generally accepted that technics can have negative effects on the environment, social structures and other surrounding systems. TA can be divided into formal and informal types. The formal TA is defining its target sys- tems in terms of mathematical models and cal- culations, whereas the informal one is based on theresearcher's own comprehension and estima- tions. The formal TA resembles systems analy- sis, the informal one a learning process. (Lars- son 1990, OTA 1993) Fig. 1.Restricting factors of agri- and horticultural produc- tion (Elonen et al. 1991). 249 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production Larsson (1990) concludes in his informal TA method study that agricultural TA can not only be based on a money scale. He draws his con- clusions on criteria of environment, biology, work environment, technics, energy and econo- my. He judges these components and concludes that the most important research and develop- ment goals in plant production are as follows: 1. Development of methods and technology to measure the efficiency of various plant production tasks. 2. Development of automatic and manual measurement methods of soil parameters. 3. Development of calculation methods which enable automatic measurement and control. 4. Development of control technics for man- ual and automatic control. 5. Development of technics needed in plant production management 6. Development of alternative technical sys- tems and sub-systems needed in future plant production. Position Dependent Control, as it is defined in this work, is dealing with a major part of the above mentioned tasks. It is a tool that enables sustainable production, if correctly used. The correct use is only possible if the target system is adequately known. This emphasizes the need for accurate local information. In turn, the qual- ity of positioning information is a central issue for proper operation of the control system. 1.2 Production Location and Position Dependent Control In traditional crop production we do not follow in-field variation of production potential or en- vironment pollution risks. The whole field is treated with constant settings. This is not, how- ever, optimal because the field consists of indi- vidual locations. These locations need variable amounts of inputs and they give different re- sponses. The production process is vulnerable to several disturbances and errors. Widely speak- ing, these negative factors have an effect on the planning process, the inputs, the location itself and the outputs. To enable generalizing, the tar- get is here named the ProductionLocation (PL). (Fig. 2) Control engineering, in general, is used to decrease the effects of disturbances and thus to reach the goal wanted with a reasonable accura- cy. The goal can be e.g. maintaining quality, economy or safety or minimizing environmen- tal stress. Feedback control is frequently the only technical solution when the target is a compli- cated process. (Haugen 1990) Geographical information describes the data and its location. The location can be expressed in coordinates or by a locating property, such as land register number. GIS (Geographical Infor- mation System) is an information system that uses geographical information.A narrowed def- Fig. 2. Error and disturbance factors connected to the Pro- duction Location (PL). The term PL is universal: agricul- tural terms are used as an example. 250 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. inition includes a configuration of computer hardware and software specially designed for acquisition, maintenance and use of cartograph- ic data (Tomlin 1990). The GIS has widened its application area. Nowadays it is widely used in administrative tasks: in 1988 there were over 30 state organi- zations and several municipal and private organ- izations in Finland that provided information for joint use. There were over 200 registers, in pub- lic administration only, including local informa- tion. (Rainio 1988) Lateron there have been much more providers, and much is invested in GIS-technic (Kosonen 1993, Rainio 1994). The technical applications of GIS include manage- ment oflocal information in different scales from local to global applications (Tomlin 1990, Rai- nio 1992, Ruutiainen 1994, Taipale 1994, Aho- nen 1993b). Position Dependent Control (PDC) is here defined as a control system that integrates con- trol engineering and the GIS to a new concept. PDC uses local setpoints to achieve locally want- ed control. The location which the setpoints are fixed to is named the Production Location. Ag- ricultural PL is e.g. an areally limited location in the field. (Fig. 3) Attaching information to Production Loca- tions has several positive effects on the control- lability of production. Production Locations tie all local information to manageable units where it is quite easy to distinguish responses of given inputs and thus to get accurate feedback. The feedback from the PLs can be used in planning the inputs (choosing their quality and setting the application rate, working depth, effect, etc.). PDC is an adaptive control method. In adap- tive control the controller parameters are con- tinuously changed to meet the requirements of the controlled process (Haugen 1990). This is just what PDC is aiming at: to adjust the control system to local needs. 1.3 Position Dependent Contro in crop production The information of the Production Locations in crop production is currently not located, i.e. there is no local information available. In Position Dependent Control, information on the need of inputs, the amount of given inputs and received outputs (production, environmental stress) is connected to the PL. Therefore all the informa- tion needed should be localized. PDC also needs local real-time setpoints. Part of the setpoints can be calculated on the basis of direct measurements, but the majority of them must be stored in a GIS. This is because direct measurement methods are not available or they are so slow that measurements can not be made in real time. There are also measurements that are to be made in a certain phase of the produc- tion, which is not the current one. In crop pro- duction, it is common that the system has con- siderable time delay: the PL integrates inputs for a variable time and then produces its output. This also requires the data to be put in a GIS. PDC needs good models for the local pro- duction process so that the outputs can be pre- dicted. In crop production this sets the need for good weather knowledge. Forecasts can be used in some cases where the effects are quite instant. Other cases may need simulation models which use different possible weathers to illustrate the risk of giving alternative treatments. The over- all system for position dependent control could consist of planning, realizing and feedback parts Fig. 3. Production Location (PL) in the field. 251 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production (Fig 4). In the figure (Fig. 4) the box 'calcula- tion of setpoints' uses production outputs as feedback of the production outputs of previous years. This stage is an adaptive controller be- cause it changes its parameters according to changes in PL. The inner control loop is taking care of the implement. It checks if the imple- ment is following the setpoints of the outer loop or not. The adaptive control loop uses the im- plement to realize its goals. Furthermore there could be additional loops which represent exter- nal legislative, social, ethological, etc. restric- tions (Fig. 1 above, comp. Larsson 1990). in virtually unlimited areas on the Earth (Au- ernhammer et al. 1994b). Specially the satellite navigation system GPS (Global Positioning Sys- tem) gains more markets. This development en- ables even the use of small robot tractors in ag- riculture (e.g. Palmer et al. 1988, Nieminen and Sampo 1993). Position Dependent Control is a new appli- cation for positioning. When this study began in the late 1980's, there were no ready-made sys- tems suitable for agricultural PDC. Currently there are several reported systems (e.g. Auern- hammer et al. 1994a, Colvin et al. 1994. Staf- ford et al. 1994). 4 Earlier work on locational control Positioning of agricultural machines is not a completely new idea. Positioning is used in tra- ditional methods to distinguish between parallel passes and to enable driving accuracy. Driving accuracy aids, other than actual positioning sys- tems, have been developed for a long time.These include traditional markers and row sensing de- vices (Schueller et al. 1994). Later these have been followed by more developed radio beacon (AGNAV 1988,Palmer 1991), laser (Shmulevi- ch et al. 1988) and other low distance sensor sys- tems (Yoshida et al. !988,Vuopala 1990,Mäkelä et al. 1991). Nowadays positioning systems have devel- oped to a state that allows accurate positioning 1.4.1 Off-line and on-line measurements Most suggestions for the realization of location- al control in crop production have been based on the idea that setpoints could be produced sep- arately from control: setpoints that are calculat- ed in office are brought to the implement with some memory media and realized. (Clark et al. 1987 ref. Mpller 1990, Petersen 1991, Auern- hammer 1990). (Fig. 5) On the other hand, on-line measurement tech- nologies for the measurement of yield and soil parameters have been developed. Larsson (1990, 79) thinks that sensor development is crucial for the development of crop production systems. This is a common conclusion of several research- ers (Auernhammer 1990, Stafford 1993, Colvin et al. 1994). The development areas of these measurement technics can be divided into soil Fig. 4. Control loops ofPosition Dependent Control (PDC). 252 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. and plant/yield measurements. Multiple exam- ples of these technologies are found in literature. Automatic soil sampling and sensing tech- nics are developed (Gaultney et al. 1988, Di et al. 1989,Schmidt 1991,Diaz etal. 1992, Thomp- son 1992,Auernhammer and Muhr 1993). New sensor types, e.g. ion-selective sensors (ISFETs, lon Selective Field Effect Transistors), are de- veloped for the measurement of soil nutrient content to be used in the determination of need of fertilizers. Research is very active in the area ofcontinuous measurement of nutrients, but the sensors are still on prototype level or sensitive to mechanical stress or impurities in the sample. Such sensors are not suitable for field use (Holm- berg 1987, Birrell and Hummel 1992, van den Vlekkert 1992). Seedbed assessment can be done by image processing (Stafford 1988a). Soil den- sity can be measured with a radar (Doolittle 1987, Stafford 1988b). Soil mechanical imped- ance is measured with a horizontal penetrome- ter (Alihamsyah and Humphries 1991). Soil moisture content is measured with e.g. dielec- tric (Arnold et al. 1992) or thermal (Altendorf et al. 1992) properties, microwaves (Jackson et al. 1987,Whalley 1991,Borgelt 1992)and Near- Infra-Red (NIR) sensors (Price and Gaultney 1993). Plant parameters can be assessed on-line by image processing (Han 1988, Blazquez 1991, Fouche 1992), light reflectance measurement (Gaultney et al. 1989) or using portable radiom- eters (Nilsson 1991, Rao et al. 1992, Richard- son and Everitt 1992, Wiegand et al. 1992). Im- age processing is also used for measurement of crop cover (Han et al. 1988) and crop residue cover (Meyer 1988,Endrerud 1994).Yield meas- urement systems are being developed in many research groups. Various methods that use either volumetric or mass flow principles are reported (Searcy et al. 1987, Roberts 1991, Borgelt and Sudduth 1992,Demmel et al. 1992,Stafford and Ambler 1992,Auernhammer etal. 1994a, Colvin et al. 1994, Stafford et al. 1994). Impact type sensors are also developed (Vansichen and De Baerdemaeker 1992). Field conditions do not allow some of the above mentioned examples of current research or prototype methods to be used. In practise it is not possible to use sensors that need extra care or constant calibration. The sensors should be rugged and fit to many soil types. There are also some difficulties with the frequency response, and speed of the analyzing, particularly. The measurement of soil nutrient content should work at least in the time that the tractor-imple- ment combination passes the soil. This means a reaction time of c. 1-4 seconds (5 m combina- tion length, 1.25-5 m/s forward speed). The same requirement is also found for other measure- ments that use sensors mounted to the tractor and where the measurement result is used for local control. The restrictions of real-time measurements in connection with the spatial nature of field parameters makes GISs very attractive in the search of efficient technologies for better con- trol of field operations. GIS is made for storage and analysis of local information. A combina- tion ofGIS- and control technology would serve the needs ofprecise plant production if econom- ical and environmental benefits cover the costs of investments needed. The ease of operation should also be one of the leading goals of “Farm- GIS” development. Fig. 5. Configuration of local control based on off-line measurement (Clark et al. 1987 ref. Möller 1990). 253 AGRICULTURAL SCIENCE IN FINLAND 1.4.2 Earlier international work on locational control Currently there are a few total solutions of loca- tional control with variable names like Site-Spe- cific Farming, Spatial Control of Field Opera- tions, Spatially Selective Field Operations and Site or Soil Specific Crop Management report- ed. Maybe the most complete system is reported by Buschmeier (1990) and Schnug et al. (1990). At the University ofKiel a concept of Com- puter Aided Farming (CAF) has been developed. A positioning method is used to attach chemical doze (herbicide and fertilizer) to the correspond- ing yield. The system includes data acquisition, data management and realization. The data ac- quisition part uses data acquisition units such as soil sampling and a yield meter installed in a combine. There is also a method for mapping. The data acquisition units are positioned so that the results can be attached to coordinates. The data are classified to once measured constant ba- sic data (e.g. geography, soil clay content), me- dium term data (usable P or K) and fast chang- ing data (usable N or S). The basic data are ei- ther constant or very slowly changing. Medium term data are measured in 2-4 year intervals, whereas fast changing data are measured many times a year. The data management part consists of a data management program, LORIS (Local Resource Information System). The data are saved in a standardraster format, where theraster size is 100-200 m 2. The program has tools for data interpolation and conversion. In the data management part the data are classified in areas that are equally treated. Classifications are com- bined to raster setpoints that are given to the re- alization part. The realization has a positioning method (GPS satellite navigation), a tractor com- puter and connection to implements. The set- points are transferred in memory cards to the tractor computer. The setpoints are given to sprayers and fertilizers. Yield is acquired with the yield meter of the combine. The system de- velopment has been going on since 1988. (Schnug et al. 1990) In the U.S.A. there are corresponding projects that use a multidiscliplinary approach. Sophisti- cated technics such as remote sensing and im- age analysis are widely used to get the huge amount of data needed in large scale natural re- source management. Measurement methods for in-field variability are widely used. Satellite- (GPS)-based positioning is initiated in the U.S. DoD (Department of Defence) so most PDC-re- lated projects use it. (Schueller et al. 1992a, b, Colvin et al. 1994) In the U.K. there are numerous projects on subjects related to PDC. PDC of fertilizer and herbicide application, control of cultivation, seedbed preparation and yield mapping are cen- tral points of these research projects. (Mpller 1990, Stafford and Miller 1993, Stafford 1993, Stafford et al. 1994) The Nordic countries conduct their research activities with slightly different focuses. Swe- den has carried out projects on methods for pre- cision farming, such as positioning systems (Ek- fäldt 1994), remote sensing (Nilsson 1992) and precision of machines (Svensson 1992). There has also been technology assessment of local control (Holstmark and Nilsson 1989, Larsson 1990). Danish projects have concentrated on yield mapping (Christensen 1991a) and tramline positioning (controlled traffic agriculture) (Wej- feldt 1990). There are also projects on machine guidance (Emgardsson 1991). Besides these above mentioned there are many related researches concerning individual parts of realizing the PDC. Measurement sys- tems, as mentioned above (Ch. 1.4.1), belong to the integrated technologies needed. Software for planning and management is being developed (Oliver 1987, Petersen 1991, Colvin et al. 1994). Control strategies and economy (Forcella 1992, Jahns and Kögl 1992,Mcßratney 1992) are con- sidered. Data formats for communication (ISO 1994d) are researched. There are several R/D- -projects to achieve flexible equipment (e.g. Au- ernhammer 1990, Mpller 1990,Auernhammer and Rottmeier 1992). Vehicle data buses are de- veloped in Germany, Denmark, France, the U.S.A. and the U.K. (Schueller 1988,Siirtola and 254 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. Alanen 1990, Stafford and Ambler 1993,Auern- hammer 1991, Auernhammer 1993, KTBL 1993, ISO 1994). An agricultural bus system is to be standardized (ISO 11783-1-11783-5). Position- ing trials are done in most countries involved in PDC (Auernhammer et al. 1994, Christensen 1991a, Colvin et al. 1994, Ekfäldt 1994, Staf- ford and Ambler 1994). 1.4.3 Earlier work at the Department of Agricultural Engineering and Household Technology In 1987-89 the author developed an on-line meth- od for the measurement of digging depth and pipe location variation in underdrainage instal- lation (Haapala 1992). On-line measurement re- quired that the system would operate at suffi- cient speed and provide accurate enough (±5 mm, 95%) results. The developed system consisted of a laser level transmitter (revolving laser beam), a laser receiver (laser photodiodes in a movable grid), a potentiometric sensor, two tilt sensors (damped inclinometers), a DAQ-unit based on a single-chip microcomputer (MC6BHCII) and a master laptop computer for control of the measurement cycle. The software controlled the measurement, displayed theresults graphically and saved themfor further use. Print- outs were available on request. In laboratory tests the system had an accura- cy of ±2,9 mm (95%). For field tests the system was installed to a plough drainage machine (Fig. 6). The tests showed that the system was able to fulfill the set requirement of±5 mm (95%). Prob- lems ocurred when there were gusts of wind that made the transmitter oscillate. This lead to a degradation of the installation accuracy. A rec- ommendation was given not to install drains in stormy weather and to keep the transmitter at a moderate distance in windy conditions. (Haapa- la 1992) The conclusion was made that the sys- tem could be used as a general method to meas- ure the vertical coordinate accurately. If posi- tioning was added to this accurate height meas- urement, a very accurate 3D-positioning system for limited area (0 300 m) use could be accom- plished. This would make it possible to have un- derdrainage without marking drain locations Fig. 6. The measurement system of installation precision on a plough drainage machine (Haapala 1992). Fig. 7. Position dependent management of production (Haa- pala 1990). 255 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production (staking-out) on the field. Furthermore, a posi- tion-based crop production system (Fig. 7) could be established. Coordinates could be used to link production outputs, planning and realization. (Haapala 1990, Haapala 1991, Fig. 7) The currently involved research projects at University of Helsinki, Department of Agricul- tural Engineering and Household Technology are concentrating on developing detailed models for planning and realizing position dependent con- trol of selected field works, such as fertilization and crop protection. Field tests are conducted in order to get information on the technical reali- zation. R/D-projects are going on to get the ma- chinery needed (more controllable drills and sprayers, aerial photography, mapping systems) and software (Farm-GIS, production models, control software) for position dependent appli- cations. (Haapala 1994b) .5 Contents of this study This study concentrates on in-field-level preci- sion of plant production. The research uses sys- tems analytical methodology (Gustafsson et al. 1982). Plant production in a field is thought to consist of the by-position-and-area-defined units, the Production Locations. The methodology deals with these restricted areas, systems. The PL-system is represented in application-specif- ic detail. It is mathematically modelled and sim- ulated. The results are validated with early re- sults and collected empiric data. Thereafter the research problems are solved by means of the models. Results are discussed and criticized. (Gustafsson et al. 1982,App. 1) The models use either modeled or measured positioning accuracy and parameter data of the target Production Location. There are submod- els both for the targeting and for the PLs. The modeled targeting error is fed to the PL-model with transfer function from the input to produc- tion output. A general system model that is divided into two separate models for targeting errors in cross- wise and lengthwise direction is constructed. These models are used to give solutionsfor some inputs and transfer functions. Besides these a semi-empiric case-study is simulated.Actual soil parameters and DGPS- (Differential Global Po- sitioning System) positioning data from position- ing tests are used together with modeled trans- fer functions to get the accuracy requirement for targeting of site-specific nitrogen fertilization. In this case-study the target-PL is a simple ni- trogen application-yield model. (Fig. 8) Fig. 8. The study consists of literature surveys, modeling and experiments. Simulations for getting the requirement for targeting accuracy use both empiric and simulated components. 256 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. 2 Position dependent adaptive crop production King (1990) defines sustainable soil fertility as a state in which nutrients are available forever. This is achieved by a closed nutrient cycle, where the nutrients taken up by the plants re- turn to the soil for further use. In a practical soil- plant system this is not, however, possible. In practise nutrients are added to and lost from the cycle. For practical farming King (1990) sug- gests that we should add only the necessary amount of nutrients and that losses should be minimized. This is exactly what the position dependent plant production is aiming at: to give site-specific inputs. 2.1 Need for Position Dependent Control Position Dependent Control integrates produc- tion processes to better manageable units, the Production Locations. These can give much more detailed information on the health of the produc- tion process and its outputs than traditional pro- duction methods. Local information is used to adjust the production to local, regional or glo- bal requirements. Differences in soils cause great variation of grain yield and quality with same fertilization in Finland (e.g. Heikkilä 1980, Mukula and Ran- tanen 1989a, b). Economic results vary for the same reasons because further uses of grain, e.g. industrial use for milling, starch or malt produc- tion, set strict quality standards for grain. The variation is due to the fact that Production Lo- cations (PLs, Ch. 1.2) have varying properties. The existence of variation has been known for a long time (e.g. Kivinen 1935, Peck and Melsted 1973, Jokinen 1983,Diaz et al. 1992, Catt 1993, Delcourt and De Baerdemaeker 1994,Puustinen et al. 1994) and various measurement methods are being developed for its assessment (Nash et al. 1990, Bhatti et al. 1991a, b, Mcßratney 1992, Lesch et al. 1992, Wendroth et al. 1992). Varia- tions cause noise in measurements that use large test plots, and must be accounted for if clear re- sults are wanted (Bhatti et al. 1991b, Wendroth et al. 1992, Finke 1993). This instability of soil properties in time and space is also seen as dis- crepancies when validating simulation results with empiric field data (Johnsson et al. 1987, Moxey et al. 1995). Production Locations are dynamic (Mcßrat- ney 1992). The structure is changing rather slow- ly whereas soil temperature, gases, humidity and water soluble ions have a periodical variation. These variations indicate soil structure changes and they follow changes in the environment. The soil also acts as an inhibitor or filter for these changes, smoothing them. Soil processes can be classified according to their dynamic behaviour (Table 1, Richter 1986). The processes get less complicated from the left to the right. On the left there are slow processes that are involved with soil formation.To the right there are main- ly dynamic plant growth processes. Applications are more interested in the upper level prosesses of the rightmost column (Table 1). Clark et al. (1987, ref. Mpller 1990) say that the most stable soil parameters are texture, hu- mus content, hardness, suitability for artificial raining and fertility. 'Semistable' ones are things that form the history of soil use: previous crops, plant protection, soil tillage and the current plant disease and pest situation. Unstable (dynamic) processes are such as soil humidity and need for artificial raining. Soil nutrients can be divided in more detailed stability groups where water sol- uble nutrients are most instable. Nutrient stor- ages and theirmineralization stabilize plant up- take. Weather conditions affect the uptake. The soil water and gas exchange systems by far de- termine the availability of nutrients. Thus they also determine with a great impact the actual effect of the fertilizer given. (Cooke 1982, Rich- ter 1986, Peltonen 1992) 257 AGRICULTURAL SCIENCE IN FINLAND Table 1. Soil processes classified according to their dynam- ics (Richter 1986). less complicated processes with increasing dynamics Humification Humus decom- position Podsolization Gleying Laterization Solodization The nutrient cycle can be viewed on several levels. In nature plant residues return to the soil. The cycle has losses and nutrient addition. Ni- trogen is added through biological fixation and precipitation; and it is reduced by soil erosion, leaching, denitrificationand volatilization of am- monia. The nutrients are in constant movement between soil solutionand organic matter or clay. Micro organisms take up nutrients from the so- lution as they decompose organic matter. This nutrient returns to the solution as micro organ- isms die. The weathering of minerals brings nu- trients to the solution Plant roots act as a sink that integrates the nutrients. (King 1990) In an agricultural nutrient cycle some of the nutrients are taken away in the yield (Auernham- mer 1990). If we want this system to work con- tinuously we must replace the harvested amount. (Fig. 9, King 1990) The cycle can be expanded to comprise an entire region. On a farm thatproduces both crops and animals, the nutrients first leave the field in the harvest and then the farm in grain, hay or animal products. A large fraction of nutrients consumed by animals return in manure. The net loss is compensated by buying fertilizers and feed. Products leave the farm and are processed and consumed. A fraction of the nutrients is de- Mobilization of Fe Clay formation Clay destruction Clay transformation Pseudogleying Erosion Salinization Mineralization Loosening Compaction Desalinization Infiltration Evaporation Heat transport Leaching of carbonate Gas diffusion lon exchange Immobilization posited in surface water or landfills. Part of these nutrients could be returned to the farm in the form of food processing by-products, effluent or sewage sludge. This is not true recycling because the processing industry gets its input from sev- eral farmers. The effect is the same though be- cause nutrients are returned to the cycle. (Fig. 10, King 1990) As PLs vary it is natural that inputs to them must vary, too: if we do not vary our production methods and their effect we do not get optimum outputs. Production methods have considerable effect to fast changing components of soil proc- esses (Richter 1986). Lack of control of these processes gives a diminished efficiency coeffi- cient in comparison with individually optimized inputs. Adaptive Position Dependent Control makes it possible to get simultaneuosly both better economy and less environmental stress (Finke 1993, Nielsen and Bouma 1993). This kind of production is based on the ideas of sus- tainableagriculture. The current methods which do not vary the inputs can not be optimal and are thus not sustainable (comp. Elonen et al. 1991,Stafford 1993). The plant and variety giv- en, varying the inputs is the only way to affect the production output. Input is here seen as effi- ciency (or level) of the site-specific crop pro- duction works (fertilizer doze, tilth effect, ploughing depth, etc.). Production strategy of PDC is reflected by the given inputs (Jahns and Kögl 1992). Alternative production methods (e.g. incorporation/surface spreading, autumn plough- ing or ploughless production) are groups of dif- ferent inputs. Some inputs need to be variated both in time and space. Seedbed preparation is very sensitive for right timing in certain clay soils, some other soil types are not so sensitive to the timing. In economic terms, there is a big timeliness effect in clays, requiring correct dimensioning of ma- chine capacity. Insufficient capacity causes in- creased costs as it leads to inaccurate timing. Var- iations in nutrient uptake in different years can cause a need for supplementary fertilizing. The timing of this additional treatment is crucial (Esala 1991,Peltonen 1992). Evidently the need 258 Haapala, H. E. S.: Position Dependent Control ofplantproduction AGRICULTURAL SCIENCE IN FINLAND Voi 4: 239-350. of seedbed preparation and adjusted fertilization varies in space as well. The same variability is true with weeds (Erviö and Salonen 1987). 