Auxiliary navigation method based on submarine topography, program, equipment and storage medium

By introducing constrained fully symmetric multicellular and twin support vector machines into the single-beam sonar subsea terrain assisted navigation method, the problems of large calculation consumption and difficulty in noise processing are solved, and the robustness and efficiency of navigation are improved.

CN119394304AActive Publication Date: 2025-02-07HARBIN ENG UNIV

Patent Information

Application Number
CN202411445578.8
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-16
Publication Date
2025-02-07
Estimated Expiration
2044-10-16

AI Technical Summary

Technical Problem

Single-beam sonar subsea terrain assisted navigation method leads to robustness and efficiency problems due to the high calculation of particle filtering and difficulty in dealing with unknown measured noise distributions of low-resolution prior charts.

Method used

Introduce constrained fully symmetric polycellular forms, extract water depth data through isometric lines and grid points, and outsourcing them to reduce calculation consumption, process unknown noise distribution, and evaluate the effectiveness of navigation results through twin support vector machines.

Benefits of technology

Without increasing system computing consumption, the robustness of subsea terrain-assisted navigation and the feasibility of practical applications are improved, and efficient and robust navigation results are achieved.

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Abstract

The invention belongs to the technical field of underwater navigation and positioning, and particularly relates to an auxiliary navigation method based on submarine topography, a program, equipment and a storage medium. According to the method, the constrained holosymmetric polytope in set membership filtering is introduced into the submarine topography aided navigation method, so that the operation consumption of the algorithm is reduced, and the unknown distributed measurement noise of the low-resolution priori chart can be processed. According to the method, the isobath and the grid points are utilized to extract proper water depth data in the prior nautical chart, and outsourcing is carried out on the proper water depth data by constraining the holosymmetric polytope, so that the robustness of the navigation method is improved on the basis that the calculation consumption of the system is not increased in the constrained holosymmetric polytope of the real water depth data; the navigation result effectiveness evaluation is performed by constraining the geometric position center water depth difference and the volume of the holosymmetric polytope, and the feasibility of the navigation method in practical application is improved.
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Description

Technical Field

[0001] The present invention belongs to the field of underwater navigation and positioning technology, and specifically relates to a method, program, device and storage medium for auxiliary navigation based on seabed terrain. Background Art

[0002] With the increasing speed of ocean exploration and development, higher requirements are placed on the accuracy and convenience of underwater positioning. Traditional inertial navigation systems cannot provide accurate navigation results in long-term underwater navigation due to the cumulative errors that increase over time, while acoustic navigation requires the deployment and recovery of underwater acoustic arrays, which is expensive and time-consuming. The underwater geophysical field-assisted navigation method does not require the assistance of external sensors, does not have cumulative errors, and has the potential to achieve long-distance underwater navigation. Among the underwater geophysical field-assisted navigation methods, the terrain-assisted navigation method has accurate data measurement and convenient prior chart measurement, and is currently the main geophysical field-assisted navigation method.

[0003] The seabed terrain-assisted navigation method that uses single-beam sonar as a data acquisition method and relies on low-resolution prior nautical charts is one of the main development directions of terrain-assisted navigation methods. However, due to the limited measurement information of single-beam sonar, high requirements are placed on the robustness of the seabed terrain-assisted navigation method. In the current seabed terrain-assisted navigation filtering method, particle filtering fits the real distribution through a large number of particles, which can obtain robust positioning results. However, a large number of particles will cause huge computing consumption and it is difficult to run on a low-cost host. At the same time, particle filtering assumes that the measurement noise of the low-resolution prior nautical chart obeys a Gaussian distribution, but the measurement noise of the low-resolution prior nautical chart is an unknown distribution, which makes it difficult to obtain robust and efficient positioning results in the seabed terrain-assisted navigation method.

[0004] The patent application with the publication date of January 21, 2022, the publication number of CN113959448A, and the invention name of "An underwater terrain assisted navigation method based on improved salp swarm algorithm" uses the improved salp swarm algorithm to realize the location of the sub-map in the seabed digital topographic map. However, the measurement sensor used in the present invention is a multi-beam sonar, and the single-beam sonar information-poor measurement is not taken into account in the navigation algorithm, and no effective solution is proposed for the low resolution of the prior nautical chart.

