Ultrasonic rangefinder with resolution in hundredths of the probing signal's wavelength for the mobile rescue robot


ACTA IMEKO 
ISSN: 2221-870X 
December 2019, Volume 8, Number 4, 41 - 46 

 

ACTA IMEKO | www.imeko.org December 2019 | Volume 8 | Number 4 | 41 

Ultrasonic rangefinder with resolution in hundredths of the 
probing signal's wavelength for the mobile rescue robot 

Stanislaw Goll1,2, Julia Maximova1,2 

1 Department of Information-Measuring and Biomedical Engineering, Ryazan State Radio Engineering University (RSREU), Gagarin Street 
59/1, Ryazan, Russia 
2 LLC KB Avrora, Skomoroshinskaja Street 9, of.3, Ryazan, Russia 

 

 

Section: RESEARCH PAPER 

Keywords: ultrasound; rangefinder; resolution; envelope; phase spectrum; rescue robot 

Citation: Stanislaw Goll, Julia Maximova, Ultrasonic rangefinder with resolution in hundredths of the probing signal's wavelength for the mobile rescue 
robot, Acta IMEKO, vol. 8, no. 4, article 8, December 2019, identifier: IMEKO-ACTA-08 (2019)-04-08 

Editor: Yvan Baudoin, International CBRNE Institute, Belgium 

Received November 23, 2018; In final form June 26, 2019; Published December 2019 

Copyright: This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, 
distribution, and reproduction in any medium, provided the original author and source are credited. 

Corresponding author: Julia Maximova, e-mail: maximova@kb-avrora.ru 

 

1. INTRODUCTION 

Extreme mobile robotic systems, safety-critical systems 
(particularly those designed for drivers, pilots, and motormen), 
and medical equipment (e.g. diagnostic and therapy instruments) 
need low-cost precision rangefinders with an effective range of 
up to 1 m and an output data rate of at least 20 Hz to measure 
both absolute and relative distances. Such rangefinder sensors 
can be used to provide the noncontact measurements of a 
person’s pulse and respiratory rates (Figure 1) – information that 
is critical for planning rescue operations, the prevention of 
human-factor accidents, and the synchronisation of medical 
equipment with a patient’s biorhythms [1]. 

Search and Rescue (SAR) operations caused by industrial 
disasters and military conflicts can be dangerous for SAR crew 
members. The main need here is to minimise the human 
presence in the danger zone by relying on telemetry data (i.e. 
victims’ vital signs and locations) to optimally plan and execute 
the rescue operation, including the SAR crew members’ efforts 
and the rescue robots, both autonomous and remote controlled 
[2], [3]. 

Detection of the injured person’s vital signs, mainly pulse and 
respiratory rates, poses a nontrivial task even for a remote 
controlled rescue robot [4], [6]. For that task, video and thermal 
cameras are considered to be the most informative sensors. Due 
to the amount of data broadcasted by these sensors, they require 
a wired connection (e.g. a LAN) between the robot and the 
human operator or the broadband wireless connection in the 
case that the former option is not possible. However, the radio 
wave-based data transmission can lead to detection mistakes due 

 

Figure 1. Positioning of the ultrasonic beam pattern by the mobile robot in 
noncontact registration of the person’s pulse and respiratory rates. 

ABSTRACT 
The main goal of this research is to increase the measurement resolution of ultrasonic rangefinders to meet the needs of vital signs 
noncontact registration based on chest movements. The two-phase method is proposed to make distance estimates by sending probe 
pulse trains, calculating the phase spectrum of the echo signal’s envelope, and tracking its relevant components. During the first phase, 
rough Time-of-Flight (ToF)-based estimates are made. During the second phase, this estimate is corrected based on the phase spectrum 
of the echo signal’s envelope, the phase ambiguity is removed, and the relevant components are determined. The final estimate of the 
human chest displacement is calculated based on these relevant components. The output data rate is the same as for the ToF-based 
measurements, but the measurement resolution is increased to one hundredth of the ultrasonic wavelength. The experiment results 
are provided for the both model and the real human chest displacements caused by the respiration and heartbeat processes. 

mailto:maximova@kb-avrora.ru


 

ACTA IMEKO | www.imeko.org December 2019 | Volume 8 | Number 4 | 42 

to interferences and non-line-of-sight and near-line-of-sight 
transmissions. Moreover, the usage of thermal cameras to detect 
body temperature can sometimes lead to a dead body being 
mistaken for a living person. 