2.2 Size of the Production Location This study concentrates on components that di- rectly affect the Production Location. The max- imum size of PL that can be treated with con- stant treatment is defined. To be able to do this, we have to know what are the consequences of giving the inputs to variable areas. This in turn needs to be considered against the variation of the true requirement of inputs in the field. When a location and its data are connected to a coordinate, the size of the area which is con- sidered as the same location is a primary ques- tion. Choosing a certain size leads to several oth- er decisions. A large area is much easier to lo- cate than a small one. A small target area leads to positioning and control problems since the target has to be detected in order to perform the related task. According to Richter (1986) soil, apart from being a connection point, is a grow- ing place for the plant. This is the smallest sep- arate unit in the field. This unit has its own en- ergy and materia flow and transport systems and produces as much as local conditions and the plant itself admit. The environmental impact is also dependent on these restrictions. The target location of Position Dependent Control, the PL, may consist of several of these units. Choosing the appropriate size of the PL can be expressed in form of a few questions as follows (Fig. 11). The first question (Fig. 11) has to be asked because we want to know if the target area has to be divided in different subareas or not (comp. Fig. 9. Nutrient flow (a) in nature and (b) in agricultural systems (King 1990). Fig. 10. Nutrient flow in a region (King 1990), 259 AGRICULTURAL SCIENCE IN FINLAND Forcella 1992). This leads to the need of a basic survey that finds out the variation type. The sur- vey should be conducted with a resolution that is at least twice higher than all predictable fu- ture applications of the data (sampling theorem, Haugen 1990, Franklin et al. 1994). The second phase is to determine the trigger value of varia- tion: how high deviations are of importance. These critical values have to be defined in terms of accepted range, frequency and local concen- tration of the variation. The size of the target is derived out of the critical values and actual vär- iation. This also leads the selection of variation measurement technics. (Fig. 11 above) The estimation of Production Location size resembles the problems found in geostatistics (App. 2): we have to find the most rational way to collect information (Clark 1984). Geostatis- tics is based on Matheron's (1971 ref. Clark 1984) Theory ofRegionalized Variables. Geosta- tistical procedures are extensions to classical sta- tistics with the assumption of sample independ- ence removed (Upchurch and Edmonds 1989). Geostatistics can be used in various applications where the location of the estimation target is known and surrounding targets are both located and measured (Oliver and Webster 1991). Ge- ostatistics is most utilized in mining (Clark 1984). Agricultural applications of geostatistics are in the areas of sampling design (Di et al. 1989,Webster and Oliver 1990,Thompson 1992, Delcourt and De Baerdemaeker 1994), interpo- lation (Bhatti et al. 1991a, Delcourt et al. 1992) and modeling (Flaig et al. 1986, Oliver 1987, Nielsen and Alemi 1989, Goovaerts and Chiang 1992, Bouma and Finke 1993, Mulla 1993) 2.3 Possibilities of realizing adaptive Position Dependent Control PDC can be viewed on several levels of tasks and in time domain. The task level consists of the creation of control strategy and its coding to setpoint values and, on the other hand, realiza- tion of these setpoints. The latter task, realiza- tion, is Position Dependent Control of the im- plements. Adaptivity is maintainedthrough feed- back and the control strategy (see Ch. 1, Fig. 4). in time domain short and long term effects must be discriminated. (Fig. 12) The strategic level concentrates on long term effects of pro- duction whereas realizing is dominated by short term thinking. Control strategy creation operates with global concepts such as sustainability: are Fig. 11. Choosing the size of the target and measurement methods according to the variation of the local information. 260 Haapala , H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. we doing the right things? Setpoint realization/ implement control finds technological solutions: doing theright things as well as possible, (comp. Elonen et al. 1991) This study is concentrated mainly on the re- alization (right branch in Fig. 12). Current projects at the Department ofAgricultural Engi- neering and Household Technology deal with the strategic level as well (Haapala et al. 1994). The required state of the controlled system is achieved through changing the inputs of the system. This in its turn needs setting the refer- ence values, i.e. the setpoints. The setpoints are given to a controller that passes them on to the system. The system itself, its innerproperties and external disturbances, decides how these inputs show up in system state and output variables. (Gustafsson et al. 1982, Haugen 1990,Fig. 13). The setpoint is set to the level desired. This level can either be constant or dynamically var- iable. The dynamics can be based on e.g. time, location or distance traveled. Setpoints are set in such a resolution that the reference is achieved with a reasonable accuracy. The most usual con- trol method is feedback control. It is based on the measurement of the output (Fig. 4 above). Other generally used methods are feed forward control (from reference and/or disturbance) and gain scheduling (parametric control). Adaptive control, in which controller parameters change realtime as a function of measured values, is getting to general use. The realization of control, in general, requires that (Gustafsson et al. 1982, Haugen 1990, Fran- klin et al. 1994): 1. The system controlled is adequately known 2. The system is controllable 3. The control is technically possible 4. The control is economically justified 2.3.1 System knowledge If the system is not known it is not possible to identify components that affect system behav- iour. It is, though, possible to act to a certain extent with so called 'black box' knowledge: we know how the system reacts to known inputs and choose the most effective inputs to be control- led. If the system model is known we can achieve good tracking and control ratios even with feed forward (open loop) control. On the other hand, feedback (closed loop) control often operates well although the system model is not known. In practise system knowledge is something be- tween the black box and complete knowledge. (Gustafsson et al. 1982, Haugen 1990, Tuomivaara 1994, Franklin 1993). Literature describes the basic performance of soil and plant systems (e.g. Jaakkola and Turto- la 1985,Richter 1987, Johnsson et al. 1987, Pel- tonen 1992, Karvonen and Varis 1992). When system knowledge is not perfect, specially with complex target systems, control realization in- Fig. 12. Levels of viewing Position Dependent Control. Fig. 13. (a) Control task. The system output is expected to follow the setpoint, (b) Solution through feedback control (Haugen 1990). 261 AGRICULTURAL SCIENCE IN FINLAND eludes testing of the system. Another option which is often used parallel to testing is simula- tion. Simulation is done with a mathematical model of the target system. (Gustafsson et al. 1982, Haugen 1990, Karvonen and Varis 1992, App. 1) PDC is a hypothetic system that is not fully testable. Therefore, systems analysis (App. 1) is used to describe the system in application- dependent detail (Ch. 1.5, 2.4). Testing shall be used in the realization phase in design and ad- justment of the PDC-controllers for individual field machines. This is, however, done later in continuing research (Haapala 1994 b , c). 2.3.2 Controllability of the crop production system The controllability of a system is dependent on which of the factors that have considerable ef- fect on the output can be adjusted and how ac- curately it can be done. (Gustafsson et al. 1982, Haugen 1990,Franklin et al. 1994) The control- lability in a system like crop production is al- ways incomplete because: 1. Part of the factors that have considerable effect on the output (e.g. weather) are not controllable or they are partly controlla- ble (e.g. pests and diseases, soil structure). In practical farming, one can not manipu- late the weather; therefore, from the sys- tem point of view, it is classified as a dis- turbance factor. 2. There are several tasks in crop production that must be carried out once at a certain time, and can not be fine-adjusted later on. Tilth and seeding are this kind of tasks. Fertilizing, on the other hand, can be com- pleted with surface or leaf application as weather conditions and resulting plant growth rate change (e.g. Peltonen 1992). 3. Realizing an optimal setpoint can be tech- nically difficult. The control system reac- tion speed, accuracy and resolution may restrict the result. Targeting the setpoint may be inaccurate. 4. The controlled implement itself limits the control: the implement is not controllable enough for optimal realization of adaptive control. 5. Properties of the material applied or the target Production Location vary in such a way that it is not possible to give the doze or treatment needed. The inhomogeneity of cattle manure limits its use in accurate control of nutrients, and some soil types have very varying tilth properties which makes it difficult to have even tilth with once-over operation (comp. Fig. 2 in In- troduction). 6. There are compensation mechanisms in the ProductionLocation (e.g. tillering) and in- teractions (e.g. alternative uptake of nu- trients with changing pH). They show up as buffer effect for some treatments and dual sensitivity of the system. 7. Reaction time varies. Some responses are immediate (e.g. tilth quality), some take a few hours (pest control), a few days (weed control), a few months (yield), a year (leaching) or several years (production methods cause gradual compaction, acid- ification or soil erosion) Technological measures can make the plant production system more controllable (the num- bering refers to the points above): I. Weather forecasting, predictions of pest or disease infections. 2. Development of cultivation methods that are less sensible to condition changes in the growing season. Use of estimates and forecasts of the production result and its environmental impact to fine-adjust doz- es and treatments that are given just once. Split application technic. 3. Automatization of control and better tar- geting. Accurate targeting is realized with additional sensors and measurements (im- age processing, sensing, positioning). 4. Better implements are developed. Control- lability is set as a primary goal. 262 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. 5. Processing of material (drying or compost- ing of manure, use of land betterment or change-over to ploughless production). 6. System reactions are tested. Achieved knowledge is used in calculation of the setpoint. Mathematical models are used. 7. Attachment of the information to some- thing else than time, e.g. position coordi- nate. Management with GIS-software. 2.3.3 Technical possibilities It wouldbe most rational to get all system knowl- edge from real time measurements. There are not, however, practical real timemeasurement meth- ods for many important parameters, such as soil nutrient content (Ch. 1.4.1). In spite of this, the setpoints must be available in real time as the implement passes the Production Location. A huge amount of local information is col- lected in PDC. A natural solution is thereforeto attach the information to position coordinates. This attachment enables adaptive control to be realized as Position Dependent Control. The set- points can be produced either beforehand or in real time. The system consists of a GIS, where there is information on local production poten- tial, environmental risks and setpoints for im- plements. The GIS also contains feedback from successes of the operations, production results and environmental impact. (Ch. 1.4,Fig. 7) GIS systems are based on positioned information. Au- ernhammer (1990) has presented positioning as a key component for environmentally sound and neccessity-based fertilizing (Fig. 14). This is the common conclusion of many other researchers as well (e.g. Palmer and Matheson 1988, Tyler 1993, Searcy et al. 1994, Stafford et al. 1994) The Geographical Information System is an effective way to combine site specific data. GISs are used more and more frequently in various applications that have localized material. A pio- neer project in new uses of the GIS was the GIS of the gas network in Tokyo (Ueno et al. 1989). The longest history of local information man- agement is in cartography. Statistical, forestal and transport applications are also areas where GIS-technologies have been used for a quite long time. (Rainio 1992). In Finland, the use of GISs has been encouraged because of their rational- izing effect in data management. The use of ge- ographic information is subject to constant re- search and development (Rainio 1988, Fig. 15). Positioned measurement data that are to be transferred to a GIS can be called local informa- tion. Local information comprises at least coor- dinate data or positioning properties (like land Fig. 14.Components of a fertilization system that is envi- ronmentally sound and the rate of which is in accordance with the yield (Auemhammer 1990). Fig. 15. Central components of geographic information (Rainio 1988). 263 AGRICULTURAL SCIENCE IN FINLAND register codes) and describing properties (Rai- nio 1988). Local information is a logical combi- nation of localizing and descriptive knowledge of the target. The localizing knowledge includes coordinates, the relative order and connections of which are called topological and geometric data. The descriptive knowledge consists of iden- tification codes, possibly a positioning proper- ty, timing data and the actual property. (Fig. 16, Rainio 1988) Location of the local information is given in coordinates or with a positioning property. When the latter one is used, coordinate information is situated separately, e.g. in Finland land register and coordinate data are stored in separate infor- mation systems and interconnection is achieved through the use of a standardized number code. (Rainio 1988) In position dependent plant pro- duction the positioning property is naturally the code of Production Location. In Position Dependent Control the local in- formation comprises Production Location spe- cific parameters, measurement data and knowl- edge of the control realized. As a conclusion, the following are the most important ones: 1. Local production potential and environ- mental risk 2. Local implement control (expressed as the setpoints) 3. Local feedback on success of treatments (actual control values) 4. Local production results and other result- ing outputs such as environmental stress caused by the production In PDC the local setpoints compensate for model and parameter changes of the Production Location (comp, adaptive control, Haugen 1990) The control technic is chosen according to the demands of the specific control task. Specifica- tions of the technic (e.g. control speed and ac- curacy) must be such that the required variation of inputs may be realized. The setpoints of the outer loop (Fig. 4 in Ch. 1.3.) are based on the perceived production strategy of the user. That is why an additional strategy loop can be thought to be added to the figure. This loop (or groupof loops) is related to the values and knowledge of the user in general. It has background variables like education, personal properties, society de- mands, values, etc. things that guide and explain the actual decisions. These can be called inter- nal and external frames (Larsson 1990) or limit- ing borders (see Ch. 1.2, Fig. 1, Elonen et al. 1991). This study mainly concentrates on possibili- ties to realize the setpoints (the inner loop in Ch. 1.3, Fig. 4). The site-specific setpoints that are stored in the GIS are realized when the imple- ment is at the Production Location. In addition to this, there are setpoints that are calculated in real time. Setpoints that are in the GIS are based on measurements and calculations that are made before the control time. Of course, both types of measurement and calculation can be used. The calculation of setpoints is not fully automatic but it is also affected by the knowledge and values of the user. (Fig. 17) Off-line (before control time) measurements include e.g. soil conditions and the calibration of the equipment. On-line (at control time) meas- urements are divided into measurements of lo- cal (mainly soil and yield) conditions and feed- backs of implement operation. Off-line measure- ments begin again after the control time with assessment of growth and quality. In all phases positioning is a very important measurement. Fig. 16. Concepts of geographical ingformation (Rainio 1988). 264 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. The technical realization of PDC includes a computing unit, a positioning device, a GIS, implement controllers and sensors. The comput- ing unit selects the right setpoint from the GIS according to position information or calculates it on basis of on-line measurements and/or the information stored in the GIS. The setpoints are realized with the controllers. Controllers need information on the operation of the implement, which is given by the sensors. Actuators com- plete the operation. Most of the measurements are carried out off-line. On-line measurements (Ch. 1.4.1) also belong to position dependent production as an integrated part. As they devel- op they can be selected instead ofoff-line meas- urements. This does not, however, diminish the need of a GIS. Data management gets compli- cated and needs GISs for the organization of the data. The GIS is a very important and efficient tool in managing huge amounts of spatial data (Rainio 1988). (Fig. 18) It is common in crop production that direct measurement is not possible. The measurement target is actually a physical variable that is in well-known relation to the variablerequired (e.g. soil conductivity - moisture content, ripeness of grain - satellite image). The result is converted with this relation to a value of the variable re- quired. If the relation is of the form y=ax+b, then the actual measurement result is as shown in following equation (eq. 1, Hari 1991); 11l y=y + e y +v y =a(x + £x +vx )a+ £t )+ b where £ = estimate of the value, measurement result y = actual value £y = random error (noise) in value determination Vy = systematic error in value determination a, b = constants x = true value of the measured variable £x = random error ( noise) in variable measurement vx = systematic error in variable measurement fit = interference caused by the measurement Fig. 17. Data flow in the realization of adaptive Position Dependent Control. Fig. 18. Measurements in Position DependentControl. The technical realization includes both off -line and on-line measurements. 265 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplantproduction It can be concluded that it is preferable to have few measurements and direct ones instead of indirect, if possible. If the result consists of several measurements, each measurement brings its own uncertainty to the result. (Dally et al. 1984). The sum of all errors connected to one measurement result is called error budget (Toft 1987, App. 9). In individual measurement ap- plications the error budget is adjusted, with the selection of instruments and methods, so that the final result is accurate enough. The range and the importance of variation in the target variable are important criteria in the selection of measurement targets and methods (Clark 1984, comp. Fig. 8). The measurement targets of Production Location are selected so that the system is controllable enough for the application. The inner control loop of PDC needs measurements on the success of implement ad- justment (see Ch. 1.3,Fig. 4 above). If the con- trol strategy is either economical or environmen- tal, it needs measurements that describe the pro- duction and the environment of the Production Location, respectively. Production rate and qual- ity and input/output ratio are the most important required measures of economy (Pehkonen 1987). There is no way to have control without set- points (Haugen 1990). The setpoints of PDC need exact criteria. For this study it is not im- portant how the setpoints are achieved. There is a necessity of money or a value scale or another scale that is at least of ordinal level. The best solution would be to have a relative scale in or- der to judge different strategies and technical choices. For this reason, environmental impact of production is converted to environmental costs. There are several ways to do this, e.g. will- ingness to pay or the costs of correcting the neg- ative impact. The environmental cost is subject to live discussion, because it is not clear which costs should be included and what is the price of immaterial or non-commercial things, such as clear water or air, a rare species, etc. If the crite- ria is 'sustainability', a concept or philosophy that has many meanings, it is also a very com- plicated issue to be handled (see Introduction, Heinonen 1993). Natural systems are dynamic: the difference between measurement data and 'reality' is changing as a funtion of time (Ch. 2.1). So the age of measurement dataaffects its accuracy and usability in control. (Gustafsson et al. 1982) Slowly varying variables can be measured be- fore control time. Setpoints can then be calcu- lated and realized when we are at the right Pro- duction Location. Instable phenomena are diffi- cult to handle. If they are known well enough we can use prediction models (e.g. Karvonen et al. 1989, Peltonen 1992, O'Callaghan 1995). Prediction models in PDC enable measurement of dynamic things some time before control time. The measurement interval can also be increased if good predictions are available. The adaptive control can manage a system, the parameters of which change. This requires measurement of system parameters. (Haugen 1990) As a conclusion, the usefulness of local data is dependent on its validity, age, accuracy and accuracy of its position. Position accuracy is further divided into positioning during the meas- urement and positioning during returning to the point. (Fig. 19) The accuracy of the data con- sists of numerical accuracy and e.g. accuracy of possible classification. Fig. 19. Usefulness of local information in Position De- pendent Control. 266 AGRICULTURAL SCIENCE IN FINLAND 2.3.4 Economy and markets of Position Dependent Control In PDC, different economical goals show up only as variable setpoints, their level and range of variation. Strategic goals are also built in the manipulation required, represented by the set- points. (Ch. 1.3, Fig. 4) Sustainable production needs to be econom- ical. To be economical the production has to be profitable and give maximum benefits. The ben- efits are normally expressed in monetary values. Generally the best total outcome is available when marginal costs equal marginal selling price. The economical optimum is located in this point. Recently economical thinking has been widened to include environmental influence of the pro- duction (Francis et al. 1990). Often this moves the optimum point. Environmental impacts of crop production are the sum of soil, air and wa- ter pollution of the technic used. Besides envi- ronmental effects there are also social, political and other such effects that are difficult to value in terms of money. The transfer function of an input to the environment should be known for each Production Location. For social and politi- cal effects this is very complicated. (Francis et al. 1990) High efficiency of inputs in the production system (measured e.g. as product units per input unit) is an important indicator of system health (Pehkonen 1987, Elonen et al. 1991, Jahns and Kögl 1992, 1993, Azelvandre 1994). This effi- ciency and the amount of production units per Production Location determine how much of the inputs are given in vain or lost outside the indi- vidual Production Location. The effect of this loss depends on the ability of neighboring Pro- duction Locations to utilize excess treatments and on the response of the environment to the amount eventually lost from the field. In some cases the environmental impact is very negative and sometimes the extra input changes over to a non-hazardous form. (Auernhammer 1990, Elo- nen et al. 1991, Francis et al. 1990) Position dependent plant production is ex- pected to have good economical effects. Palmer and Matheson (1988, Table 2) forecast that as much as half of the present production costs can be saved. The result is based on a typical Sas- katchewan farm in Canada (a farm of c. 800 ha 1/3 of which setaside). The situation requires that well-operating positioning systems are availa- ble. The table shows the economical result with a step-by-step increase in the use of positioning in crop production. First driving accuracy is improved, which reduces overlapping and non- treated area in fertilizing and plant protection. Reduced overlapping reduces costs and gives more outcome by avoiding negative effects (soil compaction, over/under dozes). The next step is to start night spraying that gives a higher effec- tivity in herbicide use (reduced wind drift and evaporation, higher relative humidity). This leads to reduced herbicide use and cost savings. The following steps, need-dependent fertiliza- tion and tillage, reduce costs because inputs are diminished in some cases. Up till this the table is based on test results. Further steps include prospects of effects of a very individual treat- ment of field parts. Small robot implements are used to achieve optimal tilth. This would elimi- nate the need for setaside. Lightweight robots do not cause much soil compaction and they are very flexible in use. The robots are expensive but they do not need driver instruments (cabins or ventilation). Full realization of the system would give savings of c. 66% in fertilizer, pesti- cide and fuel costs. (Table 2, Palmer and Math- eson 1988) The scenario (Table 2) is somewhat optimis- tic. The thought model assumes that test results are transformed to management practises. This is not easily done because local situations must be reliably identified. Identification procedures that have the necessary resolution are expensive. There are also different views on the priorities of the above mentioned technics. Many authors think that driving accuracy is not the first one to give positive effects. Position Dependent Con- trol (Site-Specific Farming, Farming by Loca- tion, Farming by Soils, ComputerAided Farm- ing or equal term) is thought to give more po- 267 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Table 2. Economical effect of using a positioning system (Palmer and Matheson 1988).The figures are in dollars. Current Over- Over- Night Need Position Plot Small situation lapping lapping spraying dependent dependent seeding/ automatic in turns in parallel fertiliz. tilth planting implem- driving ents or robots Fuel 3.61 3.25 2.93 2.93 2.93 2.93 1.95 1.76 Seed 5.00 4.50 4.05 4.05 4.05 3.64 3.27 2.94 Fertilizer 9.23 8.31 7.47 7.47 5.38 5.38 4.84 4.35 Herbicide 7.71 6.94 6.25 4.38 4.38 3.92 0.39 0.35 Pesticide 3.00 2.70 2.43 2.43 2.43 2.43 1.70 1.58 Spare parts 6.15 5.53 4.97 4.97 4.97 4.97 3.31 1.89 Machines 15.30 15.30 15.30 15.30 15.30 15.30 10.20 5.82 Cost 50.00 46.53 43.40 41.53 39.44 38.57 25.66 18.69 Tax 5.76 5.76 5.76 5.76 5.76 5.76 5.76 5.76 Insurance L22 6.92 6.92 6.92 6.92 6.92 6.92 6.92 Cost/acre 62.68 59.21 56.08 54.21 52.12 51.25 38.34 31.37 Income/acre 70.00 70.60 71.20 71.20 71.20 71.20 71.91 71.91 Result/acre 7.32 11.39 15.12 16.99 19.08 19.95 33.57 40.54 Prod, area 1333 1333 1333 1333 1333 1333 2000 2000 Total income 9760 15186 20160 22653 25439 26660 67140 81080 Year 12 3 4 5 6 7 8 tential (e.g. Auernhammer 1990, Buschmeier 1990, Larsson 1990, Moller 1990, Schnug et al. 1990, Heege 1991, Kloepfer 1991, Stafford and Ambler 1991, Muhr and Auernhammer 1992, Wollenhaupt and Buchholz 1993, Stafford 1994). Nielsen and Bouma (1993) report good econ- omy of PDC in U.S.A.. Savings in fertilizer use and increased yields met or exceeded the in- creased costs of PDC - even without inclusion of environmental benefits. Robert et al. (1991) got maximum $517/ha benefits with soil-specif- ic fertilization. Wollenhaupt and Buchholz (1993) conclude based on wide experiments in the U.S.A. that variable rate fertilizer applica- tion can give quite different returns inside soil type classes. This is because there is great vari- ability in the need of fertilizers. The situation is very clear wihen only P and K are managed. They also report that the high short distance variation is not easily manageable. Nitrogen management shows the most potential for yield improvement and efficient fertilizer use. They emphasize that even if the variable rate application would be economically as profitable than single fertiliz- ing rate approach, there are undoubtful envi- ronmental benefits. They are, though, very dif- ficult to calculate. In a study on P and K man- agement for potato production, Hammond (1993) concludes that the additional cost for the man- agemment was minor but the effects on crop re- turn could be significant. The increased returns concentrated on the low-yielding spots of the field that would get insufficient nutrient rates with conventional whole-field management. The increase in crop quality through more even grade is also a potential source of better results. A mi- nor increase in yield and a signicficant increase in the uniformity of the grade, give the potato farming returns that exceed the investment costs of variable P and K management Hammond (1993) also concludes that variable fertility man- agement is “a best management practise to en- 268 Haapala , H. E. S.: Position Dependent Control ofplantproduction AGRICULTURAL SCIENCE IN FINLAND sure environmental conservation and sustaina- bility of resources for production agriculture”. Schueller et al. (1994) say that positioning systems penetrate into the market first via large units, such as cooperatives. Crop protection co- operatives are the most probable users of ad- vancedpositioning systems in the U.S.A. In Fin- land this kind of units are rare for the time be- ing. The accurate positioning systems needed in robot tractors are costly and thus need big field areas. They are more likely used in mass pro- ductioncountries other than Finland. On the oth- er hand some special uses in certain crops (e.g. row crops, valuable crops) are possible in our conditions as well. It can be anticipated thatpart- nership in the European Union will introduce larger scale and/or more specialized farming in Finland. Probably these units will be the first ones to economically utilize Position Depend- ent Control in Finland. Prices of technics used in PDC are constant- ly decreasing. The hardware and software in- volved find many applications outside agricul- ture. (Koskelo 1990,Bäckström 1990, Choi and Charr 1994) The benefits of large-scale manu- facturing are therefore lowering the costs of ag- ricultural PDC. For the complete realization of PDC, special agricultural software is to be de- veloped. International research projects show that such programs are already available. (Buschmeyer 1990, Petersen 1991) Technology transfer from concepts developed international- ly should be used to reduce excess costs of local R/D. Holmes (1993) concludes that the speed and degree ofadoption ofsite specific farming prac- tices is mainly dependent on the success of tech- nology transfer. This must be realized through automated data collection, the development of approppriate equipment for the control needed, user friendliness of the equipment and other sys- tems used, affordable cost of the systems per unit and the sufficient amount and quality of shared data by government agencies, and positive de- velopment of the general economic factors af- fecting agriculture and the economy as a whole. As a conclusion, the economic effect of Po- sition Dependent Control in plant production is potentially positive. The technology itself is not profitable but needs to be used in such a manner that the best potentialities are found. Potentiali- ties are present in both low and high-yielding parts of the fields. In high-yielding parts the eco- nomic returns are achieved when the inputs are effectively utilized, whereas the low-yielding parts are best treated with diminished applica- tion rate. The low rates give less potential to negative environmental impacts in these parts not capable to utilize the normally applied excess doze. The control of nitrogen shows the most promising potential that has not yet been utilized very well, mainly because of the difficulties in control. Nitrogen is a most dynamic nutrient that should be applied with extra care because of the risk of leaching. Thus the control system possi- bly needs a possibility to correct the basic N- doze during the growing season (comp. Pelto- nen 1992). 