Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 14, No. 2, 2025 43 Research on Adaptive Regional Classification and Prediction for Underwater Navigation Based on Genetic Algorithm and Support Vector Machine Model Wenjie Zhang1, a 1School of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China a1723980263@qq.com Abstract: This paper primarily investigates the selection of matching regions in a gravity matching navigation system for submersibles. When employing Support Vector Machines (SVM) for adaptive region classification, traditional SVMs necessitate manual adjustment of hyperparameters according to different scenarios. To address this limitation, our work integrates Genetic Algorithm (GA) with SVM for the selection of suitable matching regions in underwater gravity-assisted navigation. The experimental results demonstrate that this approach can provide valuable references for the division of adaptive regions and the design of navigation routes for underwater vehicles. Keywords: Gravity matching navigation, Support vector Machine, Suitable area. 1. Introduction As global attention on the development and utilization of marine resources grows, the navigation and positioning capabilities of underwater vehicles have emerged as a critical area of scientific inquiry[1]. These vehicles primarily rely on Inertial Navigation Systems (INS), which are self-contained, stealthy, and offer high short-term accuracy. Despite these advantages, INS suffers from errors accumulating over time due to factors like gyro drift and accelerometer bias, making long-term mission accuracy challenging without external corrections [2].The stable and well-distributed temporal- spatial characteristics of marine gravity fields present an effective solution for correcting these INS inaccuracies[3]. By utilizing onboard gravity sensors, underwater vehicles can gather gravity field data during their journey. This data is then compared against a preloaded reference map database, enabling the identification of the most accurate matching position through specialized algorithms. The correction of inertial navigation errors using Earth's gravity field not only enhances navigation precision but also opens new avenues in the autonomous navigation of underwater vehicles. This method represents a promising research trend, aiming to leverage natural environmental features for improved underwater navigation reliability and efficiency .This approach underscores the potential for integrating environmental mapping with traditional navigation systems to achieve more reliable long-duration underwater missions[4]. 2. Constructing a Support Vector Machine Classifier 2.1. Gravity field characteristic parameters Gravity field characteristics can be described from various aspects such as statistics, correlation, and frequency [5]. (1) Standard deviation of gravity anomalies, the calculation formula is as follows: 2 1 1 1 [ ( , ) ] 1 m n i j g i j g mn        (1) Where 1 1 1 ( , ) m n i j g g i j mn     is mean gravity anomaly, ( , )g i j is the value at position ( , )i j in the gravity anomaly map. (2) Standard deviation of slope, the calculation formula is as follows: 2 1 1 1 [ ( , ) ] 1 m n s i j S i j S mn        (2) Where 1 1 1 ( , ) m n i j S S i j mn     , arctan( )S S S   , 1 [ ( , 1) ( 1, 1) ( , ) ( 1, )] 2* S g i j g i j g i j g i j scGrid         , 1 [ ( 1, ) ( 1, 1) ( , ) ( , 1)] 2* S g i j g i j g i j g i j scGrid         . (3) Roughness, the calculation formula is as follows: ( ) / 2R R R   (3) Where 1 1 1 1 ( , ) ( 1, ) ( 1) m n i j R g i j g i j n m         , 1 1 1 1 ( , ) ( , 1) ( 1) m n i j R g i j g i j m n         . (4) Gravity anomaly difference entropy, the calculation formula is as follows: 44 2 1 1 log m n ij ij i j H P P     (4) Where 1 1 ij ij m n ij i j D P D     , ( , ) ij g i j g D g   . (5) Correlation coefficient, the calculation formula is as follows:   ( ) / 2P P P   (5) 1 1 1 1 ( , ) ( , 1) ( 1) m n i j P g i j g g i j g m n           (6) 1 1 1 1 ( , ) ( , 1) ( 1) m n i j P g i j g g i j g n m           (7) 2.2. Particle Swarm Optimization Support Vector Machine 2.2.1. Support Vector Machine Principles Support Vector Machine (SVM) is a supervised learning model used for classification and regression analysis[6]. The core idea of SVM is to find a hyperplane in a high- dimensional space that separates data points of different classes as much as possible while maximizing the margin between the classes. Additionally, by employing what is known as the kernel trick, SVM can efficiently perform non- linear classification.   1 , 1 1 1 max ( ) ( ) ( ) 2 . , 0( 1 ~ ), 0 N N T i j i j i j i i j N i i i i i YY X X s t Y i N                        (8) The Gaussian Kernel Support Vector Machine (RBF-SVM) is a type of Support Vector Machine model that uses the Radial Basis Function (RBF) as its kernel. The RBF kernel, also known as the Gaussian kernel, is one of the most commonly used kernels in SVM, especially suitable for non- linear classification problems. It works by mapping the original input space to a higher-dimensional space, making it possible to find a hyperplane that can linearly separate the data points in this high-dimensional space [7]. The mathematical expression for the Gaussian kernel function is:   2 2 ( , ) exp( ) 2 i i i j x y K x x     (9) This paper adopts the radial basis function kernel, bring it into formula (7):The classification function of the optimal hyperplane is expressed as: 1 ( ) sgn ( , ) m i i i j i f x Y K x x b        (10) In the context of RBF-SVM, selecting the appropriate penalty parameter C and Gaussian kernel parameter g is vital for enhancing classification performance. Consequently, to improve classification outcomes, standard Particle Swarm Optimization (PSO) is utilized to optimize these hyperparameters. 2.2.2. Genetic Algorithm Genetic Algorithm (GA) is a search heuristic that mimics the process of natural selection and genetic mechanisms, belonging to the category of evolutionary algorithms[8]. It draws inspiration from Darwin's theory of natural selection, particularly the principle of "survival of the fittest," and addresses problems by simulating operations found in biological evolution such as inheritance, mutation, selection, crossover, and recombination[9]. The formula is as follows: x ( 1, 2 ), 1, 2i di di diD i NP   (11) For each individual in the population, the mutation vector in differential evolution is generated in the following way: 1 2 3( )i r r rv x F x x   (12) Where r1r1, r2r2, and r3r3 are randomly selected from the population such that r1≠r2≠r3, and F is the scaling factor. Typically, the scaling factor F is chosen within the range [0, 2]. Below is the crossover formula for genetic algorithms: , , , , rand