Another way of measuring human vital signs is to make 
contact measurements [7]. In that case, the robot must place 
electrodes on particular parts of the human body, which leads to 
many problems, like the process of electrode placement or the 
detection and recognition of the body parts where the electrodes 
should be placed. Clearly, these can be quite dangerous 
operations to be performed on an injured person. 

In section 2, we will discuss the relevant prior research in this 
area, including the advantages and disadvantages thereof. In the 
next section, the essence of the proposed method is described. 
The following section presents some experiments and their 
results. In the final section, conclusions are made and 
recommendations for further research are outlined. 

2. RELATED WORK 

The noncontact measurements of the pulse and respiratory 
rates can be taken by means of short-range radars [8], [10], since 

it is possible for a single integrated circuit to contain two 77 GHz 
UHF transmission lines (one transmitting line and one receiving 
line) as well as the low-frequency processing channel and the 
ADC [11]. The data gathered that way can be affected by 
electromagnetic interference and other factors; hence, we 
propose to increase the robustness of the radar measurements by 
means of the secondary noncontact measurement channel based 
on ultrasonic sensors. 

The commonly used Time-of-Flight (ToF) principle [12], [13], 
is based on measurement of the time interval between the start 
of the ultrasonic wave emission and the moment when the 
reflected wave causes the difference between the current air 
pressure and the air pressure at rest to exceed the given threshold 
for the first time. The measurement resolution of the ToF-based 
sensor depends both on the properties of the timer/counter used 
and the ultrasonic signal wavelength. The ToF measurement 

resolution for the 40 kHz ultrasound is, at a rough estimate, 8 
mm. At the same time, many of the ToF-based sensors are 
featured, with the resolution being up to one fourth of the 
ultrasonic wavelength. To achieve such resolution, various 
methods can be used: the adaptive threshold, comparisons for 
the positive and negative half-waves, etc. However, all these 
modifications are not enough to achieve the submillimetre 
resolution. 

Further attempts to improve the measurement resolution of 
the ultrasonic rangefinders are based on linear frequency 
modulation or composite modulation [14]; binary frequency 
shift-keyed signal and phase detection [15]; Vernier caliper phase 
metre [16]; and so on. However, these methods require 
broadband ultrasonic receivers and transmitters, sufficiently 
increasing the hardware cost. 

3. THE APPROACH 

In this article, we propose an algorithm to improve the 
measurement resolution of the low-cost single-tone 40 kHz 
ultrasonic rangefinders. These on the inverse piezoelectric effect 
based sensors are commonly used in the automotive industry to 
build Advanced Driver Assistance Systems (ADASs) [17]. 

The cyclic movements of the human chest are caused by both 
the respiration process and cardiac activity, with movement 
amplitudes of 4 to 12 mm and 0.5 mm accordingly [18]. The 
cardiac cycle is more frequent than the respiration cycle and can 
occur up to 200 times per minute. According to the Nyquist-
Shannon-Kotelnikov sampling theorem, the measurement rate 
of 20 Hz is sufficient to perform vital signs detection. Due to the 
comparatively high sound speed in the air medium, it is possible 
to obtain up to 100 measurements per second at a distance of up 
to 1 m using the ToF method. Nevertheless, the measurement 
resolution of one fourth of the 40 kHz ultrasonic wavelength is 
deficient in pulse and respiratory rates registration. 

We suggest an approach to improve the measurement 
resolution without changing the output data rate. First, some 
method (for example, the ToF method) is used to obtain a rough 

 

Figure 2. (a) Probe pulse trains (b) Received reflected signal (c) A single frame as it appears in the receiver. 



 

ACTA IMEKO | www.imeko.org December 2019 | Volume 8 | Number 4 | 43 

distance estimate refd . Second, the proposed method is used to 

estimate the displacement d  relative to the rough estimate refd

. Contrary to the ToF method, which uses the point in time at 
which the threshold is exceeded as the input data, the proposed 
method uses all the readings of the echo signal gathered with the 

sampling rate df 200=  kHz. 