2.4 Effect of targeting accuracy - simulation with mathematical models and empirical data To be efficient, PDC needs special implements. Current agricultural machines are poorly control- lable and adjustable because actually no in-field control is carried out. PDC needs continuously controlled machines with large adjustment rang- es. Facilities for partial width operation must be developed. Multimodal machines with momen- taneous change-over between different modes are needed (e.g. soil tillage machines with ad- justable effect, fertilizers and sprayers with mul- ti-chemical capabilities). These devices are hy- pothetical technological solutions. Justification of all these modifications should be economi- cally evaluated in continued research. This is best done by simulation because corresponding so- lutions do not exist. Targeting errors and corresponding accura- cy consist of length and cross positioning of the 269 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND 1 Haapala, H. E. S.: Position Dependent Control ofplantproduction production input compared with the right posi- tion. The targeting accuracy required sets stand- ards for the technology used in realizing the re- quired targeting, i.e. for the positioning. A new concept, the Effect Curve (EC) is here defined as a general description of the efficiency of a position dependent task. The EC describes the distribution of the effect of position dependent task in space. The EC can be calculated both along and across the driving direction. The EC is scaled to the required effect level of 1.0, meas- ured in the target. In crop production ECs can be calculated e.g. for fertilization, spraying or tilth. The most important property of an EC is its shape. In fertilizing, the changes in EC in the driving directionare due to changes in feed rate, and in the cross direction they are caused by the variation in the evenness of spread of the ma- chine. Evenness of spread is traditionally ex- pressed as a coefficient of variation (CV) or de- viations from the value aimed at (Ndiaye and Yost 1989,Auernhammer 1990,Delcourt and De Baerdemaeker 1994). This does not count for the sensitivity of CV. If the EC is sharp-edged, slight driving errors lead to a drastic degradation of the CV. A big effect is summed outside the re- quired area and total misses are found inside it. Because of the small driving errors there can be effects ranging from zero to double of the effect wanted in the field. Sloping ECs allow more tol- erance. One could imagine that accurate driving is not needed when automatic Position Dependent Control is in use. Implements are not, however, flexible enough to allow for inaccurate driving. The combination of automatic PDC of the im- plement and inaccurate driving leads to an in- creased need to adjust the implements in partial widths or to turn them quickly on or off. Fur- thermore, it is not reasonable to make imple- ments fully adjustable just because of the inac- curate driving. Most probably it is cheaper to control the total effect of the task (e.g. fertilizer or pesticide doze) than partial widths. In some tasks it is even technically difficult to adjust the working width without affecting the result neg- atively (e.g ploughing, sowing, row crop produc- tion). Inaccurate driving would also increase soil compaction and fuel consumption (Palmer et al. 1989, Nieminen and Sampo 1993). In practise, as both the working width and the output of the machine are incompletely adjustable, the produc- tion result is always affected both by driving and by positioning accuracy. The driverrealizes the route required with the help of positioning in- formationreceived either from marks in the field or from the positioning system. (Fig. 20) It is a very straightforward method to fix a CV-limit for a particular position dependent work. Instead of this generalizing, the CV-lim- its should be fixed to the properties of the pro- duction system in the PLs. In this study, the re- quirements for targeting accuracy are given in terms of the transfer functions of the PLs. CV- limits are set for the output from these functions to indicate the adequacy of the targeting accura- cy in these modeled locations. A general model of targeting and separate simulation models for crosswise and lengthwise targeting were developed. The simulation mod- els were constructed in the Stella® simulation environment (App. 3) in a Macintosh™ Ilex mi- Fig. 20. Practical Position Dependent Control of imple- ments. The most propable system does not include auto- matic guidance but there will be a driver present. 270 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. crocomputer. The platform and simulation pro- grams were selected according to comparative tests ofAutti et al. (1989). The EC is not constant but changes with time. Both the shape and the total effect vary dynam- ically. The total system of Position Dependent Control with varying driving accuracy, position- ing accuracy and EC can be simulated with the following general three- dimensional model.The model (Fig. 21, App. 3) includes converters (cir- cles) that have data tables/equations for imple- ment position (required_route, position_error and driving_error), machine ECs in cross (EC_i , iCE{ 1,2,..,n}) and length direction (effect), the sum of cross and length effects (effect_i , i(E{ 1,2,..,n}) and transfer functions (f/_(, i(E{ 1,2,..,n}) from effect_i's for individual PLs. State variables of the system (rectangulars) are work time (work_time), distance ( distance) and the outputs from the PLs included (output_i, iCE{l,2,..,n}). Res is the resolution in cross di- rection [m]. Model parameters can be input in several ways. Both measured and simulated val- ues are usable. Values of driving_error, positioning_error and effect are functions of sim- ulation time. Required_route is a function ofdis- tance. Distance is a function of simulation time and can be used to alter the driving speed in the route. Values for the parameters above are given graphically, as data values or as equations. The ECs in cross direction (EC_i's ) are constant within simulations. The shapes could be varia- ble but they are set constant for the sake ofclar- ity. In the present model they can be given graph- ically or as data values. (Fig. 21) The effect varies depending on the position dependent task that is modelled. Generally ef- fect values are higher than zero (for tasks that can not reduce the effect in PLs). Transfer func- tions (tf_i's) are task-dependent equations for effect_i's in the output_i's. They can be given independently for each PL and input graphical- ly or in data values. If connection to route was realized, they could also be site-specific in trav- el direction. For clarity, they are kept equal and constant in simulation. (Fig. 21) The PL reacts only to the input value (Effect_i). The result is given as output units per PL (e.g. yield, environmental impact, economy). The result is given at variable resolutions in cross direction by changing the res-parameter [m]. In travel direction the resolution is dependent on the smallest simulation step (dt) used. The gen- eral three-dimensional model shows the system components (Fig. 21). There are some serious drawbacks in the model. The model is not very good for setting the requirements for cross tar- geting: in practise it is not possible to give enough PLs to the model to judge large working widths or entire field widths. The same limita- tion is found when high crossweis resolution is needed. Effects of parallel driving are difficult to simulate because separate runs and summing of the output_i's is needed. For these reasons separate two-dimensional models for cross and length targeting were developed for further stud- ies of targeting accuracy (Ch. 2.4.1 and 2.4.2). Fig. 21. Stella®-diagram of the general three-dimensional model for Position Dependent Control. EC= Effect Curve. 271 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production 2.4.1 Accuracy in working width - simulation with the ECs The effects of poor targeting accuracy in the working width cause variation oftreatment. This can be more or less harmful. Basically, overlap- ping and missing are not required in any ration- al production strategy. Overlapping is specially harmful in spraying poisonous chemicals. Un- derdozes lead to wasting the chemical and low- er outputs because of a diminished effect. Prac- tical ECs (in both cross and length direction) are dynamic because of the properties of the machine (implement, tractor) itself and external interfer- ence. Machines have certain typical ECs. Agri- cultural chemicals and other applied materials have variable properties that affect the EC. Also the properties of the target PL may modify the EC (e.g. topographic effects). In individual simulations here the cross EC is set constantfor clarity; only different EC-types are separated. Practical ECs are combinationsof the types used with some variation. The EC-types used here are -the triangular (e.g. some centrifugal surface fertilizers), -the mixed (e.g. chemical sprayer) and -the rectangular (e.g. harrow, sowing ma- chine) type. The types are all derived from the basic tri- angular type. They differ only in the width of the central part and edge angle. (Fig. 22) In sim- ulation, the height of the EC (h) is constantly one unit. Edge angles (a) are 15°, 30°, 45°, 60°, 75° and 90°. In each simulation the right and left edge angles are equal. The optimum working width for an EC is such that CV in parallel driv- ing is at a minimum. This is achieved in the ECs used by “driving” the sloping edge areas half- ways overlapped. The target is to get the effect wanted in one pass. That is why the maximum value for each EC is 1.0. (Fig. 23) The main simulation variable is the working width (W ). Within it the ECs vary with the edge angle (a). (Fig. 24) As the working width is constant, diminishing the edge angle narrows the even part (Fig. 25). An edge angle of 15° would lead to a negative width of the even part. As this is not possible, usable combinations of W opt and a diminish to 23 (Fig. 26). Fig. 22. Basic Effect Curve-types.(a) Triangular, (b) mixed and (c) rectangular type. Variables are edge angle (a) and width of the even part (b). Height (h) is constant (=1). Fig. 23. Optimum working widths (W ) for basic Effect Curve-types, (a) Triangular, (b) mixed and (c) rectangular Effect Curve, a = edge angle, (i =width of the even part and h = height of the Effect Curve. 272 AGRICULTURAL SCIENCE IN FINLAND The simulation concentrates on overlapping. The target is to “drive” routes that represent op- timum overlap, i.e. to use optimum working widths. Incomplete positioning, however, leads to a location error in the parallel passes. In addi- tion to the combinations above, fixed targeting errors of 0.2-10 meters are used. All combina- tions are not reasonable. Therefore an error range ofc. 10-100% of the optimum working width is used (Fig. 26). In the resulting model (Fig. 27, App. 3) there are three ECs (Eff_curve_l-3) that are situated in positions Wl, W 2 and W 3 in the working width. The simulations for each setup are 128 in total (4 working widths, 4 to 7 target- ing errors, 6 edge angles excl. 15° in a 2-meter working width). There were four steps (A-D) in the simula- tion model development, each of which used dif- ferent transfer functions from the effect curves to the output. The basic model was modified for each simulation setup. The setups used include models that calculate the results with no addi- tional transformations and models that imitate filtering or other kind of transformations of the EC. This is done by adding a transfer function block after theEff sum -block (Fig. 27). The pur- pose of this iterative process was to show the effects of introducing nature-like transfer func- tions to the system. The effect curves (ECs) were given in two parameters (Wopt and a). The sim- ulation results were calculated as sums of the ECs (Effect Sums, ESs). The coefficients ofvar- iation were determined for the ESs. Furthermore, the requirements for targeting accuracy (Wer- rmax) were calculated for variable CV-limits. (Fig. 28) In simulations the ECs were functions of the working width. They were shaped so that the re- sult show the ES in the case that only one er- roneusly positioned EC would be inserted be- tween two correctly positioned ECs. This situa- tion is the basic element of targeting of an EC. Keeping other error sources (EC variations) con- stant, only the effect of poor targeting could be evaluated. Method A is quite straightforward; the effect curves are summed and the CV is calculated for this ES. Sample ES-curves of the simulationsare shown in the following figures. The figures show Fig. 24. Edge angles (a) in groups of optimum working widths (W )in simulation. ' opt 7 Fig. 25. Effect of the edge angle (a) on width of the even part of an Effect Curve (b.) by constant working width (W=Wopl ) and height of Effect Curve (h). Schematic. Fig. 26. Cross targeting errors (Werr) in groups of opti- mum optimum working widths (W )in simulation. 273 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production the effect sum curves for optimum working widths of 2 and 10 meters with a targeting error (Werr) of 0.2 meters. The shape parameters of the EC, the edge angle (a) and the optimum working width (Wopt) have a considerable ef- fect on the ES. Sharp edges cause high peaks and sloaping ECs have wide overlapping, even with a little targeting error of 0.2 metres. With changing working width, equal targeting errors can lead to differentpercentual overlaps. (Comp. Figs 29a and 29b) Method A does not yet count for the biolog- ical transfer function from the input to the out- put (e.g. yield or environmental stress). The ef- fect of such a transfer is smoothing: plants take their nutrients from a certain area that is typi- cally bigger than the resolution (0.1 m) used in the simulation above (Richter 1986, King 1990) This effect was imitated in method B: smooth- ing the effect sum curves with a ten-value mov- ing average. The following figures show visible change in effect sum curves (Figs 30a and 30b, comp. Figs 29a and 29b). In nature, it is common that functions for growth are logistic, “S-shaped”. After a mild starting phase the output begins to grow at an increasing speed. Then there is a phase of more or less constant growth, and finally the speed falls. In the starting phase there is an accumula- tion of “critical mass” before the growth really begins. The middle phase uses the growth po- tential until, in the last phase, some restricting factor begins to act against the growth. Some- times there is an additional phase where the out- put starts to degrade because of excess input. Mathematically the differential transfer function of growth could be e.g. dy/dx=ay-by2' where yis the yield, x is the input and a and b are constants. The transfer function is first dominated by ex- ponential growth and later by a negative feed- back. Negative feedback is the basic element of control in any system (Gustafsson et al. 1982, Haugen 1990,Franklin et al. 1994, O'Callaghan et al. 1994). Fig. 27. Diagram of the simulation model for setting the requirements for cross targeting accuracy. Wopt = optimum working width, WI-3 = actual position of the Effect Curve, Werr 1-3 = errors in locations of the adjacent passes, Eff curve 1-3 = shape of the Effect Curves, Alfa = edge angle [rad|, Eff sum = sum of the Effect Curves, nl-3 = number of working width (from left), y=cross position in meters, a function of simulation time, dy= simulation step in meters. Fig. 28. Data flow in simulations. Simulations are made in the Stella® simulation program and the other phases in Wingz®, a spreadsheet program. 274 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. The final yield in the soil-plant system re- sults from the growth process. The amount of yield with a certain amount of input depends on the sensitivity of the soil-plant system to the in- put. Field trial results show that the final result can be highly variable (e.g. Heikkilä 1980,Jaak- kola and Turtola 1985, results in Ch. 3 of this study). The formation of the yield in the plant includes the process of both taking and utilizing the input taken. These processes must be sepa- Fig. 29. The Effect Sum (ES) in method A for optimum working widths (a) 2 m and (b) 10 m. In both figures cross targeting error is 0.2 m and edge angle is 15, 30, 45, 60, 75 or 90° (from thickerto thinner line). Fig. 30. The Effect Sum (ES) in method B for optimum working widths (a) 2 m and (b) 10 m. In both figures cross targeting error is 0.2 m and edge angle is 15, 30, 45, 60, 75 or 90° (from thicker to thinner line). 275 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production rately described if detailed causes for a varying input/output ratio (sensitivity) are required (Kar- vonen and Varis 1992). The situations where dif- ferent factors restrict the growth can be catego- rized e.g. in four classes where the models of growth are a bit different (de Witt ref. Karvonen and Varis 1992). In method C, the effect of a basic logistic transfer function (Gustafsson et al. 1982) was added to the Trans-block of the simulation mod- el. No integration was implemented. The shape of the function is quite arbitrary and its accura- cy is non-relevant in this context. However, be- cause it is the natural shape of growth, it is in accordance with the growth patterns presented by e.g. Karvonen and Varis (1992) and Peltonen (1992). The transfer function was scaled so that the output would reach unity somewhat above the unity value of the EC. Full effect is achieved at an ES of c. 1.3. This was done to imitate the normal target of production where the maximum is not required but the target is to get an opti- mum output. The optimum point is normally somewhat below the maximum (Peltonen 1992). (Fig. 31) The transfer function changes the re- sult dramatically. It gives less extra output with overlapping compared with losses in the miss area. This shows as diminished output in over- lapping areas compared with the results with method A (Figs 32a and 32b, comp. Figs 29a and 29b). The effect in the missing area seems to be quite similar to method A because neither meth- od A nor method C include averaging (comp, with method B, Fig. 30). Actually the missing area gets lower effects in method C than in meth- od A because the transfer function from ES to output is quite low in the ES's range from 0 to 0.7 (Fig. 32). This result is true when we operate in the upper part of the transfer function. If the operat- ing point changes to the left (effect level dimin- ishes) the overlapping area gives more marginal output (output units/input unit). It is, though, normal to operate near the top of the transfer function, except in low-input production where the operation point is on the straight part of the transfer function or, in extremely-low-input pro- duction, in the region of exponential growth. In the latter case it can even be economically ben- eficial to have overlap if the quality changes of the product are not important. Normally, over- lapping is not required in any case because of the risk ofquality variation. If the operating point lies in the lower part the model would give same results in CV because the ECs used and the trans- fer function are symmetric. The third option would be an operation point in the linear part of the transfer function. With small changes in the input the output is analogous to the results of method A (Fig. 32), with a level shiftbecause of the difference in sensitivity. For sharp changes in EC the output is smoothed compared with the methods without integration. The next step, method D, was to combine both the integrating effect of method B, imitat- ing the gathering function of plant roots, and the logistic transfer function of method C that de- scribes S-shaped response. The output was more smoothed, as expect- ed. The output is much less sensitive to the var- ying ES than in methods A and C that do not include integration. (Figs 33a and 33b, comp, to Figs 29 and 32) CVs were calculated for the outputs. The fig- ures above show only some examples of the re- sults. CVs for all the used models (A-D) and Fig. 31. A simulated logistic transfer function dy/dx = 9y-9y2 . 276 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. simulation combinations are listed in App. 4. CV values for edge angle 15° and optimum working widthof two meters were not calculated because of the invalid negative value of b (width of the even part of EC) with these shape parameters (see Fig. 26 above) (App. 4) The simulations above would give a zero CV without the targeting error because without the error the EC would be a straight line at the ef- fect level wanted. Therefore CVs differing from Fig. 32. The output of Production Locations in method C for optimum working widths (a) 2 m and (b) 10 m. In both figures cross targeting error is 0.2 m and edge angle is 15,30,45, 60, 75 or 90° (from thickerto thinner line). Fig. 33. The output of Production Locations in method D for optimum working widths (a) 2 m and (b) 10 m. In both figures cross targeting error is 0.2 m and edge angle is 15, 30, 45, 60, 75 or 90° (from thicker to thinner line). 277 AGRICULTURAL SCIENCE IN FINLAND Haapala , H. E. .S'. : Position Dependent Control ofplant production zero indicate only the effect of the improperly positioned EC. Furthermore, as the targeting er- ror is the only affecting variable within shape groups of the ECs, the CVs can be used as indi- cators for the effect of the targeting error (with that particular EC type). The resulting CVs for a certain targeting error change with edge angle and optimum working width of the EC. The graphical presentations of the data (Fig. 34) show visually the changes in CVs when dif- ferent methods were used. There are great dif- ferences between the methods used. It can clearly be seen that the smoothing methods (B and D) that filter the high frequencies of the effect give lower CVs and therefore also an increased tol- erance. At a certain CV-level different accura- cies for targeting are allowed. Method D that includes both smoothing and an S-shaped trans- fer function gives most tolerance. (Fig 34) The requirements for targeting accuracy can now be calculated by setting a limit (CVmax) for the CV. The maximum targeting error (Wer- rmax) is linearily interpolated between rows (App. 4, Table I) that surround the CVmax want- ed as shown in following equation (eq. 2). The calculation results for different simula- tion methods are shown in Appendix 4. For ex- ample, in method A, if we have Wopt of 2 me- ters, a of 30° and a CVmax of 0.3, the maxi- mum allowed targeting error is 0.76 meters Fig. 34. The effect of cross targeting error (Werr = 0.2-20 m) on the evenness of output quality of Production Locations. The quality is expressed as Coefficients of Variation, CVs, of the Effect Sum, ES. CVs are calculated for optimum working widths (Wopt) of 2-20 m. Four different simulation models with different transfer functions are used. A= the model with unconditioned EC, B = the model with smoothed EC, C = the model with logistic transfer function from unconditioned EC and D = the model with logistic transfer function from smoothed EC. 278 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. [2] Werrmax = Werr, + (Werr 2 - Werr,) (=0.5+0.5x(0.3-0.207)-i-(0.383-0.207) meters) (see App. 4). Generally, high working widths al- low most tolerance in targeting. Narrow work- ing widths require a higher absolute accuracy with the same CV-limit as high working widths. The relative accuracy requirement is quite con- stant. The edge angle has much effect on the re- quired targeting accuracy, as expected. With methods A and B the right angle requires the most accurate targeting. With methods C and D that include an S-shaped transfer function, there is the tendency ofcutting the high and low points of the Effect Sum. There are some CV-limits that produce a curve with minimum point at an other edge angle than the used minimum, 15°. This is *(CVmax - CV,) + (CV 2 - CV,) where Werrmax = maximum allowed cross targeting error Werr. = Werr of the row with lowe rCV Werr 2 = Werr of the row with higher CV CV, = lower CV of the two rows CV 2 = higher CV of the two rows CVmax = maximum allowed CV Fig. 35. Maximum targeting errors (Werrmax) for different optimum working widths (Wopt = 2-20 m), CV limits (CVmax = 0.1-0.5) and edge angles (a = 15-90°). Four simulation models with different transfer functions are used. A = the model with unconditioned EC, B = the model with smoothed EC, C = the model with logistic transfer function from unconditioned EC and D = the model with logistic transfer function from smoothed EC. 279 AGRICULTURAL SCIENCE IN FINLAND natural because the logistic transfer function emphasizes EC level changes in between the low and high levels of the ES (Fig. 35) 2.4.1.1 Discussion of the simulations with Effect Curves The amount of integration and shape of transfer functions have apparently a remarkable influence on the results. They were not researched in de- tail because this was not the main issue in the interpretation of the results. The main result is that the model operates both technically and log- ically right. It gives increasing coefficients of variation with ascending targeting errors. The integrating effects and the transfer function which were used smooth and modify the output correctly. Therefore the results indicate a tech- nical and logical validity of the model. (Gustafs- son et al. 1982) Method D, that shows the high- est tolerance, is the most valid one of the meth- ods used because it includes the smoothing ef- fect of plant roots and the most nature-like (lo- gistic) transfer function. The practical use of the simulation model needs calibrationof these func- tions. For total validation of the models a field test setup is necessary. This was not done be- cause the target of this research was not to find the exact forms of the functions but to show their effect on the measures of targeting accuracy achieved. The main result is that the target PL should be modeled to get reasonable results. This result is the starting point of continued research that will find accurate requirements of targeting for individual cases. This continued work has begun in 1991 at the Department of Agricultural Engineering and Household Technology with case-studies that measure the variation of PLs. The Keimola case-study was the first one of them (Ch. 3). Further tests are being carried out at Vi- ikki Experimental Farm (Haapala 1994b, Hirven- oja 1995). Increasing working width decreases the re- quirements for targeting accuracy because the percentual error areas get smaller with the same position error. This is due to the fact that less passes are needed to cover the area and thus there are less possibilities for overlapping or missing. A two-hectare field (100x200 m), which is the standard field size and shape for work studies in Finland (Orava 1980), gets 5 to 50 passes with the optimum working widths used in the simu- lation above. In practical work the situation is somewhat more complicated because wide work- ing widths cause an increase in driving errors (Auernhammer 1990). Smoothing rises the al- lowed targeting error with high edge angles be- cause it cuts high frequencies (i.e. sharp edges) of the ES curve. The ten-value (1 m) smoothing filter has a bandwidth of c. 0.45 [l/m] which means that changes of ES bigger than c. 0.69 in the calculation interval used (=0.1) are attenuat- ed below -3 dB (to c. 70.8% of original ampli- tude). Expressed in edge angle this means c. 82° (=arctan(o.69/0.1)). This effect is shown in the Werr curves (Fig 35 above): methods C and D with filtering show tolerance for sharp edge an- gles. The filter together with an S-shaped trans- fer function smooths efficiently the effects of overlapping (Fig. 35). The results include only one criteria, i.e. the variation of output. If there was another simul- taneous output function, the situation would be quite different, e.g. in plant production we have the yield and the leaching functions. The over- all behaviour of the leaching process is such that leaching amounts increase along with the ferti- lization rate. It has an exponential starting phase as the nutrient uptake by the plants diminishes. If a limit is set for leaching we can see changes in the allowed targeting errors. The leaching function emphasizes negative effects of overlap- ping. Consequently the total effect of these two criteria would probably be that there is an opti- mum point (or area) where leaching is not too high and the yield is not too low. The existence of such an area further tightens the requirements for targeting accuracy, compared with method D. The simulation results apply for treatments inside the field area. Use of optimum working widths results in overlapping the field edge. Only the squared EC (a = 90°) could exactly cover the field area with the effect aimed at if accu- rately targeted. This implies that other EC types 280 Haapala, H. E. S.: Position Dependent Control ofplantproduction AGRICULTURAL SCIENCE IN EINLAND have a seed value ofCV. The CVs calculated here do not include field edge overlapping. This has little influence on the results when the field size is big as compared with the working width. It is clear that responses to an EC change as different target PLs are treated. The transfer functions change in shape and magnitude. Thus we get quite varying optimum points that also vary in tolerance. The requirements for target- ing therefore vary as well: inputs to the PLs have to be targeted with individual targeting accura- cies. The model is here used to demonstrate the need for PL-based models in estimating the tar- geting accuracy of PDC. Positioning with a po- sitioning method like GPS (see Ch. 4) is based on nearly independent positioning results. The positioning result has a basic accuracy with some random noise. The set requirements for target- ing accuracy (Fig. 35, Table 2 in App. 4) are val- ues that the positioning method should fulfill with a certainty required, i.e. at a confidence lev- el (e.g. 95%). Requirements for positioning ac- curacy are actually the targeting accuracies fil- tered through an additional transfer function. This transfer function is dependent on dynamics of the machines used in position dependent tasks. For simplification, the set limit for targeting is here used as a goal for the positioning system. Strictly speaking this is not the case as the ma- chinery used should be assessed together with the positioning system. 