[0005] The patent application with the publication date of January 3, 2023, the publication number of CN115560765A, and the invention name of "A method for terrain-assisted navigation of AUV based on window sliding" uses inertial navigation information for terrain-assisted navigation, and gradually moves by sliding the window to achieve positioning of the entire path. However, this method does not consider the problem of navigation algorithm computational consumption, and does not take the measurement noise of unknown distribution of low-resolution prior charts into account in the navigation algorithm. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that the current single-beam sonar seabed terrain assisted navigation method has high computational consumption and is difficult to handle the unknown distribution of measurement noise due to the particle filtering method, and to provide a seabed terrain-based assisted navigation method, program, device and storage medium.

[0007] A method for assisting navigation based on seabed terrain comprises the following steps:

[0008] Step 1: At the initial moment, the horizontal position coordinates (x * ,y * ) and error range; (x * ,y * ) as the center, under the premise of ensuring that the horizontal position coordinates of the underwater vehicle within the error range are all included, a constrained fully symmetric polytope with the smallest corresponding volume is constructed

[0009] Step 2: According to the inertial navigation system, obtain the motion vector of the underwater vehicle from the previous moment to the current moment, and update the constrained fully symmetric polytope at the previous moment The center position and generating vector of the constrained fully symmetric polytope after motion update are obtained

[0010] Step 3: Obtain the water depth measurement value of the underwater vehicle's current location based on the single-beam sonar and depth meter carried by the underwater vehicle;

[0011] Step 4: In the prior chart, set the search radius to (x * ,y * ) as the center to determine the search range and ensure that the actual position of the underwater vehicle is within the search range;

[0012] Step 5: Within the search range of the prior chart, taking into account the error of the water depth measurement value, all the isobaths within the error range are extracted, and the extracted isobaths are discretized into isobath points; grid search is used to extract the center point of the grid within the error range;

[0013] Step 6: Outsource the extracted depth contour points and grid center points to constrained fully symmetric polytopes, and construct a constrained fully symmetric polytope with the smallest corresponding volume while ensuring that all depth contour points and grid center points are fully included.

[0014] Step 7: Calculation and The intersection of Will The geometric position center coordinates are used as the estimated value of the horizontal position coordinates of the underwater vehicle at the current moment;

[0015] Step 8: Obtain the water depth value at the current time of the estimated horizontal position coordinate value of the underwater vehicle in the priori nautical chart, calculate the error between the water depth value and the water depth measurement value; and compare the error with The volume of is input into the validity evaluation function to obtain the validity evaluation result of the navigation result; if the navigation result at the current moment is determined to be valid, the estimated value of the horizontal position coordinate of the underwater vehicle at the current moment is fed back to the inertial navigation system for correction;

[0016] Step 9: If the underwater vehicle has not completed the mission, return to step 2 and continue navigation.

[0017] Furthermore, the step 2 is specifically as follows:

[0018]

[0019] Among them, u t-1 Represents the motion vector of the underwater vehicle from the previous moment to the current moment provided by the inertial navigation system; Represents the constrained fully symmetric polytope corresponding to the motion noise.

[0020] Furthermore, the method for setting the search radius in step 4 is:

[0021] The terrain relief of each area is pre-calculated in the prior nautical chart, and the values ​​of the terrain relief of all areas are normalized to the range of 0.5-1;

[0022] According to the error range of the inertial navigation system at the current moment obtained in step 1, determine the initial value R0 of the search radius, according to (x * ,y * ) is the normalized value of the terrain relief in the area The search radius R is set to:

[0023] Furthermore, the terrain relief is calculated as follows:

[0024]

[0025] Where M and N are the length and width of the calculation area respectively; h(i,j) represents the water depth data at the position (i,j) in the prior nautical chart.

[0026] Furthermore, the calculation in step 7 is and The intersection of Specifically:

[0027] The constrained fully symmetric polytope is constructed as follows:

[0028] Z=<c,G,A,b>

[0029] Among them, c represents the center of the constrained fully symmetric polytope Z, G is the generating vector, and A and b are the constraints;

[0030] and The intersection of The calculation method is:

[0031]

[0032] Among them, R is a matrix that satisfies

[0033] Furthermore, the method for obtaining the effectiveness evaluation function in step 8 is:

[0034] A training data set is constructed, and the difference between the water depth values ​​and the volume of the constrained fully symmetric polytope are used as the input of the twin support vector machine, and the navigation error is used as the output of the twin support vector machine. After training, the regression relationship between the difference between the volume of the constrained fully symmetric polytope and the water depth value and the effectiveness of the navigation result is obtained. The regression function is the effectiveness evaluation function.