Figure 2(a) shows pulse trains containing N = 8 probe pulses 

each with the probe pulse frequency set to usf 40=  kHz. The 

pulse trains are transferred to ultrasonic transmitter with the 

frame period being T = 10 ms. The black-coloured regions in 
Figure 2(b) represent the digital signal u , which is formed from 
the received frame sequence and can be described as the 
amplitude overmodulated signal. The white line in Figure 2(b) 
represents the demodulated envelope of the receiver’s signal. To 
compute the envelope, the modulated signal is multiplied by the 

sinusoidal carrier signal ( )sin us vv V 2πf t φ= +  sampled with 

rate df ; the low pass recursive filter with the transfer function 
2

0 1 2

2
1 2

b z b z b

z a z a

+ +

+ +
 is then applied to the multiplication result. 

Figure 2(c) shows an enlarged version of the frame bordered by 
the dotted rectangle in Figure 2(b). Each frame contains the 
deterministic transmitted pulse received when the transmitter 
emits the ultrasonic wave. This signal starts from the beginning 

of the frame and ends at time 1t . In the case that some object 

or group of objects is present in the area covered by the 
rangefinder’s beam pattern and these objects are large enough to 

reflect the ultrasonic wave with the frequency usf , the frames 

also contain the reflected echo signal at the time interval 

 2 3Δt t t,= . 

Moment 1t  is when the transmitted pulse ends is constant 

for every frame and is computed as 
1

1

us

N n
t

f

+
= . We define the 

frame containing the rough ToF-based measurement of the 

distance refd  to the closest object in the sensor’s beam pattern 

as a reference frame. The rough estimate refd  is proportional to 

the time interval reft , which is determined when the echo signal 

exceeds the comparison threshold refu  after time 1t . For every 

frame received after the reference frame time 
2

2 ref

us

n
t t

f
= −  

remains constant until the new reference frames arrive, changing 

the value of reft . The coefficients 1n  and 2n  represent the 

adjustable offsets with the integer values. 
The reference frame is used as a starting point for the 

proposed method to compute its distance estimate and can be 
set (and changed later) either by the human operator’s request or 
automatically if the absolute distance measurements acquired by 
means of the ToF method lie in some predetermined intervals. 

The moment 3 2t t Δt= +  sets the right boundary of the echo 

signal’s time interval of the constant duration Δt const= . 

On the  2 3Δt t t,=  interval of each frame, Fast Fourier 
Transform is applied to the echo signal’s envelope, and then, for 
each of its frames, the phase spectrum is computed. 

The next step is the selection of the M = 10 sequential 

spectrum components (starting with the second component), 
which are expressed as 

, where k  is the 

number of frames relative to the reference frame. This selection 

takes place at the end of each frame period T . Each component 

 mφ k  is used to estimate the displacement  md k  relative to 

the rough estimate refd . This estimate is calculated as 

   m m d k β Φ k=  , where  β  is the conversion coefficient 

(m/rad);      m m mΦ k φ k λ k 2π= +   is the absolute value of 

the phase spectrum 
thm  component after unwrapping; and

 mλ k  is the number of 
thm  component phase unwrappings 

and is calculated as follows: 

     ( )m m mλ k λ k 1 g Δφ k= − + , (1) 

where      m m mΔφ k φ k φ k 1= − − , 

( )

, ,

, ,

, ,

ref

ref

ref ref

1  ξ φ

g ξ = 1  ξ φ

0  φ ξ φ  

−  −



 −    

refφ  is the adjustable threshold of the mΔφ k[ ] . 

Figure 3 illustrates the computation of  mΦ k . When the 
new reference frame is set, the number of phase unwrappings 

 mλ 0  is zeroed for each phase component, which provides the 
recurrent Equation (1) with the initial condition. Therefore, for 
each received frame, M = 10 estimates are calculated for the 

absolute distance mh  between the sensor and the object of 

interest. Each of these estimates is calculated as 

   m ref mh k d d k= + , where  and apparently 

 

Figure 3. Phase unwrapping. 



 

ACTA IMEKO | www.imeko.org December 2019 | Volume 8 | Number 4 | 44 

represents the sum of the reference distance refd  and the 

displacement  md k  computed using the proposed method. Let 

us note that N , 1n , 2n , refu , Δt , refφ , , 

, M  are the structural parameters of the 

algorithm and are estimated empirically before the algorithm is 
applied. 

4. RESULTS 

The proposed method was used to process data gathered 
from the ultrasonic rangefinder in the three experiments. For the 
first experiment, a rectangular aluminium sheet was used as the 
object of interest, shown in Figure 4. A step motor with a step 
of 1.56 µm was used to cause the periodic sawtooth-like motion 
of the sheet with an amplitude of 50 µm along the axis of the 
rangefinder’s beam pattern. 