2.4.1.2 Conclusions of the simulations with Effect Curves Increasing working width decreases therequire- ments for cross targeting accuracy. Smoothing (method B, in method D together with logistic transfer function) raises the error allowed spe- cially with high edge angles. Method D, includ- ing both the transfer function and smoothing, shows the highest tolerance. The logistic trans- fer function changes the situation with edge an- gle (a): a critical value for the edge angle can be found. Higher and lower edge angles allow larger targeting errors than the critical angle. The model for setting targeting and corre spending positioning accuracy limits needs the EC of the implement and the transfer function from it to the output of the target PL. Otherwise the requirements are not realistic.The EC of the implement and the model of the target produc- tion system itself affect the accuracy required. On the other hand, depending on the goals of PDC, there can be different criteria for targeting accuracy. In nature there are typically logistic transfer functions. Logistic functions act differ- ently in different operating points in the transfer function curve. High level inputs are sensitive to both overlapping and missing and they are de- pendent on accurate targeting. Low-input pro- duction gives the output more linearily because the transfer function is in the phase of constant growth. Extremely low input levels benefit from overlapping but do not suffer much from miss- ing. However, the requirements for constant quality of the output set limits for targeting ac- curacy in the extremely low input production, too. Furthermore, the output is a function of in- puts to an area rather than a point. This smooths the output and sets looser targeting requirements. The used ten point (1 m in length) moving aver- age did not, however, have considerable effect on the requirement calculated for targeting ac- curacy, except for high values of edge angle. 2.4.2 Accuracy in direction of travel - a simulation model for effects of nitrogen targeting accuracy The model for setting the requirements for tar- geting accuracy should have an accurate enough model for the PL. Therefore the steps from model A to D were not repeated. Nitrogen fertilizing was chosen as an example because nitrogen is considered one of the main components in leach- ing, and its spatial nature of variation is known since the 19th century (Larsen et al. 1991, Catt 1993, Kauppi 1993). 281 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplantproduction The model for nitrogen targeting used here is not a detailed explanation model. A complete model for nitrogen dynamics in our conditions would include a layered structure, and it should have submodels for plant uptake, mineralization, immobilization, leaching and denitrification (Johnsson et al. 1987, Pesonen 1992). The ef- fect of solar energy variation in different grow- ing seasons should be incorporated (O'Callaghan et al. 1994). Furthermore, to achieve best results in Finland, the effects of the cold winter period should be incorporated (Rekolainen and Posch 1993).A somewhat simplified model would use submodels for plant uptake and nutrient utiliza- tion (Varis 1989, Karvonen and Varis 1992). An explanation model is out of the scope of this study. The model presented is simplified to show the problem area: length targeting with a target system that has two logistic transfer func- tions. The model is not suitable for other uses (e.g. for yield forecasting). The model includes transfer functions for yield formation and nitro- gen leaching. Other growth factors than nitro- gen are not expected to modify these system outputs. The transfer functions are scaled with available data to get reasonable fit to the real processes of yield formation and leaching. Dy- namics is introduced to the models through var- iable positioning error that introduces targeting data. The model has two branches: the optimum (theoretical) branch (to the right in Fig. 36) where the targeting is perfect with no errors, and the other one with targeting error (to the left in Fig. 36). Both branches have the same actual var- iation in available soil nutrients, i.e. "the test field" is equal for both branches. The error branch reads the setpoint according to the meas- ured position. If there is a big enough error in targeting the error branch reads wrong setpoints. The error can be divided into error in position- ing information and human error in driving. Dif- ference variables for the two brances can also be counted. (Figs 36 and 37) The following simulation results (Fig. 38) are for a ten-meter random length positioning error and a half-meter random driving error. The fer- tility is assumed to change in sinus form. The examples show that, on a varying field, it is pos- sible to have remarkable errors in yield, and some in leaching as well, when fertilizer target- ing is poor. The transfer functions that were here quite ambigous, determine the exact errors. It is clear, though, that the magnitude of the error Fig. 36. Upper level Stella® diagram for the model for set- ting requirements for length targeting accuracy in N-ferti- lization (Haapala 1991). Fig. 37. The model for setting requirements for length tar- geting error in N-fertilization. 282 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. affects the results, and a ten-meter error is not adequate. Further simulations used Jaakkola and Turtola's (1985) material on yield of barley and leaching on Finnish clay soils to calibrate the transfer functions. Data of 1980 was selected because it represented a normal year with no special growth-limiting environmental factors. The fertilizing level was calculated based on the simulated soil nutrient content. The advice of Kemira Ltd that is commonly used in Finland (Viljavuuspalvelu 1990), was used. Lodging was introduced to the functions by setting a limit for N uptake whereafter the yield would collapse. Fig. 38. A simulation for N fertilization, (a) Sinus function for soil fertility changes, (b) Length targeting error (Lerr). The error consists of a ten-meter positioning error and a half-meter driving error. Both error components are random, (c) Error in measured fertilization need (Fertility_diff). (d) Error in fertilization (Fertilization_diff). (e) Error in yield (Yield_diff). (0 Error in leaching (Leaching_diff). Errors in (c), (d) and their consequences in (e) and (0 are due to the length targeting error (b) (Haapala 1991). 283 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplantproduction The requirement s for accuracy were set by finding (iteratively) the most sensitive factor in the output of the PL. First the setpoint change (fertilizing) was a single, square wave that got up in the distance of 100 m and came down at 200 m. Amplitude of the wave was increased from 5 kg/ha to 50 kg/ha. The targeting error was either 5, 10, 15 or 20 meters. The simulation step, dt, was one meter in distance. The Runge-Kutta method (Gustafsson et al. 1982) that produces accurate results with some more calculation ef- fort needed, was used in solving the differential equations. The simulations show how the con- stant targeting error and the variable height of the square wave affect the yield. All the runs have the same basic soil N-content, 50 kg/ha, and the same lodging point, 70 kg/ha (in N-uptake). The results for a square wave height of 50 kg/ha are very clear whereas heights of 10 kg/ha and 5 kg/ ha are quite insensitive (Fig. 39). The constant tar- geting error affects only the length of error area. Secondly, the effects of dense steps in the setpoint were tested. The aim was to check the effect ofconstant steps on the output when there is also a constant (systematical) error in target- Fig. 39. Simulated yield difference with a square wave set- point change in N-fertilization. Length targeting error is 10 meters. Wave height is (a) 5 kg/ha, (b) 10 kg/ha and (c) 50 kg/ha (Haapala 1991). Fig. 40. Simulated yield difference with a sinus wave set- point change in N-fertilization. Wave height is 50 kg/ha. Length targeting error is (a) 10 meters and (b) 20 meters (Haapala 1991). Fig. 41. Simulated yield difference with a sinus wave set- point change in N-fertilization. Wave height is 50 kg/ha. Length targetin error is (a) randomly ±5 meters and (b) ran- domly ±lO meters (Haapala 1991). 284 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. ing. The targeting error was increased from 0.5 meters to 20 meters. The step height was sys- tematically increased. Other variables were kept constant. Results show that with a suitable con- stant targeting error even high steps are not counted for in the yield output. This is because of resonance: the setpoints are taken from a po- sition where it is right for the current PL. (Fig. 40) This critical error is hypothetical because in natural variation the resonance situation can not last long. In further tests it was found that in- field variation is quite random including a spec- trum offrequencies (Ch. 3). The resonance situ- ation is importantbecause in fields there can be areas, specially boundaries of soil types, with undulating properties. If a systematical error is found in targeting, e.g. because of a systemati- cal error in the positioning device used, the res- onance can cause lodging or increased leaching. Therefore a systematic error is not wanted in any circumstances. In reality the positioning error is not constant but varies randomly, as found in literature and enclosed positioning tests (see Ch. 4). This ran- dom nature of the output of positioning devices affects targeting through the transfer functions Fig. 42. (a) Actual (thick line) and simulated (thin line) soil fertility, (b) The used sample ofmeasured positioning error in travel direction (Lerr) of post processed DGPS (Differ- ential GlobalPositioning System), (c) Theoretical optimum (thick line) and simulated (thin line) fertilization, (d) Yield with theoretical optimum (thick line) and simulated (thin line) fertilization, (e) Leaching with theoretical optimum (thick line) and simulated (thin line) fertilization. The sim- ulated values are calculated with positioning errors based on DGPS test results in Viikki on day no 351 in 1990. The fertility values are from measured yields in Keimola in 1991. 285 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production of the equipment used, smooth the output and hide the findings that were made in simulations with constant errors (Figs 38-40 above). In high N-levels the random positioning error can cause random lodging patterns. This can happen also with low N-levels, apart from the previous re- sults of simulation with constant error, when boundary areas of different fertilization needs are treated. The transfer function of N-fertiliz- ing to yield is logistic or spherical (Waddington et al. 1983, Peltonen 1992). This implies that high N-levels are the most sensitive ones. As stat- ed in the previous chapter with cross targeting error there is a certain optimum area in the ferti- lizer doze. Based on the simulations above, it was rea- soned that the most critical combination is found on a field where there are high changes in need for fertilization and where high N-levels are used. A simulation series was run with raising N-levels. Eventually, in an N-level of 220kg/ha aimed at (an N-fertilizing level of 170 kg/ha), it was found that lodging became the restricting factor. This N-level is of a slightly higher level compared with recommendations of the leading fertilizer supplier in Finland (Kemira Ltd) (Pel- Fig. 43, (a) Actual (thick line) and simulated (thin line) soil fertility, (b) The used sample ofmeasured positioning error in travel direction (Lerr) of on line DGPS (Differential GlobalPositioning System), (c) Theoretical optimum (thick line) and simulated (thin line) fertilization, (d) Yield with theoretical optimum (thick line) and simulated (thin line) fertilization, (e) Leaching with theoretical optimum (thick line) and simulated (thin line) fertilization. The simulated values are calculated with positioning errors based on on line DGPS test results in Viikki in 1993. The fertility val- ues are from measured yields in Keimola in 1991. 286 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. tonen 1992). At this level, a wave height of 50 kg/ha showed clear increase in lodging pattern as the targeting accuracy got poorer. An error of +5 m was found to get no lodging but ±lO me- ters had a few lodging patterns. (Fig. 41) The final simulations were made with the empiric data from Viikki positioning tests (see Ch. 4) and Keimola yield variation tests (see Ch. 3). This test was made to compare the results with those that were achieved with hypothetical targeting and soil variation data. The setpoints for N-fertilizing were calculated, quite mechan- ically, so that the greatest negative deviation from the average yield would get 100 kg/ha of information, 100-meter samples of the position- ing data from 1990 and 1993 were selected for modeling the targeting accuracy. The data came from the same test route position (from the re- sults between check points 6-9, Ch. 4, App. 10) to enable comparison of the positioning accura- cies of the two different positioning devices. In the first set of data from 1990, the accuracy in travel direction was ±7.9 meters (95%). (Fig. 42) The second set of data was selected from the on-line DGPS-tests in 1993. The length position- ing was much more accurate (± 3.34 m (95%)) (Fig. 43). The results with data from 1990 posi- tioning tests show five considerable lodging pat- terns (Fig. 42 above). Data from more accurate positioning in 1993 shows no lodging (Fig. 43). With the leaching function used there were no alarming differences in the amount leached be- tween perfectly positioned and with both of the samples used of GPS data. 2.4.2.1 Discussion of the simulations in the direction of travel The results are scaled for the fertilization ofbar- ley. In the tests of Keimola (Ch. 3) wheat was used. The crop is not, however, important but the shape of the transfer function which is simi- lar (e.g. Waddington et al. 1983, O'Callaghan 1995). On the other hand, theresults do not show general requirements. It is doubtful if general requirements could ever be set because the PLs have considerable variation in their capability to convert inputs to yield (comp. Bouma and Finke 1993, Delcourt and De Baerdemaeker 1994). The model developed can be used to cal- culate requirements for targeting accuracy in length direction if the involved transfer functions are calibrated to local conditions. Alternative triggers of poor targeting can be accomplished (comp. Han and Goering 1992, Delcourt and De Baerdemaeker 1994). Lodging part of the model worked well but leaching as a trigger showed little reaction to the N-levels used. This is due to the low sensitivity of leach- ing in the reference material used (Jaakkola and Turtola 1985). In other conditions, specially in sandy soils, leaching might be a good trigger for environmentally poor targeting of inputs (Catt 1993, Kauppi 1993). 2.4.2.2 Conclusions of the simulations in the direction of travel The method developed for setting the require- ments of targeting and positioning accuracy can be utilized in other applications of PDC. Other transfer functions and trigger values must then be selected. The thought model and procedures are generally usable. The results show that in a varying field, with a high operating point of a logistic transfer func- tion, the targeting must be most accurate. With constant targeting error and a square wave set- point change, the area of erroneus output is pro- portional to the targeting error. With an undu- lating setpoint there might be areas ofresonance where the control amplifies or smoothens the output. Actual positioning systems, however, which most often have random noise compo- nents, smoothen the findings ofsimulations with constant error. Random components may also cause local overdrafts which may introduce lodg- ing in such places where a corresponding con- stant error did not show any of it. Lodging as a trigger of poor targeting leads to requirements around ±5 meters (95%). In situations where there are comparable parameter values leaching does not react sensitively enough to be used as the main trigger. 287 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production 2.4.3 Accuracy in space for PDC - conclusions based on simulations of cross- and length targeting accuracy The requirements for targeting accuracy for PDC are highly dependent on local conditions. Pro- duction Locations vary in space and time. The most sensitive parameter, the trigger for poor tar- geting, may change if circumstances vary. The level of production inputs has considerable ef- fect on the choice of trigger. Low-input and high- input production strategies need different indi- cators. Simulations in work direction and in cross direction were made a little differently. Cross requirements for accuracy can be found if a lim- it for the variation of yield is set. In work direc- tion the requirements depend on a trigger varia- ble. This difference is due to the fact that the production system is more sensitive to sideways errors. This is because Effect Curves of the im- plement tend to be more varying in this direc- tion and the shape of the ECs is such that it needs better attention (driving accuracy). Driving along previous pass sets requirements for a much high- er order to the sideways accuracy. Simulations suggest that the most sensitive situations for targeting are on a highly varying field and on high expectations of yield. There is a risk of lodging which is the most sensitive trig- ger. On the other hand product quality limita- tions set limits to targeting errors in low-input systems because input responses are high and poor accuracy would lead to varying quality. The first situation yields an accuracy limit of ±5 meters to targeting of N-fertilizing in work di- rection. In cross targeting the requirements de- pend on allowable variation of production out- put. Equal levels of CV for each direction is a possible strategy for selection of the criterium. It is not easy to set this accurately on the basis of the simulations made because of different in- put levels. Dependence on edge angle is to be considered in cross targeting. The requirements varied considerably depending on the working width used too. The values for a two-meter work- ing width for a CV-limit of 0.1 is 0.214 meters and for a 20-meter width it is 0.395 meters. When the limit is raised to 0.3 the figures are 0.434 and 3.736 respectively. (Table 1 in App. 4) Gen- erally the requirements in driving accuracy are 2-10 times higher when compared with those for length direction. Typical requirements for ferti- lization would be ±0.5 meters in cross and ±5 meters in length direction. For other PDC-works requirements are set accordingly. Evidently there are situations where specific methods for the measurement of every single one of the three space directions is needed. The need for sideways accuracy and accuracy of the height coordinate, which is not specially treated in this study, are typically higher than that of the work- ing direction. Detailed requirements depend on the specific work. The height is normally refer- enced to some surface. The same priciple of ref- erencing is possible in some cases with driving accuracy. This difference in requirement stand- ard needs to be considered when positioning sys- tems are selected. 288 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. 3 The Keimola survey 3.1 Soil fertility and yield variation of spring wheat The aim of the survey was to evaluate potential- ities of position dependent control with a case data of in-field variation. In PDC, in-field vari- ation of yield (Searcy et al. 1987, Borgelt and Sudduth 1992, Stafford and Ambler 1992) and related soil properties (Diaz et al. 1992) are im- portant inputs for local decision-making. Inter- nationally the existence of in-field variation of soil properties and plant growth has been known for quite a long time (e.g. Peck and Melsted 1973, Catt 1993). In Finland corresponding re- sults can be found in the works of e.g. Kivinen (1935), Kaila and Ryti (1951), Jokinen (1983) and Puustinen et al. (1994). Researching into this local variation is quite laborous because of the dense sampling needed to get accurate local estimates (Jokinen 1983, Delcourt et al. 1992). The variation requires dif- ferent sampling strategies to be followed accord- ing to the accuracy and resolution desired (Lindén 1981, Jokinen 1983, Di et al. 1992, Haa- pala 1992). Representative samples for a certain area consist of subsamples the number of which can be calculated as follows (eq. 3, Snedecor 1948 ref. Jokinen 1983): p where n = required number of subsamples t = Student' s t - statistic v = coefficient ofvariation p = allowable error in percentage As a conclusion, the variation can be seen either as a cause of measurement uncertainty or as true indications of the state of the real world. The variation indicates that the soil-plant sys- tems are individual and need different control inputs. Actually this difference in interpretation does not mean different theories of the origin of the variation but rather shows the scale of inter- est of the observer with a certain application in mind. The survey consisted of measurements of soil fertility and yield of spring wheat in a 1.56 ha field in Keimola, Vantaa (Fig. 44). The field was in ordinary grain production. The whole area was of the same crop and equal treatments had been given to all parts of the field. No animal manure had been used in the near past. Within the field the main reason for variation was the inherent variation and cultivation history. The measurements were carried out on Au- gust 31st just one day before harvest. Two 50 m sample lines were selected. The aim of the se- lection was to get a varying (line 1) and an even (line 2) line. The criteria for the selection were plant height, colour and visually judged density of the plant population. There was a slight slope (c. 2.5%) in line 2. (Fig. 44) Samples were taken at 0.5 m intervals from two neighboring seed lines. Yield samples were taken out of areas of 1/8 m 2 (0.25 m x 0.25 m) in such a manner that the two seed lines were cov- ered. Immediately after this the soil samples were taken from the same locations. (Fig. 45) The samples were taken in the direction of fertilizer rows to avoid effects reported by Urvas and Jus- sila (1979). The grid size was selected accord- ing to the possible error of yield measurement. The same resolution was selected for soil sam- pling because accurate joining of soil and yield sample data was needed. The placement error of the sample grid in distance along the sample lines was estimated to be maximum ±1 cm with the method used. This error is due to a human error in setting the grid to the right position. The worst case is found when the area where the grid should hit is com- pletely empty of stems and the surrounding are- as are at the highest density of the population. 289 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production In this hypothetic situation an infinite error could be reached. In practise this is not probable. An empiric worst case error for a single sample was calculated: the highest measured population den- sity was assumed outside the right grid position and the lowest one inside it. The range of meas- urements (Ch. 3.1.2) was from 304 to 864 l/m2 (19-54 stems in sample). In theoretical extreme case, where 864 1/m2 is outside and 304 1/m2 inside the right position, an error of ±1 cm in grid position can introduce an error of±1.4 stems (=l/25x(54-19)) to the sample value and the er- ror is +7.4% (=+l ,4/l9x 100%) of it. In opposite case, where 304 1/m2 is outside and 864 1/m2 inside, a -2.6% (= -1.4/54x100%) error in sam- ple value is found. Actual probable errors for single samples caused by grid positioning are smaller because in real populations maximum and minimum values are not parallel. Minimum and maximum variable values also indicate the trend in population. In yield samples there is no clear trend but neighboring values show some big differences. However, the greatest differenc- es are rare. Therefore the actual estimated error is far below ±5%, as wanted. This is the case for the soil samples, too. Apart from yield there are soil variables with clear trends but neighboring samples have comparably small differences. The main error source is not the sampling but ana- lyzing error. (Ch. 3.1.1 and 3.1.2, Dally et al. 1984, p. 545) 3.1.1 Soil variation Soil samples were collected in little boxes the numbers of which were mixed before sampling. The mixing was successful because the box number and distance in the sample line showed low correlation (r (Spearman) was -0.331 in line 1 and 0.142 in line 2). After the sampling the boxes were organized in ascending order. The samples were analyzed in this number order (per- sonal conversation with Mr Mäntylahti from Vil- javuuspalvelu Ltd 1995). Dual samples were tak- en in five meter distance, ten dual samples per line. These operations were done to enable judge- ment of the analyzing error (accuracy, autocor- relation). The samples were analyzed in Viljavuuspal- velu Ltd for pH, total-N, P, K, Ca and Mg. The analyses were those included in normal soil fer- tility analysis (Vuorinen and Mäkitie 1955) with the addition of total-N analysis. The pH was measured from soil-water suspension with a gal- vanic element. Total-N was measured with the Kjeldahl method (Walsh and Beaton 1973). For further analyses an extraction with acidous am- Fig. 44. The test field in Keimola showing positions of the test lines I and 2 and the elevation curves in centimeters above mean sea level. Fig. 45. Taking the yield samples. The samples were the total yield (straw and grain) from areas of 1/8 m: in a sam- pling distance of 50 cm A 50-meter measurement tape and a sampling grid of steel (0.25 m x 0.25 m) was used. 290 AGRICULTURAL SCIENCE IN FINLAND monium acetate (0.5 M CH 3 COONH4, 0.5 M CHjCOOH) was done. Thisextract was analyzed with photometers to get values for P, K, Ca and Mg content. In addition to these, soil organic matter content and soil type were determined with manual methods (Vuorinen and Mäkitie 1955). In Keimola, the pH was quite high, 5.9 - 7.1, the mean value 0.5 units higher in line I than in line 2. Variation was small (CVs of0.03), quite as expected (comp. Jokinen 1983). In line 1 pH- values had a positive trend in direction of soil sloping: pH increased as the soil declined. Dual samples indicated some differences of 0.2 units with pH-values smaller than 6.6. Soil total N was at a 33% higher level in line 2 than in line 1. It showed no trend inside the lines. Dual samples indicated poor repeatability of concentration measurement. P-values had a negative trend in the direction of soil sloping in line 1. There were some local jumps in the values, some more in line 2 than in line 1. Dual samples had some peak differences which mean that the jumps may be caused by analyzing errors. K varied very little inside the lines. In line 1 it seemed to have a negative trend in direction ofsoil sloping. There was a considerable (c. 80 mg/1) difference in the mean value between lines. Dual samples had lit- tle difference excluding one point in line 2 where the peak seams to be an analyzing error. Ca-val- ues had a clear trend in line 1,reaching high lev- els in the lower part of the line. The analyzing system had apparent difficulties in measuring such high values. In line 2 the level was lower. Dual samples had low differences in both lines. In line 1, Mg had a strong positive trend in soil slope direction. In line 2 the trend was not very clear. In line 1 the values exceeded 1000 mg/1 whereas in line 2 the values were around 500 mg/1. Dual samples showed an outstanding ac- curacy. (App. 5) In Finland organic matter content of soil is given in six classes (Jokinen 1983, Viljavuus- palvelu 1990): <3% vm "little organic matter" 3-5.9 m "some 0.m." 6-11,9 rm “rich in 0.m.” 12-19.9 erm “very rich in 0.m.” 20-40 Mm “mull soil”Mm “mull soil” >40% “peat” In Keimola threeof these classes were found. In line I there was a trend towards more organic matter in direction of soil sloping. In line 2 the organic matter content was lower and there was no trend. Dual samples gave little evidence on misjudging. Only some differences were found in transition zones between classes. (App. 5) Mineral soil types are classified according to main fraction diameter. The classification dif- fers a little from that of e.g. Great Britain (Hei- nonen 1978 vs. Mott 1988). The types found in Keimola and theirEnglish counterparts are; HsS silty clay or silty clay loam HeS clay or clay loam HtS sandy clay or sandy clay loam LjS sandy clay with 2-6 % of organic matter The sandy soil classes HtS and LjS were com- bined (HtS/LjS). In line 1 the soil had a trend from clay to coarser types. In line 2 the soil was coarser and no trend could be found. Dual sam- ples showed only normal differences in zones where soil types changed. (App. 5) The dual samples showed that some meas- urements (pH, K, P and N) had error sources. The differences in dual sample results (App. 5) show that there might be differences in accura- cies of the analysis methods for individual nu- trients. The same extract was used for P, K, Ca and Mg analyses (Mäntylahti 1995) and possi- ble changes in analysis results should occur si- multaneously. As this is apparently not true (App. 5), the errors are most probably connected with the analysis phase itself, not the extraction. Autocorrelation analysis was performed to find out if the analyzing technic had a “memo- ry” error where the previous sample value would affect the next one. The autocorrelations were calculated for the data in right sampling order and in analyzing order of the boxes. Results (App. 6) show that pH, N and K analyzes have 291 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production Fig. 46. Yield results in Keimola in 1991. Yield of spring wheat at 15% (w.b.) moisture content (a) in line 1 and (b) in line 2. Straw yield of spring wheat at 15% (w.b.) moisture content (c) in line 1 and (d) in line 2. Plant density [l/m 2 ] of spring wheat (e) in line 1 and (f) in line 2. STD =standard deviation. CV = coefficient of variation. 292 Voi 4: 239-350. autocorrelation in box number order, whereas P, Ca and Mg are less autoregressive. The autocorrelations give evidence that the measurement of pH, N and K have memory ef- fect and P does not have it. The analyses of Ca and Mg have a slight memory effect. Differenc- es in dual sample values of pH, N and K (App. 5) could be caused by the memory effect. Dif- ferences in dual P analyses (App. 5) are not, how- ever, due to autocorrelation but they are of ran- dom nature. Autocorrelations cause interference to further statistical analyses (comp. Ch. 2.2, Eq. 1). Statistical analyses for pH, K and N are there- fore somewhat inaccurate. 3.1.2 Yield variation The yield samples gave density of plant popula- tion [l/m 2 ], water content of grain and straw [% w.b.], grain yield [kg/ha] and straw yield [kg/ ha]. Plants were calculated manually from the samples and the total sample was weighed. Ker- nels and straw were separated and weighed. The water content of the grain and straw were meas- ured with ASAE's oven method (130°C for 19 hours, unground sample) that should give repeat- ability of better than 0.2 %-units (ASAE 1989). Yield samples weighed 10 gramms and straw samples 3 gramms before the oven treatment. Grain and straw yields were corrected to 15% (w.b.) water content. The average yield was some 500 kg/ha high- er in line 2 than in line 1. Line 2 was very even in visual judgement but actually the yield com- ponents varied nearly as much as in line 1 (Fig 46). The difference in appearance was due to the low frequency straw yield variation in line 1 (Fig. 46c). Population density was c. 30 1/m2 higher in line 1. Its variation was high (CV was 0.18 - 0.19) in both lines.(Fig. 46) In Keimola, the yield was measured with a higher resolution (0.5 m) than in normal yield measurements made in most other researches. This gives possibilities of simulating various sampling methods, as done later on in chapter 3.2. The true variation can be viewed with e.g. geostatistics (see Ch. 1, App. 2, Clark 1984). Semivariograms gave interesting results on the form of yield variation. (Fig. 47). The sharp rise in the semivariogram shows (Clark 1984) that the yield is a quite random phenomenon. Subsequent yield measurements Fig. 47. Semivariogram for (a) unconditioned grain yield and (b) for filtered grain yield. Fig. 48. The test setup for measurement of feed rate dy- namics of a drill. Schematic (Fig. is based on Nousiainen 1995). 293 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplantproduction have little influence on each other. This confirms that the production locations are individual (comp. Ch. 1)and leads to the need ofdense yield measurement. The range of influence is in raw data approx, half a meter and in the filtered data approx, one meter. There are also fluctuations that seem to be of a constant wavelength. Filter- ing the data with a ten-value moving average leads to a clearer picture of 2-2.5-meter long waves (Fig. 47 above). The probable reason for this sinus form var- iation is some object that has rotating parts. Most probably this is due to variations in seed and/or fertilizer output of the combined drill used; the output of a roll feeder tends to oscillate. In tests made at the Department of Agricultural Engi- neering and Household Technology (Nousiainen 1995), an electric motor was used to turn a com- bined drill that was placed on a test stand. A set of sampling buckets (10x10 pcs, 125x100 mm) were drawn at a constant speed from under the operating feeders. The turning speed of the mo- tor and the feed axle and the velocity of the moving sampling bucket jig were measured.The samples were weighed with a laboratory scale connected to a PC computer with RS-232-C se- rial interface. Corrections for irregularities in sampling bucket form and forward speed were calculated. (Fig. 48) For further calculations four additional points were interpolated in between each subsequent pair of the fertilizer flow values measured. This data was further smoothed with a moving aver- age of three values. The procedure reduces high frequencies in theresults but they are higher than that of the variation of interest. A clear oscilla- tion with c. 0.5 meter wave length is shown in Fig. 49. Output of granular fertilizer of a combine drill feeder in tests in Viikki in 1993.Setpoint = 400 kg/ha. Output of ten feeders in figure, (a) Unconditioned data and (b) smoothed data. (Calculated based on Nousiainen 1995) Fig. 50, Sernivariogram of the feedrate of a combine drill in tests in Viikki in 1993. (Calculated based on Nousiainen 1995) 294 AGRICULTURAL SCIENCE IN FINLAND the resulting output (Fig. 49). Semivariograms were constructed to find out possible periodical behaviour of the output. Lin- ear interpolation was used to add 9 points be- tween measurement points. This reduces only such high frequency variations which are not interesting in this case. The resulting semivari- ograms (e.g. Fig. 50) confirm that the output seems to oscillate in sinus form. The oscillation is due to the feeder construction that accumu- lates some of the fertilizer and pushes it out in quite regular intervals. The fact was found in summer 1994 during video analysis of the feed- er output. 3.2 Extracting Production Locations from the Keimola data Position Dependent Control needs exact Produc- tion Locations. The PLs should be located effi- ciently to get the best results. In this study, Kei- mola test data was used as case data to evaluate possible methods for PL extraction. Statistical analyses were made to find out which measured variables had influence on the grain yield. The hypothesis was that the data had spatially varia- ble structure and position-fixed PLs would give the best determining (local) regression models, (comp. Bhatti et al. 1991, Wendroth et al. 1992) 3.2.1 Linewise Production Locations The data was first calculated separately for the two sample lines with no assumption for spatial variability inside the lines. The variables meas- ured were coded (Table 3). The effect of individual variables on the yield were first analyzed. Correlation analysis showed that there were no clear correlations except for internal crop variables (state variables of the Table 3.Coding of variables in statistical analyses of spring wheat yield in tests in Keimola in 1991. x ( - x ? are input variables and x 8 and x 9 state variables for the grain yield. = constant of the regression eq. = pH-value X, = CONST X 2 = PH x 3 = ca = Ca content = total nitrogen = P content X = N TOT4 X 5 = P x 6 = k x 7 = mg X„ = POP X, = STRAW = K content = Mg content = density of plant population = straw yield Table 4. Influence of individual soil parameters on spring wheat yield in tests in Keimola in 1991. Partial correla- tions are calculated separately for the two sample lines. Variable Corr. coeff. F-value P Line 1 n=lol PH CA -0.1793.272 0.074 -0.1321.767 0.187 0.0220.047 0.828 0.1271.631 0.205 -0.0150.023 0.879 -0.1111.224 0.271 0.68286.127 o.ooo*** 0.802178.031 o.ooo*** N_TOT P K MG POP STRAW Line 2 n=lol PH CA -0.1381.929 0.168 0.1051.11! 0.294 0.024 0,057 0.811 -0.0050.002 0.962 0.2245.219 0.024** 0.32611.763 o.ool*** 0.65875.716 o.ooo*** 0.897406.100 o.ooo*** N_TOT P K MG POP STRAW production system) such as density of plant pop- ulation (POP) and straw yield (STRAW). Input variables (inputs of the production system) K and Mg had somewhat higher correlations. The cor- relations were generally higher in line 2 than in line 1. (Table 4) . Corresponding regression estimates also showed that only the state variables had a con- 295 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Table 5. Coefficients of determination (r2 ) and regression coefficients of the best regression functions in regression analyses of spring wheat yield in tests at Keimola in 1991. Both input and state variables for the yield are included. Function r 2 Cj c 2 c 3 c 4 Line 1 f 3 *** 0.670 6528***-667** -6.62 o.s3*** Line 2 f4 *** 0.814 4669** -451 -4.66 o.s2*** Table 6. Coefficients of determination (r2 ) and regression coefficients of the best regression functions in regression analyses of spring wheat yield in tests at Keimola in 1991. Only input variables for the yield are included. Function r 2 Cj c 2 c 3 Line 1 f 7 0.033 11550*** -989 0.12 Line 2 f 7 *** 0.147 11128*** -1326** 5.52*** siderable coefficient of determination. Regres- sion estimates were calculated separately for the two lines. (App. 7) Linear stepwise regressions were calculated for nine different functions as follows (see classification above) to find the structure of interactions: 1) 2 x 9 2) f 2=c 1+c 2 xg+c 3 x9 3) f 3=c1+c2x7+c 3 x 8+c 4x9 4) f4=c,+c 2 x2+c 3 x9 5) fs=c,+c2x 2+c 3x 4+c 4x9 6) f6=c,+c 2 x 2 7) f7 =c,+c2x 2+c 3x 7 8) fg =c l+c 2x 8 9) f9=c,+c 2x9 The functions f(-f5 have both state and input variables (see Table 3 above), f 6 and f ? input var- iables and fg and f 9 internal ones. The results show thatbest coefficients ofdetermination were achieved with functions f, and f, which include3 4 Mg content (x 7 ), population density (xg ) and straw yield (x 9 ) for line 1 and pH and straw yield for line 2 (Table 5) . In Position Dependent Control, the input var- iables (Xj—x? ) are more interesting than the in- ternal ones (state variables xg and x 9). The pri- mary question is how the inputs affect the yield. Therefore stepwise regressions (f 6 and f ? ) with no state variables were calculated. The best co- efficients ofdetermination were achieved in both lines with function f 7 that includes pH (x 2 ) and Mg content (x ? ) (Table 6) . It was found thatfg including population den- sity (x g ) was the best one of the only-state-vari- able models (Table 7) . The coefficients of de- termination of input variables were very low. There are several reasons for this. The input var- Table 7. Coefficients of determination (r2 ) and regression coefficients of the best regression functions in regression analyses of spring wheat yield in tests in Keimola in 1991. Only state variables are included Function r 2 ct c. '2 Line lfg *** 0,643 1551*** o.s2*** Line 2fg *** 0.804 1374*** o.s2*** iables were measured straight after yield meas- urement. There are, however, differences in the take-up schedule of the nutrients. Some nutri- ents are mainly taken up in the beginning of growing season and others later (e.g. Karvonen and Varis 1992). Thus the measurement timing was not perfect. The measurements express the fertility situation in the upper root zone at har- vest time. They also express the level of nutri- ents in the field for slowly varying nutrients (P, Ca). Autocorrelations in determination of soil sample nutrients (Ch 3.1. above) have also a neg- ative effect on the validity of the results. 3.2.2 Yield-based Production Locations The next hypothesis was that equal yield levels in a varying field would stand for equal Produc- tion Locations. In this case, the situation is viewed from the output, the yield, to the trans- fer function of the PL. The thought model is that as the fertilizer input has been constant all over the field and the yield is still varying, there must be areas within the lines that have different trans- fer functions (see Fig. 46 above). On the other 296 Haapala, H. E. .S'.; Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND hand. Position Dependent Control has the inbuilt assumption of locally varying transfer functions. The contrary hypothesis claims that measured yield levels do not indicate the model of the PL. The question is whether the yield level is strong enough as an indicator of the differences in PLs or not. 3.2.2.1 Simulation of yield level selection To evaluate the hypotheses, areas for calculation of local regressions were selected from the yield data based on the lenghts of equal yield levels. Several algorithms were developed for this se- lection. A good area selection algorithm should react to possible sharp changes in yield level. These changes indicate that the soil is altering. Furthermore, a good algorithm should select rea- sonable amount of areas with a suitable number of observations for the calculations. The basic yield data was measured with such a high reso- lution (0.5 m) that the data could be used as ref- erence of “true variation” in calculations that simulate the action of other, more sparsely sam- pling yield measurement methods. For compar- ison, different sampling technics were simulat- ed. Simulations of automatic integrating and various line and point sampling methods were made. Representative results of these calcula- tions are gathered in the following figure (Fig. 51). Automatic sampling, such as measurement of grain flow in a combine harvester (e.g. Demmel et al. 1992), integrates the yield (Vansichen and De Baerdemaeker 1992). The measurement re- sult is integral of the yield from the previous few meters. This effect was imitated by filtering the densely measured Keimola yield data with a moving average. Changes in this filtered data were compared with a trigger value. When the data changed more than the trigger, a change in yield, an edge, was found. The edges were signs of yield level change. According to the hypoth- esis, these changes are signs of different Pro- duction Locations. A 150 kg/ha trigger value was found to give over ten edges per sample line (Fig. 51a). Pure edge detection does not, however, work properly: slow changes are not detected.A modified edge detection algorithm with averag- ing of the integrated data was developed (Fig. 51b). Averaging smoothens the integrated result and leads to more valid indications. A higher (e.g. 200kg/ha) trigger valuereduces the amount of detected PLs , as expected. This is natural because there are less high edges in the yield level to be detected. Accumulative line sampling was simulated by accumulating the raw data samples and aver- aging them. Sample values were calculated at fixed intervals. The results show that this kind of sampling leads to fewer detections of yield changes than automatic sampling with same av- eraging distance (comp. Figs. 51a and 51c). When compared to the modifiedautomatic sam- pling algorithm, the accumulative line sampling algorithm gave approx, the same amount of de- tections but in different locations (comp. Figs 51b and 51c). Increasing accumulation distance in accumulative line sampling smoothened out the result and hided apparent areas of different production potential (comp. Figs 51c and s ld). Again, higher trigger values would reduce the amount of detections. The last simulations were done with point- sampling. Single samples were chosen from the Keimola raw data with various distances. Point samples showed great variation in sample val- ues and lead to quite random decisions in find- ing the edges (Figs 51e and 5 If).This is analog- ic to the results with the measurement of drain quality (deßoer 1987, Haapala 1992). Again, a higher trigger value(e.g. 200 kg/ha) would lead to fewer detections. The result is, though, very sensitive to the points selected. Normally manual sampling is not pure point sampling but includes some averaging (Jokinen 1983, eq. 3 above). This was simulated with lo- cal averaging (Figs 51g and 51 h). Eleven points (5.5 meters in distance) of the data formed one sample. Sample intervals ofup to 20 meters were used. The filtering effect is quite strong, and thus higher trigger values have little effect on the number of PLs encountered. 297 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production Fig. 51. Edge (150 kg/ha) detection in Keimola wheat yield measured with simulated (a) automatic sampling (moving average of 10 values), (b) automatic sampling with further integration (local averages of 11 values), (c) accumulative line sampling (avg. of 10 values), (d) accumulative line sampling (avg. of 20 values), (e) point-sampling with point distance of sm, (f) point-sampling with point distance of 20 m, (g) averaging point sampling (avg. of 11 points) with point distance of sm, (h) averaging point sampling (avg. of 11 points.) with point distance of 20 m. 298 AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. 3.2.2.2 Choosing sampling methodsfor extracting PLs from yield data In position dependent adaptive crop production, the sampling methods should make it possible to find different areas in the field. This is true both for the yield and other measurements such as the nutrient content, soil type, pest infections, etc. The sampling method should have a suita- ble resolution for each individual case. The sim- ulations with yield measurements show that sam- pling methods have built-in differences in reso- lution and thus also in the capability to find the areas. This is due to the introduction of filtering (integration/averaging) of the data. (Comp. Haa- pala 1992) Yield-based area finding algorithms should include edge detection and averaging. Pure edge detection does not count for slow changes in measurement values. A better algorithm includes comparing the current measurement value with an average of preceeding measurements. Area finding algorithms should be calibrated for each kind of variation individually. The calibration procedure needs information in the true varia- tion of the target and the resolution wanted. Practical sampling mostly includes estima- tion (interpolation) because it is not economical to collect all available data (Clark 1984, Lesch et al. 1992). Total sampling is not feasible for most inputs (e.g. soil sampling) and state varia- bles such as biomass: it would interfere with the on-going production processes. The yield meas- urement, however, can be made with total sam- pling. Automatic total sampling, e.g. measurement of the yield with a real-time yield meter in a com- bine harvester, is a good method because of its capability to give continuous measurement val- ues and thus to give a good coverage with little effort. On the other hand influences of integra- tion must be corrected, e.g. the driving direction should be known to be able to shift the results back to the right location in driving direction. Time delay from the PL to the registration of its yield and forward speed of the combine should be known. In a Minnesota experiment (Ault et al. 1993) the best available resolution of auto- matic yield measurement was 12 meters. This was due to integration and spread of the grain inside the combine. For best results, cutting width measurement is also needed. (Searcy et al. 1987,Demmel et al. 1992, Stafford and Am- bler 1992, Vansichen and De Baerdemaeker 1992) Point sampling, if used, has to be dense and/ or each sample should consist of several sub- samples. This is analogical to soil sampling (comp. e.g. Jokinen 1983, eq. 3 above). Other- ways PL-areas are not properly detected. Manu- al point sampling is very laborous and can not be used in this context. Automatic sampling machines should be used to get enough data for PDC. The sinus variation of the yield, which is most probably due to variation of the combi drill's output (Ch. 3.1.2 above), has to be considered when sizes of the PLs and measurement meth- ods for finding their limits are selected. Auto- matic continuous sampling was chosen because it is the most probable measurement method for the huge amount of yield data needed in PDC. Moving average of20 values was used to smooth the sinus wave. For Keimola data, iterative cal- ibration resulted in a trigger value of 110 kg/ha that gave sufficient amount of data per subarea and reasonable distribution of the subareas. (Fig. 52) Fig. 52. Simulation of automatic sampling. 110 kg/ha edg- es are detected from integrated wheat yield in Keimola. Moving average of 20 values is used in integrating the raw data. Areas A..F are selected. 299 AGRICULTURAL SCIENCE IN FINLAND 3.2.2.3 Local regressions for PLs that are selected on the basis of yield levels Six subareas (A-F in Fig. 52 above) were se- lected for the calculation of local regressions. Input variables pH, Ca, N, P, K and Mg were used in stepwise regression analysis. The only function from the previous linewise calculations that got a reasonable coefficient of determina- tion was f 7 which included pH and Mg. Addi- tional functions were used as follows: 10)f,o=c . '!) f „ =C l +C 2X5 12) f, =c|+c 2 x2 +c,x5+c 4 x6 13) fl3=c,+c2 x2 +c3 x3+c 4 x4 Some areas had higher coefficients of deter- mination than those calculated for whole sam- ple lines. Some areas had, however, very poor r 2 s (Table 8, comp. Table 7 above). 3.2.3 Fixed-length Production Locations The variation ofr 2 seems to have some correla- tion with the area size: the smallest PL, C, has the best r 2. PL C also has the most detailedmod- el. (Table 53 above) This is in accordance with the idea of position fixing. A hypothesis can be made that the models are local and cannot be judgedwith the measurement of outputs, e.g. the yield, alone. For comparison of this hypothesis and the previous one with yield level as the fixing vari- able (Ch. 3.2.2), stepwise regressions were cal- culated for fixed 5-meter lengths. Stepwise re- gression analysis was done for the 5-meter lengths of unconditioned yield data from Kei- mola. New functions (f]4-f27 ) were introduced: H) f,=c | +c 2x 3+c 3x 6 15)f.=c.+c2x6 16) f, 6 =c,+c 2x 2+c 3x3 +c4 x 7 M) f,=c | +c 2x6 +c 3 x 7 18) 2x4 +c 3x6 19) f„=c | +c 2x 2+c 3x3 +c4 x5 +c5 x6+c 6 x 7 20) f2o=c,+c 2x5+c 3x6 21) f 2 ,=c,+c2 x 2+c 3x3 +c4 x 4 +c5 x 7 22) f22 =c,+c 2x 5 23) f23 =C l +C2 X 2 +C 3X3 +C4 X 4+C5 X5+C 6 X6+C 7 X7 24) f24 =c,+c2 x 4 +c 3x5 +c4 x6 Table 8, Coefficients of determination (r2 ) and regression coefficients of the best regression functions in regression analyses ofyield of the Keimola tests. Only input variables included. PL n Function r 2 c, c, c, c.I 2 3 4 A 33 f |o 0.000 3428 B 25 f„ 0.087 9194 99.2 C 14 f |2 0.589 14279 -2309 243.2 -52.6 D 23 f|o 0.000 8713 E 19 f, 0.254 1770 1513 17.4 F 30 f, 3 ** 0.282 26633***-3102** 0.55 -8521* 25) f 2s =c,+c 2x4+c,x7 26) f2=c,+c 2x2 +c ,x4+c 4 x5 +c 5 x6 +c 6 x7 27 ) f27= C l +C 2X 4 Some very high r 2 's (0.8-0.99) were achieved. As can be seen, the best functions are locally different. This indicates soil variation within short distances. Again, there are spots with very poor coefficients of determination. These spots may have influencing factors other than those measured, e.g. plant diseases. All the poorly regressing areas have only the constant as significant predictor which also points to some extra influence. (Table 9) 3.3 Discussion of the Keimola tests Soil and yield variability in Keimola was of the same type as in international studies. There was great variation of the soil and nutrients in short distances, as reported by e.g. Peck and Melsted (1993), Mulla (1988), Ovalles and Collins (1988), Ndiaye and Yost (1989), Goovaerts and Chiang (1992), Delcourt et al. (1992), Bouma and Finke (1993), Delcourt and De Baerdemaek- er (1994) and Mcßratney (1992). Domestic re- search is also in accordance with the variation types found (Kivinen 1935,Kaila and Ryti 1951, Jokinen 1983 and Puustinen et al. 1994). 