 

 

Figure 4. The experimental setup and the sawtooth-like displacements of the 
sheet. 

 

  

Figure 5. Changes in absolute values of the phase spectrum components  mΦ k  caused by aluminium sheet displacement (proposed method): a – amplitude 

of 50 µm, b – amplitude of 4 mm; c – ToF-based displacement estimates for the movements with the amplitude of 4 mm. 

Algorithm: displacement estimation 

 



 

ACTA IMEKO | www.imeko.org December 2019 | Volume 8 | Number 4 | 45 

Figure 5(a) contains ten graphs showing the absolute values 

of the phase spectrum components  mΦ k  changing due to the 
aluminium sheet displacement with the amplitude of 50 µm. 
Figure 5(b) shows the absolute values of the phase spectrum 

component  mΦ k  for the sheet’s displacement with a 4 mm 
amplitude. Figure 5(c) shows the ToF-based displacement 
estimates for the movements with an amplitude of 4 mm. 

For the second and third experiments, the human chest was 
used as the object of interest. Figure 6 shows ten graphs 
demonstrating the absolute values of the phase spectrum 

components  mΦ k , changing due to human chest 

displacement during the respiration process, such values having 
been computed using the proposed method. 

Figure 7 contains the ten graphs of absolute values of the 

phase spectrum components  mΦ k , changing due to cardiac 
activity while a person was holding their breath. 

5. CONCLUSIONS 

It is possible to empirically select the relevant (i.e. those that 
are the most correlated with the object’s movements) 

components of  mΦ k  from the series computed by the 
proposed method. For the first experiment, these estimates are 

 

Figure 6. Absolute values of the phase spectrum components changing due to the human chest displacement during the respiration process. 

 

Figure 7. Absolute values of the phase spectrum components  mΦ k  changing due to the human chest displacement caused by cardiac activity. 



 

ACTA IMEKO | www.imeko.org December 2019 | Volume 8 | Number 4 | 46 

under numbers 5, 6, 10; for the second experiment, these 
estimates are under numbers 7, 8, 9; and for the third experiment, 
these estimates are under numbers 5, 6, 8.  

Since the aluminium sheet used in the first experiment was 
moving with an amplitude of 50 µm, we can make a rough 
estimate of the proposed method’s resolution, which is less than 
50 µm and, consequently, less than one hundredth of the 

ultrasonic wavelength with a frequency of usf 40=  kHz, making 

it sufficient for the purposes of respiration and heartbeat 
detection. However, the aforementioned estimate is highly 
conservative and will be a subject of future research. 

According to the experimental results, the ToF method is 
inadequate for plotting the respiration and heartbeat graphs, due 
to its measurement resolution. It should be also noted that in all 
of the experiments, a considerable part of the target object was 
covered by the sensor’s beam pattern, and the waveform of the 
echo signal’s envelope depends highly upon object’s shape. So, 
in the first experiment, all the surface points move equally 
linearly, but in the second and third experiments, the shape of 
the surface is subject to the nonlinear three-dimensional changes, 
causing sufficient changes in the waveform of the corresponding 
echo signal’s envelope. For that reason, the ToF-based results 
contain more noise for the second and third experiments than 
for the first. Consequently, for most of the applications, the 
measurement resolution of this method is in close proximity to 
the wavelength. 

Since the displacements caused by the respiration and 
heartbeat can be considered to be concentrated in the small 

neighbourhood of refd , it is possible to provide accurate 

estimates based on the phase components. The proposed 
method is robust to such displacements, since the only thing that 
changes during the process is the set of the relevant phase 
spectrum components. The main source of such robustness is 
the fact that both the time at which the envelope exceeds the 

comparison threshold refu  and all the information it contains is 

used to perform calculations. However, to survive the significant 
nonlinear changes in the object’s surface over time, some 
combinations of the specific phase components should be used. 

Therefore, the proposed method is suitable for small 
movement detection happening in any region of the sensor’s 
beam pattern and can be applied by mobile robots to detect 
human’s vital signs during a SAR operation. 

An algorithm for the automatic selection of the most relevant 
phase spectrum components or combinations thereof based on 
a priori information about the target object and the measuring 
conditions poses another subject for a future research. Topics of 

interest also include the impact of the rough estimate refd  on the 

relevant phase components selection and the compensation of 
the distortions caused by the air streams on the territory covered 
by the sensor’s beam pattern. 

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