300 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. Table 9. Coefficients of determination (r2 ) and regression coefficients of the best local regression functions for yield in 5- meter lengths in Keimola tests. Only input variables included. PL n Function r 2 c, c, c, c. c, c, c,12 3 4 5 6 7 1 10 f, O 0.000 5112** 2 10 fM 0.632 7240*** 2.28** -24.0 3 10 flO 0.000 6962** 4 10 f, 5 0.196 6579* -16.2 5 10 f|6 0.667 4278* -1926 -0.38 9.42** 6 10 f|7 0.450 7064*** -33.9 11.1* 7 10 f |8 ** 0.622 583 10263* -28.9* 8 10 f„ 0.986 5646*** -8333*** 0.11 90.3** -119*** 49.9*** 9 10 f 2O 0.606 3688 256 -53.9** 10 II f2| 0.686 3492* 3795 0.41*15006* -13.2* 11 10 f, 4 0.370 8781 -1.4514.0 12 10 f22 0.273 6077*** 121 13 10 f2 0.994 15559** -2909*** o.97***-30967*** 431** -18.1*** -13.7*** 14 10 f lg ° 0.547406.9 12163* 18.7* 15 10 f24 0.639 6065** 9445 612* -53.3** 16 10 0.532 8080 -14969 32.2** 17 10 f26 0.862 -1972 -2470 32265** -364 18.1* 56.6** 18 10 f, O 0.000 7684* 19 10 f |o 0.000 7418*** 20 11 f27 0.228 13093** -18712 Position-fixing proved to be efficient in those points where the models used included enough parameters and the parameter measurement (sampling and analyzing) was accurate enough. The selection of the starting point of distance measurement in test lines was totally random and the PL size used (5 m in length) was constant. In spite of this simplification the results were good: local fixed-length PLs were found to give best r 2's of the methods used. The PL size used (5 meters in length) is in accordance with the previous simulations (ch. 2.4.2) and with the judgements of international researchers (e.g. Auernhammer 1990, Stafford and Ambler 1990, Petersen 1991, Han and Goer- ing 1992). The PL-based method used is differ- ent from these technic-based approaches. It is based on the variation of PLs rather than possi- bilities of the current technic. Therefore the method is more accurate and valid. The basic reasons for some low coefficients of determination (r2 's) in the 5-meter PLs are measurement methods and conditions in the field. The measurements did not cover all effects. timing of sampling was not perfect, analyzing accuracy of the samples was not adequate in some parameters and fertility of the soil was (too) good. In some locations there could be dominat- ing factors that were not measured (e.g. soil com- paction, variations in input level, see Fig. 2 in Ch. 1). The soil parameters measured have dy- namic behaviour. Therefore measurement time is important if good correlation is needed. The samples were taken just before harvest, and for dynamic parameters like soil total N and K (Richter 1986) the results show only the left-over amount of nutrients that is not necessarily cor- related with plant uptake (Karvonen and Varis 1992, Peltonen 1992). Autocorrelations that in- dicate memory effect in analyzing the pH and the nutrients K and total N (App. 6) introduce an additional error component to the regression analyses and the coefficients of determination (Dally et. al 1984, Hari 1991, Lankinen et al. 1992, eq. 1 above). The field was in good fertil- ity state. It was rich in Ca, K and P. There was 33-213 mg/1 total N in the soil. The pH was 5.9- 7.1 which is a very good level for silty or sandy 301 AGRICULTURAL SCIENCE IN FINLAND 2 clays. The organic matter content was above 3% (3-19.9%). The yield level was comparably high for a Finnish field (3072-7775 kg/ha). All these figures show that there was no eventual short- age of nutrients. In these conditions some PLs are sensitive to fertilizing and others are domi- nated by different factors. The error budget of measurements and mod- eling was varying and no exact value for every part of it can be shown (comp. Fig. 19 above). However, the measurement methods and the data was equal for all the compared methods of PL extraction (line, yield and fixed-length based PLs). Therefore the results are comparable and only dependent on the success of finding the PL sizes and their locations. In the good regressing PLs both the model, its parameters and related measurement technic are adequate. It is assumed that, with adjusted fit to the actual in-field vari- ation, even better results are achievable with position-fixing as compared with the other meth- ods. However, all the results depend on the ac- tual variation (comp. Delcourt and De Baerde- maeker 1994 and Fig. 11 above) 3.4 Conclusions of the Keimola tests Soil fertility varies within very short distances. Values of pH, Ca, Mg, N, P and K all show var- iation and usually also a trend in the sample line. This variation of soil properties is seen in yield variation. The case data showed that, in a nor- mal wheat stand, yield variation can be 15-17% of the mean value (CV 0.15-0.17). Densely measured yield can be found to vary in sinus form. This is probably due to the variation of seed output of the drill. This effect can easily be filtered out from the data if the scale of interest is not on below-one-meter variation. Soil analyzing methods may have a memory effect: subsequent analyses affect each other. In Keimola such effects were found in pH, N and K analysis. This error source should be elimi- nated if accurate results are required. In prac- tise, as memory effect is not easily removed, neighboring samples should be analyzed one af- ter another. This is because memory effect smoothens sharp changes in data that are more likely in samples that are in random order. Selecting the Production Location size and its location has a remarkable effect on the con- trollability of the production. Good PLs give quite high coefficients ofdetermination for con- trollable soil fertility parameters in regression analyses of the yield. Selection of the PLs on the basis of yield variation does not give good results. Equal yield levels do not stand for equal PLs: PLs have very different transfer functions from the input parameters to the yield. A simple distance-based selection gives better results than yield based selection. The good fit found in some Production Lo- cations ensures that position-fixing can be effi- cient if the PLs are adequately well known. For best practical results, the PLs must be intensively measured and the data be fixed to the position. We need to have a network of PLs with a varia- ble resolution (in this case-study a constant res- olution of 5 meters was adequate for quite good controllability) and results from measurements of the input and output variables of these PLs. The variables, including automatic yield meas- urement, shouldbe measured with a method that gives values in the resolution required, either directly or through interpolation (e.g. with the methods ofkriging). It must be realized that measurement meth- ods of in-field variation affect the accuracy of knowledge of the variation achieved. For this reason, variations measured with different meth- ods should not be compared. Automatic sampling methods integrate the data and most manual sam- pling methods average it. The sampling meth- od, whatever it is, should be calibrated for each kind of variation. The calibration should begin with knowledge of the resolution wanted. There- after suitable method and averaging and integra- tion within the method are selected. Economi- cal methods for the measurement of the huge data amount required are necessary. 302 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND 4 Positioning Positioning methods are crucial in Position De- pendent Control where local information is used. Positioning is used to localize the information measured. It is also used as a control input for the PDC e.g. in variable rate application (Au- ernhammer 1990, Harrison et al. 1992). 4.1 Coordinate systems Position is referred to “the location of a point with respect to a specific or implied coordinate system” (Oxford Illustrated 1984). Positions are given in these coordinate systems agreed. In sur- veying, several coordinate systems are used. On theresulting maps the position is often expressed as level coordinates. There are equations for making conversions between the different coor- dinate systems. (Langley 1992, Lankinen et al. 1992) Coordinate systems can be global or lo- cal. Globalsystems have reference ellipsoids, i.e. mathematical surfaces that estimate Earth sur- face. Local systems are referred to locally de- fined datums that can be defined by local gravi- ty and astronomic north (Local Astronomic co- ordinate system, LA); or direction of normal to a reference ellipsoid and geodetic north (Local Geodetic coordinate system, LG). (Lankinen et al. 1992) Besides these there are various freely defined local coordinate systems that have local fixes. Surveying is traditionally done in the gravi- ty field of the Earth. The gravity field defines the orthometric height H (height from mean sea level). (Milbert 1992). One special potential lev- el is the geoid that corresponds to the local mean sea level (Oxford Illustrated 1984). The geoid surface is given as height difference from sur- face of an Earth-estimating ellipsoid.(Fig. 53) The curvature of the Earth is a significant error source in leveling. The curvature is e.g. 78.5 millimeters in one kilometer distance. The curvature is expressed with (eq. 4, deßoer 1987): s 2[4 ] Curvature = R where s = distance and R = radius of the Earth (c. 12800 km) Non-geocentric ellipsoids are used in geodet- ic coordinate systems (G). There are traditional- ly many geodetic reference ellipsoids in use; e.g. the ellipsoids for North America and Europe are different. This dates to historical reasons and the fact that good local fit to the geoid is required. Geodetic(ellipsoidal) coordinates ofpoint P are the (geodetic) latitude and longitude. Latitude (((>) is measured in the meridian plane that pass- Fig. 53. Ellipsoid and geoid in leveling. Plumb line devia- tion is the angle between the normals of ellipsoid and geoid (Toft 1987). 303 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND es through P. It is the angle in this plane between the equatorial plane (x-y) and a line perpendic- ular or normal to the surface of the ellipsoid at P. Longitude (A.) is the angle measured in the equatorial plane between the zero-meridian and the meridian plane that passes through P. Height coordinate, h, is measured along the normal of the ellipsoid. (Fig. 54, Langley 1992,Lankinen et al. 1992) Now that positioning is getting global there is a need for a standard ellipsoid with the origin at Earth center (geocentric ellipsoid). It should have good global fit to the geoid. This kind of ellipsoid, the WGS72 (World Geodetic System 1972), was first introduced in connection with the Transit satellite navigation system. The new- est version currently in use is WGSB4. Position- ing results that base on global ellipsoids differ considerably (e.g. 500 m) from local geodetic coordinate systems. For this reason satellite po- sitioning receivers often have built-in coordinate conversion software to convert WGSB4-coordi- nates to the local system. (Toft 1984, Langley 1992) On the other hand, national surveying is moving towards the use of WGSB4 in many countries, including Finland. In Finland, besides the geodetic coordinate system that is based on an international geocen- tered reference ellipsoid from 1924 (the Hay- fords ellipsoid) and European (geodetic) Datum 1959 (EDSO) there are local coordinate systems (e.g. the so called Helsinki coordinate system). Mapping is based on KKJ- (abbr. of the Finnish word for map coordinate system. Fig. 55, MMH 1988) level coordinates and N6O-heights (N6O is referred to the mean sea level in Finland in 1960). (Rainio 1988, MMH 1988, Lankinen et al. 1992, Ahonen 1993) Local information is usually presented in lev- el coordinate systems. Three-dimensional space coordinate systems are needed in measurement and calculation of these level coordinates. (Toft 1987. MMH 1988, Langley 1992, Lankinen et al. 1992, Milbert 1992) Position Dependent Control needs both lo- cal and global coordinate systems. PDC of farm machines is a local solution. The working area is usually so small (fields of one farm or a sin- gle field) that the variation of coordinate sys- tems has neglectful effects on positioning accu- racy. Positioning accuracy requirements are moderate (targeting accuracy of ±5 meters in PDC of fertilizer application, Ch. 2 above). Fur- thermore, these applications do not need abso- lute but relative coordinates. It is good enough to have the location relative to a local reference point (Stafford and Ambler 1991). Local solu- tions can have local coordinate systems with vir- tually no connection to global systems. Simple levelled instruments could be used in position Fig. 54. (a) The geodetic coordinate system, (b) An exam- ple of different reference ellipsoids. Flattening and geoid changes are exaggerated for clarity (Langley 1992). 304 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND measurements because the curvature of the Earth (eq. 4 above) is not significant in short distanc- es. On the other hand, this locality also gives us the freedom to choose the coordinate system to work with. For simplicity and to avoid transfor- mation errors it is good to adopt one coordinate system in which the whole Position Dependent Control system (planning, realizing, measure- ment of output) works. WGSB4 that defines the coordinate system of GPS satellite navigation is a good choice to work with because, in future, most carthogra- phy will be based on it. These kinds of global systems can be used to tie several local meas- urement systems together and enable local in- formation transfer to wide area information sys- tems. The easiest way to get coordinates for the ProductionLocations (Ch. 1.2 above) is to round the WGSB4's ellipsoidal coordinates (latitude and longitude) down to the wanted resolution. WGS is ellipsoidal so the obtained metric reso- lution on Earth surface depends on the latitude. The flattening of the ellipsoid is so small (c. 1/ 300) that spherical coordinates can be used in calculations (eq. 5, notations: Fig. 56). Accord- ing to this calculation, in southern Finland (c. 60°) a resolution of 1/1000' in cp and A would give around 0.9x1.8 meters (x and y) and in northern Finland at 70° c. 0.6x1.8 meters, respec- tively. This is adequate for positioning in PDC- applications with a targeting accuracy require- ment of a couple of meters (Ch. 2). Fig. 55, The KKJ map coordinate system. Finland is divid- ed in four projections (Gauss-Gruger cylinder projections), the center meridians of which are 21°, 24°, 27° and 30° eastern length and the origins are (approx.) at the intersec- tion of the center meridian and equate. (MMH 1988) Fig. 56. Notations for equation 5. 305 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND 4.2 Positioning, orientation and navigation Positioning is closely related to vehicle naviga- tion. Navigation (lat. navigare, to sail) includes determination of the location of the user and the target. lEEE (1989) says that navigation is “the process of directing the movement of a craft so that it will reach its intended destination”. De- termination of the user's location is positioning. Target position (direction and distance) tells us how we are orientated in relation to the target. If the vehicle moves in a fixed network (e.g. street or road network), navigation also needs route selection and guiding (Karppinen 1990). Harris and Krakiwsky (1989) divide vehicle navigation into locationing (determination of geographic coordinates), positioning (converting coordi- nates to a format suitable for digital information system), route selection (selecting the best path from existing road network), kinematic position- ing (constant measurement of coordinates) and route guidance (giving driving instructions) (Fig. 57). Navigation aids are needed if a previously defined route is to be followed. The driver can have a map screen where the actual position is marked. Route guidance signals can be shown on the same screen. The route guidance can be given to the driver with various signals, such as directing arrows or audible signals. Driving in- structions can also be coded to synthetic speech. Whatever the media is, it is important that the information is qualitatively and quantitatively right. The information must be important and in a useful format. Information ergonomics is re- searching this information exchange process. (Lunenfeld 1989, Karppinen 1990) Adaptive Position Dependent Control offield operations needs both positioning and naviga- tion. Collection of local information includes positioning. If we want to return to the sample points (e.g. same soil sampling locations every year), navigation may be needed. Local infor- mation is also collected during the realization phase. This information consists of measured output and functioning of the machines and real- time measurement data from the production lo- cation. In theory, the realization phase does not necessarily need navigation, because setpoint values are takenfrom the GIS. It is, though, rea- sonable to have orientation and speed measure- ment to better be able to adjust machines accord- ing to future setpoints in the direction of travel. Full navigation is needed if the vehicle is to be driven along a preset route. Vehicle navigation can also be used to facilitate the driver's task and free her/his capacity for other purposes than steering. This enables her/him to concentrate on the actual work task. It is even possible to use autopilots or automatic steering.(Table 10) 4.3 The map in Position De- pendent Control A map can be used to enhance positioning accu- racy. The so called Map Matching Technic re- quires that the operation area has certain allowed routes e.g. roads (Karppinen 1990a). An algo- rithm compares the measured vehicle position and the possible routes and corrects actual posi- tion to the route if necessary. (Fig. 58) Fig. 57. Concepts of vehicle navigation (Harris and Krak- iwsky 1989). 306 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND Table. 10. Need of positioning, orientation and navigation in Position Dependent Control. The cases in brackets have some use of the technic but it is not necessary to use it. Positioning Navigation Collection of local information - registration of the information X - returning to the location X Realizing the control (X) - real time measurements X - control of the machines X - functioning of the machines X - driving along preset route X (X) X Map matching algorithms have been devel- oped both for crossroad and direct driving. Al- gorithms find straight parts and crossings and correct the position if needed. If a vehicle runs a certain distance without changing its direction beyond a specified limit, the algorithm regards the road at that time as straight. One or more corresponding vectors of the map are selected. The number of possible vectors are limited through determining an area where the vehicle most probably exists. The correction is made to the selected route if necessary. (Harris et al. 1988. Morisue and Ikeda 1989) 4.3.1 The digital map Navigation and automatic vehicle positioning systems require digital maps that enable exten- sive calculations. The map matching technic described above can be utilized in areas that are numerically mapped. Numerical mapping meth- ods are widely adapted so that electronic maps, stored in e.g. CD-ROM disks, and map match- ing are expected to belong to all independent positioning systems in the future. (Morisue and Ikeda 1989, Karppinen 1990a) Digital maps come both in raster and vector format. So called hybrid maps contain both types. In raster format the mapped area is divided into small sized squares for coding. Vector format includes the targets, e.g. outlines of the areas and roads, con- verted to straight lines (vectors). Vectors are giv- en with their start and end points and nodes. Generally, raster maps use much memory and require more calculation power than vector maps. This, however, changes with the complexity of the data presented. Vectors are better for sym- bolic representation (interpretation of “what”) and rasters for that of positions (“where”). (Karp- pinen 1990,Tomlin 1990, Artimo 1992, Lanki- nen et al. 1992, Parmes 1994) Finnish mapping is switching over to digital methods. Old map originals are digitized and new maps are converted to digital format from satellite and aerial photographs or land surveys. Digitizing the old maps is both manual and au- tomatic. Manual digitizing is done through point- ing the position on the map attached to a digitiz- ing board and inputting the local information on the keyboard. Automatic digitizing includes map scanning to raster format and raster map vector- izing with dedicated software. Local information of the old maps can often be automatically trans- fered through scanning in color, line width and other such parameters. Stereo mapping is done with special aerial photographs. The 3D-image is viewed with special equipment that enables the user to pinpoint the surface with a cursor and input the local data to that 3D-point. Surveying is turning digital concurrently with increased use of digital tachymeters and geodetic satellite nav- igation devices. Roads are mapped with inertial and satellite navigation. (Byman and Koskelo 1991, Rainio 1991, Offermann 1993, Ahonen 1994b) Fig. 58. Principle of map matching in crossroad driving (Wiedenhofand Van Hooren 1987). 307 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND The accuracy of old paper maps is sometimes too poor for vehicle guidance that is one of the most demanding applications (Juhala 1993). New maps should be based on more accurate surveying. New standardized Electronic Chart Display Information Systems (ECDIS) are be- ing developed that use accurate digital maps. Maritime use ofelectronic nautical charts is cat- alyzing this development. (Montgomery 1992, Alexander 1994) Normally, map manufacturing includes coordinate conversions and error fix- ing (Lankinen et al. 1992). Positioning methods are used to get reference points (GCPs, Ground Control Points) for the fixing so that the map fits better to the actual world. (Byman 1990, Perry 1992) Mapping without ground control is the ultimate goal in the development of Global Navigation Satellite Systems (GNSS). This de- velopment is expected to come true when the GNSSs provide an accuracy of better than one decimeter (Lapine 1994). 4.3.2 The map in Position Dependent Control of field operations Maps are important in Position Dependent Con- trol; the data used is position-fixed and thus a map is the natural way to represent it. The PDC data is stored in a Geographical Information System (Ch. 2.3.3). The GIS-user may get the local information partly in map format and part- ly by inputting it at a map coordinate. The map also acts as a graphical user interface to the GIS and map screens and printouts of the GIS data are produced on request (Rainio 1988, Artimo 1992). Furthermore, the map is used as a guide in navigation (Karppinen 1990,Langley 1993) In PDC of field operations the map is need- ed in planning and realizing of field tasks. The planning requires information on relative orien- tation of the production locations and individu- al fields. The planning phase uses maps for de- cision support; thematic maps are shown on the computer screen. If local information is fed to the GIS via the map image, then accuracy of the map should be such that the requirements for targeting accuracy and resolution are fulfilled in the following realization phases. For position dependent control of nitrogen application a tar- geting accuracy of ±5 meters and coordinate res- olution of 1/1000' (in WGSB4) were set in pre- vious chapters. Some other position dependent tasks may need better performance. Moore et al. (1993) reports the need for goodresolution maps for terrain analysis in connection with the soil specific management. Much of the local information is given in raster format, e.g. results of satellite or aerial photograph processing (Tomlin 1990). This is true in agriculture, too. Satellite and aerial IR- and NIR- (Near Infra Red) images and video re- cordings give information on numerous agricul- tural parameters, such as plant variety, plant de- velopment stage, the need for plant nutrients, raining or plant protection, and effect of treat- ments. (e.g. Williams and Shih 1989, Blazquez 1990, Evans 1992, Fouche 1992, Hough 1992, Gupta 1993). This information must be shown on the map screen with overlaying possibility of different data. The realization phase needs the map for showing vehicle/equipment position to the user. In this task the map is not acting as a coordinate input media but rather as a background. If the user uses on-line data input to the GIS, then the positioned coordinate could be used as an index and the accuracy requirement is put on the posi- tioning system instead of the map. It is, though, preferrable to have also the option to select tar- get points outside the current positioned loca- tion of the user for data input, e.g. when areas of abnormal plant growth are documented. Good map accuracy is then necessary. In the field there are normally no fixed net- works, except with the use of so called tramlines or when row crops are produced. The tramlines are made by leaving some seed lines without seed in regular spacings, e.g. four meters. These lines act as guiding lines for the following tasks. The tramlines, if mapped, can act as the necessary fixed network, and map matching algorithms can be used. A kind of map matching is also possi- 308 Haapala, H. E. S.: Position Dependent Control ofplantproduction AGRICULTURAL SCIENCE IN FINLAND ble in row crop production. In tasks that use par- allel passes the previously drivenroute could be used as a guide for the next pass. Maps for PDC must be up-to-date because local control is required. Therefore it must be easy to make possible changes in the shape of the fields. In Finnish official registers there are considerable differences in farm sizes. This is due to different mapping systems and various calculation methods ofarea changes. Area chang- es are results of e.g. partitioning of the estates (Ahonen 1994a), and during the past century drainage operations have made considerable changes in field shapes (Puustinen et al. 1994). Pipe drainage has made it possible to change crop production patterns freely. The mapping system must be very flexible to manage these yearly dy- namics of production locations. Digital ground referenced maps, that are fre- quently updated, are the only types meeting these requirements. Hybrid maps with both raster and vector data are needed. In practise the mapping is done with satellite navigation (GPS- satellite navigation equipment, see Ch. 4.4 and 4.5) and the map is stored in a GIS-database for further processing. Requirements for up-to-date infor- mation are met when the mapping information is in GIS-format and the necessary changes are done frequently. As a conclusion, the digital GIS-based maps are needed for the use of agricultural and envi- ronmental planning. Different requirements are set by the farmers, extension service, adminis- trationand research (Salo 1994). The spatial data exchange through network services which is under construction (Rainio 1988), could be used to spread the spatial data including the digital maps. New GPS/GIS-based surveying is produc- ing high quality maps. However, only some are- as of agricultural Finland are currently covered. This work should be completed to get the maps necessary for Position Dependent Control. How- ever, the need for up-to-date high precision maps may need the use of complementary mapping methods. For this purpose, updating the field map can also be assisted with high-resolution aerial photography (comp. e.g. Fouche and Booysen 1991). A light-weight RC-plane with a small camera or video and GPS is a potential source of cost-effective map updates (Haapala 1994b). 4.4 Classification of positioning systems Positioning systems can be divided into many kinds of operational classes, e.g. Stafford and Ambler (1991) divide them into global and lo- cal methods. Global methods are globally avail- able whereas the local ones are, according to their name, just for local use. Satellite naviga- tion systems are global and vision-based route finding is local. Karppinen (1990a) classifies the methods into autonomous and non-autonomous. The autonomous ones need no external informa- tion to the vehicle. The non-autonomous meth- ods use external information sources and infor- mation exchange. In autonomous positioning the charges are all paid by the user and in non-au- tonomous systems the costs can be divided into private and community parts. Inertial navigation and Dead Reckoning (DR) are autonomous whereas GPS (Global Positioning System) sat- ellite navigation is a non-autonomous navigation system. Muhr andAuernhammer (1992) combine the classifications for agricultural vehicle navi- gation purposes (Fig. 59). Fig. 59. Classification of positioning technics of agricul- tural vehicles (Muhr and Auernhammer 1992). 309 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND The following classification that is used in presenting differentnavigation systems is mainly based on the division of Karppinen (1990a) and Stafford and Ambler (1991), and the terminolo- gy of Muhr and Auernhammer (1992). 4.4.1 Autonomic vehicle sensor systems Inertial and Dead Reckoning (DR) navigation are autonomic sensor systems (Karppinen 1990a). Inertial navigation is used in ships and aero- planes. Inertial navigators are expensive so they are not commonly used in land navigation ex- cept in tanks and corresponding military tech- nology. (Fig. 60) The inertial navigation begins at a determined point. The change of position is calculated out of acceleration and time. The best accuracies are 10-50 ppm (of the distance traveled). The sys- tem is independent of electromagnetic waves, re- fractions, line of sight and weather conditions. Thus it is possible to measure the position even beneath water and under the ground. Drawbacks of the system are, in addition to the high price, theregular need for calibration and the long start- ing phase. Newer technics include laser gyros which are cheaper but somewhat more inaccu- rate. (Karppinen 1990a, Santala 1992) Dead Reckoning that was first utilized in maritime is nowadays used for many purposes. It is also called vector navigation. DR is defined as “the determining of the position of a vehicle at one time with respect to its position at a dif- ferent time by the application of vector(s) rep- resenting course(s) and distance(s)” (Douglas- Young 1981, lEEE 1984). Positioning informa- tion is achieved by vehicle start point, heading and distance measurement (Fig. 61). Heading and distance are generally measured with odom- eters, which are distance measurement devices. They are installed to vehicle transmission. The most common way is to measure the rotation of wheels or shafts. Heading measurement is inac- curate because slippage, tire pressure changes, tire wear, angular velocity of the tires and lane changes affect the accuracy. (Hakala 1992) In practise, it is necessary to have other methods for heading measurement. The most common method is to use an electronic compass, and ul- trasonic beacons are also used. The ultrasonic beacon transmits ultrasonic waves that reflect back from the soil surface. The drive speed is calculated from the Doppler effect of transmit- ted and received signals. The heading can be cal- culated with two of these beacons which are in- stalled at opposite sides of the vehicle. One posi- ible technic is the gas rate gyro, where the di- rection change of the vehicle is sensed with ac- celeration-induced flow changes of circulating gas. (Karppinen 1990a) The accuracy of Dead Reckoning is typical- ly c. 3-4 % of the distance measured (Hakala 1992). This is because each point is based on all the previous points and their cumulated meas- urement errors (comp. eq. 1 in Ch. 2.3.3). Er- rors can be reduced if the driver checks out the reaching of the target point or feeds in the right point coordinates at regular intervals. The right coordinates can also be fed in using external bea- cons, but then the system is no longer purely independent. In city conditions these external reference beacons can be found in e.g. traffic lights (Morisue and Ikeda 1989, Nobbe 1990 ref. Karp- pinen 1990b, Fig. 62). GPS satellite navigation can also be used in reference measurements Fig. 60. Schematic picture of an inertial navigator. The nav- igation isbased on revolving gyros and accelerometers (Slat- er 1964ref. Karppinen 1990a). 310 Haapala, H. E. S.: Position Dependent Control ofplantproduction AGRICULTURAL SCIENCE IN FINLAND (Vuopala 1990). Karppinen (1990a) says that pure Dead Reckoning-devices can no longer be marketed as vehicle navigators but other support- ing systems must be integrated. This is also what the market situation shows with increased sell- ing of hybrid navigation systems (Krakiwsky 1994). 4.4.2 Transmitter/receiver systems Non-independent positioning systems are most- ly based on the use of radio waves. The exact position of either the transmitter or the receiver, the one which is stationary or otherwise fixed, must be known. The distance between the trans- mitter and the receiver varies from a few meters to thousands of kilometers. In addition to radio navigation, laser positioning is used in some transmitter/receiver applications. The latest de- velopment is networking the transmitter/receiv- er systems. (Harris and Krakiwsky 1989, Iwaki et al. 1989,Palmer 1989,Saito and Shima 1989, Shmulevich et al. 1989, Karppinen 1990a, Rin- tanen 1992, Lapine 1994) 4.4.2.1 Short and medium distance systems Short distance radio navigation has been devel- oped for city navigation as illustrated above (Fig. 63 above). Independent navigation systems like DR are often supported by this kind of methods and/or compass devices to correct for cumula- tive error. The situation can also be the oppo- site: independent methods support non-inde- pendent ones. This was the case with a Finnish road mapping system, where Dead Reckoning was acting as a backup for GPS. DR had to be used in 3-10% of the traveled distance (Byman and Koskelo 1991). Maritime radio navigation equipment is mainly designed for coastal navigation, but it is also used in land navigation (Chandan et al. 1989). DECCA was developed during World War 11.LORAN-C and Omega are the other common- ly used maritime radio navigation systems. Ra- dio beacons are much used in maritime applica- tions. DECCA consists of land stations that con- stantly transmit synchronized (70-130 kHz) sig- nals. DECCA covers the most important Euro- pean coasts. The method measures phase differ- ences of the signals ofat least three stations. Two land station signals can be used to calculate a hyberbola on which the vehicle is located. The third signal forms an other hyberbola with one or the other of the previous signals. The vehicle is situated on the intersection of these hyberbo- las. (Douglas-Young 1981, Henttu and Nyman 1990,Fig. 63). One DECCA chain covers a range of 450 km in average and positioning accuracy varies from 20 meters to three kilometers (10, Fig. 61. Principle of Dead Reckoning. Heading (6) and dis- tance (D) are measured cumulatively to calculate positions (P) (Hall 1986ref. Karppinen 1990a). Fig. 62. A short distance radio beacon navigation system attached to traffic lights (Nobbe 1990). 311 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND see. App. 9 for the representation of accuracy). The master is located in the center and the slaves are at 80-250 km distance. The accuracy gets worse when the angle of locating hyberbolas di- minishes. The optimum is reached when the an- gle is 90 degrees. Other components that impair the accuracy are local interferences caused by the islands and the coastline, internal chain er- rors, thunderstorm, space reflections, bad weath- er and interferences caused by vehicle instru- ments. The accuracy is generally best during the day when the weather conditions are stable. In spite of its errors DECCA is widely used, spe- cially in fishing fleets, because of its constant availability and high repeatability of the posi- tioning result. (Toft 1987, Renttu and Nyman 1990) LORAN-C -navigation system (Long Range Navigation) is also based on hyberbola geome- try. The secondary (slave) transmitters are situ- ated at a longer distance than those of DECCA, so the coverage is broader. There are three to four secondary transmitters 500-1000kilometers from the master. LORAN-C chains cover all American coastal areas, Japanese waterways, areas in the Pacific, the nortern Atlantic, the Mediterranean and parts of northern Europe. Apart from DECCA, all stations transmit con- stant (100 kHz) signal bursts. The stations are identified by timing of these bursts. Also the hy- berbolas are determined from time difference in signals instead of phase measurement. Accura- cy ofLORAN-C is affected by the same compo- nents as in DECCA. Absolute accuracy can be around 500 meters (2o) and relative accuracy some 15-60 meters (la) (Toft 1987, Henttu and Nyman 1990) Omega, a third hyperbola navigation system, was initiated in 1961. The navigation system consists of eight land stations (named A-H) in total. They are at long distance from each other (up to 6000 nautical miles). The stations trans- mit phase-synchronized signals (10.2, 11.05, 11.33, 13.6 kHz) and a station-specific extra fre- quency. Because of the deflections in low fre- quency transmission it is possible to reach glo- bal coverage with only eight stations. The posi- tioning is based on phase measurement as in DECCA. The absolute accuracy ofOmega is typ- ically two to four nautical miles (2a). (Toft 1987) Radio beacons are widely used. They are nondirectional radio transmitting stations that operate in the low frequency (LF) and medium frequency (ME) bands. A radio direction finder (RDF) is used to point the bearing of the trans- mitter. Accuracies of typically 3° (2a) are achieved (this means c. 50 m at 1 km). Aero- space and maritime applications use radio bea- cons. There are also a number of private radio location systems on the market that operate in frequency areas of c. 100 kHz to 9500 MHz. Their range decreases with increasing frequen- cy. They are used whereradio determination (de- termination of position and velocity with radio waves) coverage is not available, accuracy is not sufficient and the availability is not continuous. (GPS World 1994, RTCM 1994) Laser positioning is much used in geodetic surveying using so called tachymeters (combined electro-optical distance and angle measurement devices). For positioning of moving vehicles a servo tachymeter can be used. It follows a prism attached to the target. Some experimental sys- tems use scanning or rotating lasers with beam angle measurement and prisms and/or fotodiodes in the tranceiver or receiver. Outstanding accu- racy (typically c. 5 mm/km) can be achieved in moderate distance (1-3 km) of the transmitter. Fig. 63. Principle of DECCA hyberbola navigation (Rent- tu and Nyman 1990). 312 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND (Shmulevich et al. 1989,Lehr and Prasuhn 1990, Rintanen 1992) 4.4.2.2 Long distance systems Satellite navigation is a long distance (space- based triangulation, see fig. 60 above) radio nav- igation method. By definition, satellite naviga- tion is “...a method to derive navigational pa- rameters like position and velocity by using ra- diosignals transmitted from satellites” (Kruger et al. 1994). In most systems the positioning is globally available. Important global satellite positioning methods are Transit/NNSS, GPS and GLONASS, which are based on orbiting geosyn- chronized satellites and RDSS that is geostation- ary. (Karppinen 1990) Besides these there are local satellite positioning systems, e.g. Starfix that operates in the U.S. continent (Ott 1988). Transit/NNSS (Navy Navigation Satellite System) was originally developed for the U.S. Navy for the positioning of Polaris-type subma- rines. There are seven satellites orbiting the Earth at an altitude of 1075 kilometers. The position- ing is made on the basis of Doppler shift of the satellite signal as the satellite passes the vehi- cle. The main drawback of the system is the time of 35-100 minutes between each position deter- mination. Various intelligent receivers have been developed that use DR to keep track on vehicle dynamics between theTransit positioning points. For single frequency (400 MHz) receivers the absolute accuracy is 80-500 meters (2a) and for dual frequency (150 and 400 MHz) receivers it is 25-37 meters (2o). The improvement is due to corrections of ionospheric delay of the sig- nal. Since the Transit technic is getting old and newer systems replace it, the system is to be shut down in 1996. (Toft 1987, Ollaranta 1988,Karp- pinen 1990). RDSS (Radio Determination Satellite Serv- ice) satellites are geostationary. RDSS receivers also act as transmitters. (Lähteenmäki 1987, fig. 64) The RDSS system has a low positioning ac- curacy (c. 250 m). It is mainly used for data trans- mission in IVHS- (Intelligent Vehicle/Highway Systems) applications (Kxakiwsky 1994). The U.S. NAVSTAR GPS (Navigation Sys- tem with Time and Ranging Global Positioning System) is based on 21 geosynchronized satel- lites. The satellites orbit the Earth at c. 20200 km altitude, the orbiting period being c. 11 hours and 58 minutes. The constellation (relative ori- entation of the satellites in the sky) ensures that at least four satellites are constantly and global- ly at Least 5 degrees above the horizon. It means a 24-hour global coverage for 3D-positioning. (TOFT 1987, Hartman 1992,Kruger et al. 1994). GPS positioning service is currently (1995) free of charge - users just have to buy a receiver to begin to use it. The price of the receiver is in the order of that of a common microcomputer. There Fig. 64. RDSS (Radio Determination Satellite Service) sat- ellite navigation (Lähteenmäki 1987). Fig. 65. Orbits of GPS (Global Positioning System) satel lites (Sonnenberg 1988). 313 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production are numerous makes and models available. The smallest receivers are about the size of a credit card. (Chan and Schorr 1994, GPS World 1995) GPS is widely used on dry land and on sea. In the future air traffic will use it too. Using GPS in the airplanes was not possible for safety rea- sons until recently because of the incomplete sat- ellite constellation. In 1994 the constellation was fully realized, consisting of 21 active satellites and 3 spares (GPS World 1994). GPS uses the geocentered WGSB4 reference ellipsoid (Ch. 4.1 above) as its basic coordinate system. Position- ing results can be converted and given in other coordinate systems as well. Three-dimensional positioning (e.g. latitude, longitude and altitude) requires four satellites. Three satellites are used to measure the spatial location and the fourth is for time correction. The timecorrection is need- ed to synchronize the receiver's clock with the satellite clocks. (Toft 1987, Figs 65 and 66, Bäckström 1990, Parm 1992, Tyler 1993, Van Dierendonck 1995) System clocks of GPS are very precise be- cause in radio navigation an error of one nano- second causes a 30-centimeter error in position. Cesium and rubidium atomic clocks are used. GPS signals are transmitted in two carrier fre- quences LI and L2. LI is 154 times and L 2 120 times the basic frequency (10.23 MHz) of the atomic clocks in the satellites, i.e. 1575.42 MHz for LI and 1227.6 MHz for L2. The carriers are modulated with two types of digital codes: one or two of the so called PRN-codes (pseudo ran- dom codes) C/A- (coarse acquisition) and P- (precise), and navigation message. The satellite joins the PRN-code and navigation message for modulation. The combined codes are often called C/A- and P-codes according to the PRN-code type used in modulation. The combined codes include the information needed for position de- termination and system health control. There are also receivers, so called codeless receivers, that do not use the PRN codes but the carrier phase for position determination. (Toft 1987, Tyler 1993, GPS World 1994,Kruger et al. 1994) A new accurate GPS technic is the so called RTK- (Real-Time Kinematic) GPS. It is a very accurate carrier-based GPS method with a real- time positioning accuracy around 30 millimeters. The technic is based on OTF (On-The-Fly) am- biguity resolution, which determines the correct number of initial integer cycles in carrier phase measurements. This number of cycles is known if the receiver can continuously track all the needed satellites but, in case of losing lock on a signal, a phase slip may occur. There are several ways to calculate the ambiguities e.g. using a search space and various validation and rejec- tion criteria. The search space is a probable vol- ume in the space where the right phase could have been lost. Confidence limits of 95 to 99 % are used in defining this ellipsoidal space. A cod- ed solution, using the PRN-codes can be used during the phase slip, or the remaining satellite connections can be used to limit the search space. The speed of ambiguity solution algorithms and related datalinks is a bottle neck for the accura- cy of RTKGPS. (Tyler 1993,Abidin 1994, See- ber 1994) Full accuracy of GPS is not available for all users. The best accuracy is reserved for author- ized use such as the U.S. military. The basic ac- curacy ofGPS (permitted accuracy for unauthor- ized use), denoted by SPS (Standard Position- ing Service) uses only the C/A-code on LI, and is set to the level of c. 100 meters (95%). To achieve this, degradation of accuracy, Selective Fig. 66. 3D-positioning with GPS. Four satellites are need- ed (Toft 1987). 314 AGRICULTURAL SCIENCE IN FINLAND Availability (SA), was introduced by U.S. DoD. SA was realized through adding intentional ran- dom timing errors in the navigation message. In addition to this the P-code is encrypted (an- tispoofing, Y-code) to prevent unauthorized use. the best accuracy, the so called PPS (Precision Positioning Service), that is in authorized use only, uses both LI and L 2 and the P-code. (Toft 1987, Tyler 1993, Van Dierendonck 1995) Sup- plementary information on GPS technics is in app. 10. GLONASS (Global Navigation Satellite Sys- tem) is a satellite navigation system ofthe former Soviet Union currently run by Russia. It is a sys- tem corresponding to GPS, where the satellites are situated a bit differently than in GPS. The altitude is 19100 kilometers and the orbiting period is 11 h 15 min. The orbits are such that GPS is reported to have some difficulties in cov- erage near the polar regions and GLONASS near the equator. In comparison to GPS, GLONASS expresses satellite positions in a slightly differ- ent format and uses a different reference ellip- soid (SGS-85). GLONASS-satellites use trans- mission frequences in the L-band as GPS. The frequencies are, however, different for each sat- ellite and individual satellite codes are not present in the transmitted data. GLONASS con- stellation is not yet fully realized, though, it is anticipated that all the 24 satellites will be oper- ational in 1995. Joint GPS/GLONASS receivers are developed and tested. These receivers give full global coverage with good accuracy. Cover- age problems are not a major issue to land users but to aerospace where true 100% coverage is needed for safety reasons. (Hartman 1992, GPS World 1994, Johnson 1994). Enhanced satellite navigation Currently satellite navigation, specially GPS, is conquering the market of vehicle navigation. It is superior in the sense that it is globally availa- ble, relatively cheap and accurate enough for most navigation applications. In spite of this sat- ellite navigation has some weak points that lead to a necessity of backup systems and special enhancement technics. GPS is used here as an example. GPS needs constant visibility to four satel- lites for 3D positioning. The 5° cutoff angle, that was used in dimensioning the satellite constel- lation for 24-hour coverage, is too low in terrain use. A clear line-of-sight is not possible and short positioning pauses occur. On the other hand, sat- ellite geometry (relative orientation of the satel- lites in the sky) also affects positioning accura- cy. The best geometric situation for satellite po- sitioning, which is based on several range meas- urements, is the right angle (90°) between all satellite signals. If the angle is very sharp (or wide), the intersection point is unclear and the accuracy declines. (Toft 1987,Fig. 67) In vehi- cle receivers a higher cutoff angle is used to get better reliability of continuous positioning. This is done on the cost of somewhat degraded accu- racy. (Krakiwsky 1994) As mentionedabove propagation ofradio sig- nals can get interference from obstacles and at- mospheric effects. Reflections and interference sources ofvehicle instruments must also be con- sidered. These lead to possible interruptions in the availability of GPS positioning. This is why satellite positioning systems are often equipped with integrated technologies such as e.g. DR, inertial navigation, map matching, LORAN-C, radar, LEO- (Low Earth Orbit) satellites and RDSS-satellites. The above mentioned technics act as backups, complementary systems or fully integrated parts of GPS positioning (Farm 1992, Alexander 1994, Krakiwsky 1994). Fig. 67. Effect of satellite geometry on positioning accura- cy (Toft 1987). 315 Voi 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Various technics are being developed to en- hance GPS accuracy in spite of the Selective Availability (SA) and encryption of the P-code (antispoofing, Y-code). In differential GPS (DGPS) there is an additional fixed GPS-receiv- er, the reference station, the position of which is accurately known. The fixed receiver is not mov- ing so it can continuously calculate corrections to the positioning results. In total the accuracy can be corrected to 2-meter level. (Toft 1987, Koskelo 1990, Bäckström 1992, Parm 1992, Kruger et al. 1994, Mueller 1994) The above mentioned codeless receivers that use the carri- er phase and estimate the ambiguities offer an expensive but accurate solution. Advanced kin- ematic carrier phase technics can give real-time DGPS accuracies of below 10 centimeter. For this, short distance (<2O km) to the reference station is required. (GPS World 1994, Fig. 68) Differential corrections remove the effect of Selective Availibility (SA) almost entirely but the corrections lose their validity after a period of time as SA changes. Improvements of c. ±lOO meters (in average 30 meters la) can be achieved. lonospheric refractions can introduce errors of 3-6 meters at night and 20-30 meters during the day. An improvement of c. 0-4 me- ters can be achieved through elimination of ion- ospheric effects when there is moderate distance (< 100-200 km) between the receivers. Tropo- spheric delays can cause up to 30-meter errors with low satellite angles. They are easily mod- elled. Variations in the index of refraction be- tween the receivers can, however, cause errors of c. 1-3 meters. Different paths of signals and variability of the ionosphere and troposphere cause so called decorrelation which increases with distance. Fig. 68. Differential GPS. (a) Geometry of DGPS, (b) dif- ferential reference station block diagram and (c.) DGPS- receiver block diagram (RTCM 1994). Fig. 69. Simulated data link strength of the Differential GPS network of the Finnish National Board of Navigation (Bäck- ström 1990). 316 Haapala, H. E. SPosition Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND Ephemeris errors (difference between actual position of the satellites and the position report- ed in navigation message, c. 3 meters, max. 30 meters under SA) are removed. Satellite clock timing errors are removed. (Toft 1987, Bäck- ström 1990, Koskelo 1990, Tyler 1993, RTCM 1994) DGPS transmission is standardized by the U.S. Coast Guard Radio Technical Comittee for Maritime Services (RTCM-SCIO4-standard). This standard expresses the recommended data message format and user interlace. (RTCM 1994) There are both post-processed and real-time differential systems. Post-processed DGPS uses post-processing software to calculate corrections to the GPS signals saved. Post-processed DGPS is used in applications where realtime accuracy is not needed, e.g. in collecting data from ran- dom locations or locations that are not found with positioning. In real-time DGPS the accuracy is enhanced during the work. Differential correc- tions can be sent to one or several moving re- ceivers if they are equipped for it. Normally the transmission is done through radio beacons or modems. (Toft 1987,Bäckström 1990, Koskelo 1990, Pärm 1992, Tyler 1993, Ekfäldt 1994, Kriiger et al. 1994, Mueller 1994) Basic DGPS is a local system (0 100 - 200 km max.) because it is necessary that both the moving receiver and the fixed one use the same satellites. The distance to the base station the affects reliability of the differential correction. The terrain can block the visibility of satellites. Updating frequency of the correction has also a significant effect on the accuracy, so datalink speed is important. Furthermore, the improve- ment is much dependent on quality of the used differential correction software and hardware. (Bäckström 1990, Koskelo 1990, Ekfäldt 1994, Kriiger et al. 1994) Differential corrections can be either locally or more globally available. The latest development in DGPS is the use of Wide Area DGPS (WADGPS-) systems that are based on reference station networks. In future, these networks can offer global differential corrections (Mueller 1994). In Finland the National Board of Navigation (NBN) has built public differential correction stations mainly in the coast areas (Bäckström 1990,Fig. 70). They send differential corrections according to RTCM-SCIO4-standard (Langley 1994,RTCM 1994, App. 8). This service can be used for DGPS within some hundreds ofkilom- eters, on land not so far as on sea. To use this service a special RTCM-radio receiver is con- nected to the moving DGPS-receiver. The RTCM reveiver is quite expencive (c. 10000 - 25000 FIM). Though, this is less expensive than to build a separate differential station (c. 200000 FIM). In Finland the service is still free of charge. The use of public RDS (Radio Data System) radio stations to transmit RTCM differential correc- tions was initiated in Finland in the summer of 1994. This is more economical than the use of the NBN system because of the relatively low prices of RDS-receivers (1500-3000 FIM in 1995). The situation is changing when annual fees are introduced to the RDS service (e.g. c. 5000 FIM/a for an accuracy of 5 m 95%; the sit- uation in 1995). Achievable accuracies ofdifferent GPS tech- nics are shown in following figure (Fig. 70, Kriiger et al. 1994). The absolute and differen- tial modes are separated. The accuracy of dif- Fig. 70. Accuracies of different GPS (Global Positioning System) methods.DGPS = Differential GPS. (Kruger et al. 1994) 317 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND ferential mode is very much dependent on the devices and software used. Thus the figures must be regarded as approximations. Differential GLONASS (DGLONASS) is expected to have accuracy comparable to DGPS, or maybe an even better one. As GLONASS de- velopes towards operational stage in 1995, stand- ardization of differential GLONASS technic is initiated. (RTCM 1994) In future, one of the goals in satellite navigation is to develope Glo- bal Navigation Satellite System. This networked system will include GPS and other global satel- lite systems integrated to an all-civil system (Kruger et al. 1994). Many countries do not r;ly on pure GPS because it is owned by a single na- tion and run by its military. The development of GNSS is specially hoped for in the European countries (Preiss 1994). On the other hand GPS is turning partly civilian when U.S. DoT (De- partment of Transportation) is taking partial duty of GPS system management (Parkinson 1993, Wiedemer 1993). 4.5 Positioning methods for Position Dependent Control in agriculture The agricultural need of positioning methods is potentially high, but in the short term the mar- ket volume is neglectful compared with other uses. The agricultural dilemma is that the tech- nics shouldbe very resistant to harsh field con- ditions and have a low price at the same time. That is why no dedicated agricultural devices can be developed. There are, though, some spe- cial requirements in agriculture so, when other sources are used, some R/D should be made. In future special agricultural positioning systems can be available (Mangold 1994). The car in- dustry is the most probable source for agricul- tural positioning electronics because of its high volume and low prices. It has concentrated on fleet management and route guidance (Karppi- nen 1990, Krakiwsky 1994). Agricultural and automobile positioning requirements differ at least in speed range and environmental condi- tions. The accuracy requirement for fleet man- agement is not very high. On the other hand, field operations also lack the fixed road network. Maritime and aerospace technics are partly applicable to land navigation. (Karppinen 1990, Bäckström 1990, Forssell 1994) Some of the methods used (e.g. Decca and Loran-C) are not accurate enough for some agricultural needs (Gill and Ward 1989, Rhoades et al. 1990), but the basic dead reckoning (DR, measurement of speed and angle) is widely used (Vuopala 1990, We- jfelt 1990, Rintanen 1992). DR is often a vital part of integrated navigation systems (Hakala 1992, Krakiwsky 1994). Inertial navigation can be used in applications where the high cost can be tolerated (Santala 1992). There are some dif- ficulties in optical positioning (e.g. Schmulevi- ch et al. 1987) in field conditionsbecause an un- interrupted line-of-sight is required. Further- more, the use of prisms and other optical devic- es needs extra care. Satellite navigation is the newest general positioning technique. It finds increasing mar- kets in almost all areas of positioning and navi- gation (Toft 1987,Karppinen 1990, Moller 1990, Juhala 1993, Tyler 1993,Chan and Schorr 1994, Krakiwsky 1994, GPS World 1995). The major drawback of satellite navigation is that the most usable systems (GPS and GLONASS) are built for military uses. This leads to some uncertainty of availability in international crisis situations. 4.5.1 Earlier applications of positioning in agriculture Various methods have been used in agricultural positioning tasks. Part of these could be used in Position Dependent Control. Autonomous posi- tioning methods (classification of positioning methods: Ch. 4.4 above) have been the first ac- tual positioning methods in agriculture. For quite a long time steering accuracy has been enhanced by using so called tramlines. In agricultural plant production the tramlines act as guiding lines. The 318 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND tramline system requires implements that are multiples of the tramline spacing in width (e.g. a 4-meter seeder, a 12-meter fertilizer and a 16- meter sprayer). Recently distance measurement has been added to tramline systems to get a sim- ple in-tramline positioning. (Schumacher and Fröhlich 1989, Auemhammer 1990, Wejfeldt 1990,Fig. 71). Positioning can also be independ- ent of the tramlines if we have the previous pas- sage clearly visible and measure the distance along it. This kind of positioning has been used in yield mapping (Stafford and Ambler 1992, Au- ernhammer et al. 1994) and in a Japanese mini- combine and grass cutter (Yoshida et al. 1988). In row plant production it is also possible to position the machines in this way (Brown et al. 1991). Dead Reckoning is a widely used autono- mous positioning method in agriculture. Distance measurement is quite easy to implement with pulse or radar sensors (Hakala 1992). Heading measurement is most usually accomplished with an elctronic compass. Inertial navigation is also tested but it is too expensive formost uses (Bern- hardt and Damm 1992). Applications include fertilizing (Schumacher and Fröhlich 1989, Au- ernhammer 1990), spraying (Landers 1992) and yield mapping (Auemhammer and Muhr 1992). DR is used both as the only positioning method or in combination with other methods. Often DR is used as a backup method for other methods (Krakiwsky 1994) or as an integrated part of a hybrid positioning system (Patterson et al. 1985, Schumacher and Fröhlich 1989,Auemhammer 1990, Bernhardt and Damm 1992). Ultrasonic and other types of proximity sen- sors have been tested in off road situations (Schu- macher and Fröhlich 1989, Mäkelä et al. 1991). These systems are suited for fixed routes where the route can be marked and followed. Machine vision applications are being developed for some areas (Searcy and Reid 1989, Möller 1990, Brown et al. 1991, Mäkelä et al. 1991, Brown and Wilson 1992). These also require some ob- jects to identify. The above mentioned methods find some applications in row crop production. Positioning of vehicles that move freely in the field is technically very challenging. This has recently been applied to plant production. These free positioning applications can be divided into local (AGNAV 1988,Palmer 1989, Shmulevich et al. 1989, Searcy et al. 1990, Palmer 1991, Nieminen and Sampo 1993) and global (Auern- hammer 1990, Petersen 1991, Roberts 1991, Hough 1992) systems. Local systems require in- frastructure, a transmitter-receiver (transceiver) network, and are therefore quite expensive. In global systems only part of the costs are paid by the user. GPS satellite navigation, which is of the latter type, is expected to be a general posi- tioning system for agriculture, too. (Möller 1990, Auemhammer and Muhr 1991, Larsen et al. 1991, 1994, Petersen 1991, Goring 1992, Perry 1992, Bauer and Schefcik 1994) Non-autonomous transmitter/receiver posi- tioning systems have been developed after the autonomous ones. In research, optical position- ing methods have been used (Shmulevich et al. 1989, Mäkelä etal. 1991, Rintanen 1992). There are, though, limitations for optical methods in agriculture because an uninterrupted line-of- sight is needed to get the positioning result. This is difficult to fulfill because transmitters and senders are near the ground level. It is also dif- ficult to install and keep clean the mirrors and prisms. Radio-based systems are the major research topic in transmitter/receiver (or non-autono- mous) positioning in agricultural positioning today. First, maritime radio navigation systems were used. Land use of DECCA has been tested in University of Dublin. The results show that Fig. 71. Tramline positioning (Auemhammer 1990) 319 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplantproduction e.g. trees, electric transmission lines and other obstacles interfere considerably with the posi- tioning. The achieved accuracy (36-107 m) does not fulfill agricultural requirements. (Gill and Ward 1989) The design accuracy of LORAN-C was 0.25 nautical miles (0.46 km, 95 %) and the relative accuracy is typically 20-100 meters (RTCM 1994). Besides maritime use LORAN- C is used in the U.S.A. and Canada in naviga- tion of civilian air traffic. Land use in fleet man- agement is under research. The accuracy is ex- pected to be around a few hundred meters (Chan- dan et al. 1989, RTCM 1994). Rhoades (1990) reports an accuracy of 50 meters for LORAN-C in survey work. Rhoades et al. (1990) obtained an accuracy of 16 meters (90%) in locating soil salinity samples. These results are achieved in static measurement through filtering. LORAN- C covered c. 90% of Canada in 1990(Lachapelle 1989). In 1991 LORAN-C coverage was expand- ed to the mid-continent of the U.S.A. (RTCM 1994). Local radio and microwave systems have been introduced for agricultural use. The cover- age is 750-1500 meters. The accuracy can be in good weather as good as 0.1-0.25 meters. The accuracy is so good that these systems are used as replacement for marker systems. Local topog- raphy, specially big height differences, and ob- stacles cause interference. (AGNAV 1988, Palm- er 1989, Hane ref. Mpller 1990, Searcy et al. 1990, Fig. 72) Unmanned fully automatically steered vehi- cles have been developed for restricted areas such as mines, industry or military. These are applications that can afford the high price of the infrastructure needed and where safety require- ments can be met. (Choi et al. 1989, Mäkelä et al. 1991, Petersen 1991,Juhala 1993) Some ex- perimental local applications are also developed for agricultural uses (e.g. AGNAV 1988, Schmulevich et al. 1989, Yoshida et al. 1989, Palmer 1989, Nieminen and Sampo 1993) 4.5.2 Choosing the method for further tests: Why GPS? Choosing positioning methods for agriculture is a matter of compromize and it is an individual task for every single application. Agricultural requirements for positioning accuracy range from a few centimeters to several meters (e.g. Choi et al. 1989, Auernhammer 1990, Larsson 1990, Ch. 2.4.2, App. 4). The need for accuracy can be viewed from different directions and at several levels. The starting point can be the tech- nic used or the target. If we use the technic we come to the decision that the accuracy could be something dependent on the span of a boom, width of a cutting blade, length of the machine, spacing of nozzles, etc. If the target, the biolog- ical process in the field, is more important, then we must design our machines accordingly. Then the positioning accuracy is limited by the proc- ess and its sensitivity to errors in the site-spe- cific tasks. (See Ch. 2 above) The most promising use of navigation is Po- sition Dependent Control. In agriculture this means adaptive in-field control of agricultural machines. DGPS accuracy is in the order need- ed in agrochemical application (Ch. 2). DGPS is expected to be used in applications that need an accuracy of c. 2-5 meters. (Buschmeier 1990, Mpller 1990 Buschmeier 1991. Kloepfer 1991, Petersen 1991, Schnug et al. 1991, Auernham- mer etal. 1994a, Stafford 1994) Applications that need sub-meter accuracy, and can afford the cost, Fig. 72. An example of using a local radio positioning sys- tem in agriculture. 1. The driver drives once around the field, In spot 2 she/he sets a portable beacon to the ground and puts it on. An other beacon is set in spot 3. Then the driver drives in parallel to the previous pass. Thereafter the work continues with parallel passes. In the turning the driver presses “next pass” button. The driver has an indicator that shows deviation from the right route (AGNAV 1988) 320 AGRICULTURAL SCIENCE IN FINLAND may use RTKGPS (Real-Time Kinematic GPS) (Abidin 1994). Local positioning systems (AGNAV 1988, Palmer 1989, Mäkelä et al. 1991, Rintanen 1992) are not suitable for general use. They are suited for applications that can afford the high price and operation range limitation of the infrastruc- ture needed (Auernhammer et al. 1994b). The high price must be justified with corresponding increase in the output. This means that all or most of the users in the region must join the system installed. This is not necessarily possible because it presumes some homogenity in the production profile. Local positioning systems are to be con- sidered in connection with special applications where product prices are high and PDC is very favorable (e.g. some vegetable production). Sometimes it is not possible to achieve accurate enough positioning with other methods, e.g if the area is badly covered. Then local systems are the only alternatives. Satellite navigation GPS is an outstanding choice for Position Dependent Control. Its ben- efits are (Toft 1987, Hirvenoja 1993,Tyler 1993, Auernhammer et al. 1994b, Chan and Chorr 1994, Krakiwsky 1994, GPS World 1994, GPS World 1995): 1. Global availability. 2. Relatively low total costs. 3. Simplicity of use. 4. Growing markets. 5. Intensive use in vehicle navigation systems GPS is a very user-friendly positioning sys- tem. After powering the receiver on it starts to give coordinates. When using GPS all the com- ponents of the positioning system, except the possible differentialreference station, can be put inside the vehicle. It does not need user calibra- tion because the receiver is digital and calibra- tion during operation is done in the control seg- ment. There is no need for local infrastructure, which would be too costly. This is true especial- ly in countries like Finland where farms are small and heterogenous in production, thus making it difficult to adapt any uniform regional position- ing methods. The basic reciever is not expen- sive. It is small: hand-held receivers are about the size of a cellular phone and a six-channel 'black box' receiver with an antenna fits into a packet of cigarettes. Today almost all units are designed to work with a computer. (Hirvenoja 1993, Chan and Chorr 1994, GPS World 1995) GPS is also widely recommended for agricul- tural use. (Auernhammer 1990, Moller 1990, Buschmeier 1991,Kloepfer 1991,Petersen 1991, Schnug et al. 1991) GPS has been used in e.g. yield mapping (Christensen 1991a, Christensen 1991b, Roberts 1991), remote mapping of agri- cultural land (Perry 1992) and sprayer control (Petersen 1991, Stafford et al. 1994). The main drawbacks are: 1. Need for backup in some situations. 2. Dependence on military policy. 3. (Affordable) accuracy is not good enough for some purposes. Backup systems include DR that operates during possible GPS pauses and various sign- post systems that give external reference on re- quest (Mäkelä et al. 1991, Hakala 1992, Kra- kiwsky 1994). In-field navigation is somewhat more difficult than on-road navigation, because of slippage and the fact that no fixed reference structure exists. Slippage is a main problem for distance measuring odometers. Compasses, ground speed radars and inertial navigators are better than wheel sensors in this sense. (Hakala 1992). Image analysis is also a potential system for supporting otherpositioning systems (Brown et al. 1991, Mäkelä et al. 1991, Juhala 1993). All of the above mentioned systems are more expensive than odometer-based DR (Hakala 1992). The lack of road network makes map matching technic more difficult to utilize. Sens- ing the previous pass is a kind of modification of map matching. Actually the traditional aids like marker systems can be used to enhance driv- ing accuracy while GPS is giving the position for site-specific implement control. Odometers, electric compasses and/or doppler sensors can be used to backup GPS and measure distance travelled on the pass identified by GPS. An ordinary GPS-receiver is not suitable for agricultural use because of its inaccuracy. A typ- ical value is around 100-150 meters (RMS). A 321 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND DGPS system is quite expensive (>IOOOO FIM including data links, GPS World 1995) but it is still much cheaper than optical (Rintanen 1992) or local radio beacon (AGNAV 1988) systems. The accuracies of DGPS-sets vary quite much, mostly depending on calculation technics, make and version. The best versions are claimed to be capable of a sub-meteraccuracy in real-time kin- ematic mode. This is still not usable when try- ing to guide autonomous robot-tractors, but it seems to be a realistic option when talking about spatially selective field operations. (Auernham- mer 1990. Buschmeier 1990, 1991,Stafford and Ambler 1991) Real-time kinematic GPS (Tyler 1993, Abidin 1994, GPS World 1994) may be used in autonomous applications. It is, howev- er, very expensive (GPS World 1995). Palmer (1989) criticizes GPS economy. He urges that integrated systems are required and that they are too expensive. He thinks that iner- tial navigation should be used as a backup sys- tem. The research, however, is very eager at pro- moting cheap integrated systems that use e.g. DR and DGPS (Chandan et al. 1989, Hakala 1989, Harris and Krakiwsky 1989,Karppinen 1990a, Rintanen 1992, Haapala 1994a, Krakiwsky 1994). Positioning is getting cheaper as the mar- ket grows (Koskelo 1990, Chan and Chorr 1994, GPS World 1995). All in all, it is not possible to get a single solution for accurate and reliable positioning. The solution is unique for the application and consists of various integrated technics. GPS is a potential component in the major part of these solutions that include vehicle navigation (Krak- iwsky 1994). 4.6 Positioning tests at Viikki Experimental Farm On the basis of literature and simulations of tar- geting accuracy requirements (Ch. 2.4 above), GPS and DGPS were selected for tests (Ch. 4.5 above). Based on literature (Ch. 4.4), DGPS was expected to fulfill the set accuracy requirement of better than ±5 meters (95%). The aims of these tests were to check the suit- ability of the GPS-technic used for the needs of agricultural positioning. Positioning data was also used in simulations of the effect of target- ing accuracy (Ch. 2 above). Positioning tests were conducted in a test route. The route was positioned with geodetic measurements with an absolute accuracy of better than 5.3 centimeters (10, App. 8). The acquired GPS-data was com- pared with this known route. In addition to the test route the receivers were tested on road and in urban areas, both in quite covered situations. Final test reported here were done in connection with practical drilling work. The tractor was driv- en along an accurately located reference formed by a revolving laser beam. Two basic types of GPS receivers were test- ed. Post-processed differential GPS and real-time differential GPS. The first receiver type was an accurate geodetic receiver and the other one a vehicle receiver with a facility for DR-backup module. The relative inaccuracy ofvertical coordinate measurement in GPS compared with its horizon- tal coordinates was expected not to cause any trouble because Finnish fields are rather plane (Puustinen et al. 1994, comp. Tyler 1993). Ac- tually, it is possible to lock GPSs height meas- urement to a certain level, in cases where height fluctuations are neglectible, and use 2D-position- ing (Toft 1987). If this is not the case, it is even possible to add a more accurate height measure- ment to the system (Haapala 1990). On the oth- er hand, differential GPS could be accurate enough so that no remedies would be needed. The sensitivity of GPS signals to obstacles such as trees or buildings was expected to call for a backup system (comp. Lachapelle and Hen- riksen 1995). Dead Reckoning was selected as a commonly used economical solution (Karppinen 1990, Krakiwsky 1994) for this purpose. Intelli- gent filtering of the positioning result was ex- pected to be needed in field conditions where driving speed is comparatively low and where multiple turns are made. It was expected that 322 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. heading information could be needed. Weighing the positoning results in driving direction would then be a solution for the possible problems for low-speed driving, where in-built filters of the GPS-receivers are not efficient enough. 4.6.1 The test route The test route was situated at the Viikki Experi- mental Farm near the Department of Agricultur- al Engineering and Household Technology. It was selected in such a way that it would consist ofopen and covered areas. The route was c. 2200 m in total length. There were five datums that were geodetically positioned. The absolute po- sitioning accuracy of these points was better than max. ±33 mm (RMS) (accuracy of starting tri- angulation points max. ±8 mm and accuracy of geodetic GPS ±25 mm, App. 9). Ten assisting checkpoints were added. Checkpoints were used to input check codes to the positioning file. Check codes were input when the vehicle passed the checkpoint. Their accuracy was c. one meter in distance (due to manual input). The route was later measured with a tachymeter with an accu- racy of better than c. ±2O mm (the inaccuracy was mainly due to manualpositioning of therod). The total inaccuracy of the route position was in the worst case max. c. ±53 mm (this equals a 33 mm probable error: Dally et al. 1984). (Fig. 73) Fig. 73. Test route for DGPS tests at Viikki Experimental Farm. Driving direction is shown with arrows. "Fix" = fixed point at the Dept. of Agric. Engineering and Household Technology. Check points are marked with numbers (1-10). 323 AGRICULTURAL SCIENCE IN FINLAND 4.6.2 Tests with post-processed DGPS A geodetic GPS-receiver (Ashtech XII) was test- ed in December 1990and March 1991.Two such receivers were in use, one of which was station- ary and the other in the moving vehicle (a Land Rover). Differential corrections were made with post-processing in the office. (Fig. 74) During the tests, positioning data were saved in the memories of both receivers and they were later downloaded to a PC via an RS-232C serial interface. Because of the geodetic origin of the receivers the positioning file (c. 1 MB per test) included much useless information which was rejected in further analyses. Coordinates, check codes, time, satellite availability data and GQ- (Geometric Quality) parameters (see App. 12) were kept for further use. Differential corrections were done with a special post-processing software in office with the positioning results of the stationary and the moving receiver. The resulting coordinates were transformed from WGSB4 ellipsoidal coordinates to kkj map coordinates (Lankinen et al. 1992, Fig. 55 above). The transformationwas complet- ed with a computer program made in C-program- ming language by the supplier of the receiver. 4.6.3 Tests with real-time DGPS In 1993 tworeal-time DGPS-receivers (Trimble® Placer GPS/DR.Fig. 75, and Trimble® SVeeSix) were tested. Both receivers are based on the same receiver technics and are suitable for vehicular applications. They are designed for the use of differentialcorrections. The Placer GPS/DR can also use Dead Reckoning . Differential correc- tions are made in (near) real time (max. timelag ofc. 2 seconds). In the tests the corrections were received with a special radio receiver (Trimble Navßeacon XL) from a correction station of the Finnish National Board ofNavigation in Porkka- la (Fig. 69 above) or from a local reference. The transmission protocol of the corrections was RTCM 104 v. 2.0 (Langley 1994, RTCM 1994). A dead reckoning module, including an elec- tronic compass, was attached to thereceiver. The DR-module also used pulses (130 1/m) given by the doppler radar of the tractor for distance meas- urement. An odometer (a distance wheel) was used as a separate distance reference measure- ment. The measurements were synchronized in time. An agricultural tractor (Valmet® 805-4, Figs 76-78) or an off-road car (Toyota Landcruiser) was used as installation platform. Fig. 74. Tests in 1990-91. (a) The stationary receiver. (b)The vehicle with an installed receiver. GPS antenna shown on the roof. (Photos: Hannu Haapala). 324 Haapala, H. E. S.: Position Dependent Control ofplantproduction AGRICULTURAL SCIENCE IN FINLAND Fig. 75. (a)The DGPS/DR (Differential GPS satellite navigation with DR backup) receiver (front view, size c. 150x50x250 mm) and the DR module and (b) the RTCM-radio beacon (c. 150x75x250 mm). (Courtesy: Trimble Navigation Inc) Fig. 76. Components of 1993 DGPS/DR (Differential GPS satellite navigation with DR backup) tests. Fig. 78 The tractor with distance wheel. (Photo: Markku Hirvenoja). Fig. 77. The DGPS/DR installed in an agricultural tractor in 1993. (a) the GPS/DR module and (b) the RTCMreceiv- er installed in tractor cabine. (Photos: Markku Hirvenoja). 325 Vol. 4: 239-350. AGRICULTURAL SCIENCE IN FINLAND Differential corrections were calculated in the receiver in real time.The data were collected into a portable PC that was connected to the DGPS/ DR receiver via an RS-232C port. Optionally, the PC's RS-232C port was used to control the receiver. DR operated automatically: if the re- ceiver did not get GPS positions at a certain time, it started to use the piezo chrystal and the radar signals for backup. The positioning data (e.g. Fig. 79) included information on the type of po- sitioning currently used. 4.6.4 Positioning accuracy in the test route In vehicle positioning and navigation, repeated measurements are usually not possible because of the movement. The measurement error can not be reduced through pure averaging. That is why various dynamic filters are developed. The sim- plest ones are based on floating weighed aver- age and the advanced ones employ statistical modelling (e.g. the Kalman filter) (Bäckström 1990). In 1990-91 the receiver used doppler filter- ing with an assumption of forward movement. This caused the filter to lose its direction when the vehicle was stopped. The positioning result started to wanderaround the actual location. The East-West component was just about a fourth of the North-South component. This may be due to the momentary satellite constellation. (Fig. 80) When the vehicle was moving there were no problems with the filtering. Even quick turns were adequately positioned. In 1993 Trimble DGPS/DR used a Kalman filter (a statistically weighed filter. Toft 1987). It did not react to stop- ping the vehicle but caused slight stretching in turns. (Fig. 81) The accuracy (see App. 9 for def- initions) was separately calculated for standard deviations (s) of the errors in cross and length direction. The standard deviations measured were multiplied by 1.96to get error axes in 95% confidence level. (Dally et al. 1984, Toft 1987, Lankinen et al. 1992, App. 9) An uncertainty- ellipse was calculated with these axes. (Fig. 82). The accuracy was calculated for a selected dis- tance (from checkpoint 6 to 9 in Fig. 74 above) in the southern part of the route. 122-285 points were included in each calculation because of different driving speeds. This does not affect the Fig. 79. A sample of the positioning data in 1993. The format in view is TAIP (Trimble ASCII Interface Protocol. Option- ally TSIP (Trimble Standard Interface Protocol, binary) or NMEA 0183 (National Marine Electronics Association, ASCII) can be used. (RTCM 1992) Fig. 80. The positioning result when the vehicle was stopped for a moment (c. 12 seconds) in location P. 326 Haapala, H. E. S.: Position Dependent Control ofplant production AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. results because GPS positioning results are prac- tically independent of each other, i.e. each point was separately positioned (Fig. 83). Covariance of the errors in direction of the cross and length coordinate axes (Lankinen et al. 1992) was in- significant. In 1990-91 there was no reference measure- ment of the distance travelled. In calculations the positions were projected to the road line. As the forward speed was kept constant and posi- tioning frequency was constant, it was assumed that the actual distances between the points were constant. The measured distance data was cen- tered to the test distance. Deviations were cal- culated as above (see Fig. 82 above). Because of the slow driving speeds, frequent measure- ment and variation in GPS result, some 4-20% of the calculated distances were negative. In 1993 a distance wheel (2000 pulses per revolu- tion) was used to check for forward speed. The speed measurement was used to select lengths of data for comparison. Differential corrections were calculated in (near) real time at one sec- ond intervals. The DPGS results show that there Fig. 81. Positioning in a tight turn with the doppler filter of Ashtech XII receiver (post-processed DGPS) and with the Kalman filter ofTrimble Placer DGPS/DR receiver (real-time DGPS). Two separate runs with both receivers are shown. Fig. 82, Calculation of positioning accuracy, (a) Differences of actual positions and positioning results were calculated, (b) standard deviations oferrors (oWm and oUrr) were multiplied by 1.96 to get radius of uncertainty (95% confidence level). 327 AGRICULTURAL SCIENCE IN FINLAND Haapala, H. E. S.: Position Dependent Control ofplant production were some points with exactly same coordinates. They were probably due to an overload of the receiver in differential calculations; the amount of these errors was smaller with the differential disabled. The results were calculated with and without these double points. A summary of selected positioning results is shown in the following table (Table 11). It in- cludes values from the same checkpoint interval in the test route. The table includes results for differential GPS with post-processed (1990- 1991) and real-time differential corrections. For comparison, one test with no differential correc- tions (93 0801:3) is shown. (Table 11) Addition- al data from the tests appear in Appendix 11. The results indicate a considerable difference in the accuracies of the receivers. The vehicle receivers were able to achieve as accurate results without differential corrections as the geodetic receiver with them. However, the difference is much due to the differences in geometric quali- ty between test years. In 1990-91 PDOP- (Posi- tion Dilution of Precision) values (App. 12: ge- ometric quality indicators) were adequate only a few hours a day because of the incomplete sat- ellite constellation. In 1993 the constellation was ready with good geometric quality (all PDOPs were below 2.25). (Fig. 84) The comparison of different sources of dif- ferential correction gives no significant differ- ence. The level of accuracy with both systems is very good, except for the link failure in last test run. (Table 11) Fig. 83. Effect of number of the points used in calculation on the area of uncertainty-ellipse for(a) testswith post-processed DGPS and (b) tests with real-time DGPS. DGPS =Differential Global Positioning System. Fig. 84. PDOP values and corresponding uncertainty in positioning in positioning tests in Viikki in 1990..-91, The tests are numbered in chronological order (see table 11). 328 AGRICULTURAL SCIENCE IN FINLAND AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. Table 11. Accuracies (95%) for positioning tests in test route at Viikki Experimental Farm in 1990, 1991 and 1993. Results for the south part of the test route (reference points 6-9, Fig. 74 above). Test id is in format [YYMMDD:N] where Y=year, M=month, D=day and N=test number in that day. -test with NBN'sdifferential correction, b=test with differential correc- tion from a local reference station, **=results without dual points. GPS = Global Positioning System. PDOP = Position Dilution of Precision. 1990-91:Ashtech® XII geodetic GPS-receiverwith post-processed differential corrections. test id cross length height ellipse, m 2 n PDOP comment 901218: 1 öi? Z49 izii 646.62 279 236 901218:2 7.78 6.26 14.69 612.02 285 2.30 901219:2 8.06 8,40 23.35 850,79 141 3.50 901219:3 7.59 8.50 13.21 810.72 140 2.40 901219:4 6.75 6.96 10.38 590.37 135 2.30 901219:5 10.66 16.70 15.50 2237.09 122 3.10 901220:2 6.74 7.47 12.68 632.69 182 2.50 901220:3 8.52 7.80 12.07 835.11 159 2.60 901220:5 12.52 7.30 20.20 1148.52 90 3.70 910304:1 5.83 6.77 13.84 495.98 125 2.58 time resolution better 910304:2 4.88 5.01 16.34 307.23 149 2.55 time resolution better 1993: Trimble® Placer GPS/DR vehicle navigation module, real-time differential corrections with Trimble® Navßeacon XL and DR (Murata® piezo compass + dopplerradar). test id cross length length** ellipse, m 2 ellipse, m 2 ** n comment 930730:1 060 123 30.39 24.35 194 930730:2 1.79 3.26 1.10 73.33 24.74 190 930730:3 1.59 2.97 0.28 59.34 5.59 186 930730:4 1.18 4.12 1.13 61.09 16.76 198 930730:5 1.04 4.51 0.40 58.94 5.23 188 930801:1 3.92 6.64 0.65 327.09 32.02 118 930801:2 0.89 3.77 0.92 42.16 10.29 301 930801:3 50.09 4.01 3.33 2524.09 2096.07 169 without differential 1993: Trimble® SVeeSix vehicle navigation module with real-time differential corrections received with Trimble® Navßeacon XL from NBN's reference station in Porkkala (fig. above) or with Satelline® 2-ASx radio modem from a local Trimble® reference station . testid cross length height ellipse, m 2 n PDOP comment 931202:1“ 338 ÖTs Ö93 228 L54 931202:1" 3.03 0.18 0.46 6.85 228 1.54 931202:2“ 1.06 0.16 3.00 2.13 218 1.36 931202:2" 0.50 0.16 3.73 1.01 221 1.38 931202:3* 2.21 0.16 5.03 4.44 239 2.14 931202:3" 0.78 0.16 0.95 1.57 223 2.14 931202:4“ 2.47 0.18 3.62 5.59 237 1.54 931202:4" 1.74 0.55 0.62 12.03 248 1.72 931202:5“ 0.55 3.21 1.90 22.19 228 1.20 931202:5" 6.42 2.71 2.52 218.63 273 1.20 radio link failure 329 4.6.5 Positioning accuracy in road tests In addition to the tests in the test route, some road tests were made in order to get more infor- mation on the reliability of DGPS in covered cir- cumstances. The geodetic receiver was tested in 1991 on a ten-kilometer road test along the Hel- sinki bypass road “Ring-I”. In Ring-I there are several sight obstacles, mainly road bridges and noise walls. Because of the covered situation, differential positioning was not possible except in a few points. This was due to the incomplete satellite constellation; a calculation of differen- tial corrections needs the same satellites to be used for positioning of both the fixed and the moving receiver. Also the receiver had slow re- covering time when satellite contact was lost beneath the bridges. In 1993, with the real-time DGPS, the same test and some extra driving in even more covered situations were made. The results show remarkable progress: obstacles (road bridges, high houses) make only short pauses to GPS measurements. (Fig. 85) In 1993, dead reckoning was used as a back- up. In case of loss of sight to the satellites the Dead Reckoning was activated. The first version of the tested DR-software was not operating cor- rectly but caused sudden jumps in the position- ing result (positions with arrows in Fig. 85)Lat- er on the software was updated and the error was corrected. 4.6.6 Positioning accuracy in field work In 1994 the DGPS tests continued in connection with actual field works. A six-channel Trimble SVeeSix® DGPS receiver module was installed in the tractor and the differential corrections were received in RTCM from a nearby (<2OO m dis- tance) reference station. The transmission was done with a radiomodem (9600 bps). The drive routes required were planned in office and marked with the help of a digital tachymeter in the field. A laser transmitter with revolving la- ser beam was placed at the end of every second of the drive passes. The tractor driver drove along the laser plane with the help of directing arrows. (Fig. 86) The location of the laser beam was estimat- ed to be accurate within c. ±2O mm. This esti- Fig. 85. Road test with a real-time DGPS-receiver in 1993. Arrows indicate positions where the system used Dead Reckon- ing instead of DGPS. The route is drawn on a numeric map of the area supplied by National Survey. DGPS = Differential Global Positioning System. 330 Haapala, H. E. S.: Position Dependent Control ofplantproduction AGRICULTURAL SCIENCE IN FINLAND Vol. 4: 239-350. mate consists of the numerical error of calcula- tions and the human error in positioning the ta- chymeter (c. ±lO mm in total) and placement of the laser transmitter (c. ±lO mm). The driving accuracy of the driver was c. ±BO mm. The esti- mations yield a worst case error budget of c. 100 mm for the tractor, which also was detectable in the resulting grain stand. In addition to this, as the receiver antenna was mounted on the roof of the tractor, there are high frequency error sourc- es due to the oscillations of the tractor. These are, however, compensated for by the filter in the receiver. All in all, the error sources are ne- glectful (<5%) when compared to the actual po- sitioning errros of the receiver. Thus the refer- ence was accurate enough for the test, and can be assumed to be a straight line in the field. The results (Fig. 88) show good positioning accuracy. The positioning results of the paral- lell passes did not cross each other in the field. In practise this ensures that the error was below 2 meters during the test. This is better than the specifications for the receiver ( 1.5 (Toft 1987, Kruger et al. 1994). In three-dimensional case the term is called PDOP (Position Dilution of Precision) and it is typically > 2.5. Horizontal and vertical components are called HDOP and VDOP, respectively. Their valkues are typically > 1.5. A general term for these indicators is GQ ( Geometric Quality). (Toft 1987, Kruger et al, 1994) Fig. I, Different coordinate systems and the obtainable ac- curacy in position determination, (a) Direction finding (e.g. visually or by radio beacon) , (b) distance and direction (e.g. radar), (c) two distances (e.g. GPS) and (d) hyperbola (Loran, Decca and Omega). (Gloersen ref. TOFT 1987) Fig. 2. The resulting position accuracy is best when the two coordinate lines intersect each other at an angle of90°. The total inaccuracy is illustrated by the hatch-marked prop- ability area, which is a circle with a radius of \2 times the range accuracy. (Toft 1987) AGRICULTURAL SCIENCE IN FINLAND