[0035] Furthermore, the constrained fully symmetric polytope obtained in step 7 is After that, the dimension and complexity are reduced to reduce the algorithm computational cost.

[0036] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-mentioned seabed terrain-based assisted navigation method.

[0037] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned seabed terrain-based assisted navigation method.

[0038] A computer program product includes a computer program / instruction, which implements the steps of the above-mentioned seabed terrain-based assisted navigation method when executed by a processor.

[0039] The beneficial effects of the present invention are:

[0040] The present invention introduces the constrained fully symmetric polytope in the set membership filter into the seabed terrain assisted navigation method, which reduces the operation consumption of the algorithm and can process the measurement noise of the unknown distribution of the low-resolution priori nautical chart. The present invention uses isobaths and grid points in the priori nautical chart to extract appropriate water depth data, and outsources it through the constrained fully symmetric polytope, so that the real water depth data is in the constrained fully symmetric polytope, which improves the robustness of the navigation method without increasing the system calculation consumption; the effectiveness of the navigation result is evaluated by the water depth difference and volume of the geometric position center of the constrained fully symmetric polytope, which improves the feasibility of the navigation method in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a structural diagram of the present invention.

[0042] Figure 2 It is a flow chart of the present invention.

[0043] Figure 3 It is a flow chart of navigation result effectiveness evaluation in the present invention.

[0044] Figure 4 It is a schematic diagram of the process of reducing the complexity and dimension of constrained fully symmetric polytopes in the present invention. DETAILED DESCRIPTION

[0045] The present invention is further described below in conjunction with the accompanying drawings.

[0046] In order to solve the problem that the current single-beam sonar seabed terrain assisted navigation method has high computational consumption and is difficult to handle unknown measurement noise distribution due to the particle filtering method, the present invention provides a seabed terrain assisted navigation method.

[0047] At the same time, in order to address the problem that in practical applications, the validity of navigation results cannot be known, which limits the application of terrain-assisted navigation methods, the present invention provides a method for evaluating the validity of navigation results. The method applies set membership filtering theory to the submarine terrain-assisted navigation method. On the basis of ensuring the robustness of the terrain-assisted navigation method, the computational consumption of the navigation method is effectively reduced, and efficient and robust submarine terrain-assisted navigation is achieved. The validity evaluation of the navigation results is completed by studying the set obtained by set membership filtering.

[0048] The specific process of the present invention is as follows:

[0049] Step 1: Using the inertial navigation system carried by the underwater vehicle as a reference, at the initial moment, obtain the horizontal position coordinates (x * ,y * ) and error range; (x * ,y *) as the center, under the premise of ensuring that the horizontal position coordinates of the underwater vehicle within the error range are all included, a constrained fully symmetric polytope with the smallest corresponding volume is constructed

[0050] in, To constrain the center of the fully symmetric polytope, is the generating vector constraining the fully symmetric polytope, and is a constraint condition;

[0051] Step 2: According to the inertial navigation system, obtain the motion vector of the underwater vehicle from the previous moment to the current moment, and update the constrained fully symmetric polytope at the previous moment The center position and generating vector of the constrained fully symmetric polytope after motion update are obtained

[0052]

[0053] Among them, u t-1 Represents the motion vector of the underwater vehicle from the previous moment to the current moment provided by the inertial navigation system; Represents the constrained fully symmetric polytope corresponding to the motion noise;

[0054] Step 3: Obtain the water depth measurement value of the underwater vehicle's current location based on the single-beam sonar and depth meter carried by the underwater vehicle;

[0055] Step 4: In the prior chart, set the search radius to (x * ,y * ) as the center to determine the search range and ensure that the actual position of the underwater vehicle is within the search range;

[0056] The terrain relief of each area is pre-calculated in the prior nautical chart, and the values ​​of the terrain relief of all areas are normalized to the range of 0.5-1;

[0057] The calculation method of terrain relief is:

[0058]

[0059] Where M and N are the length and width of the calculation area respectively; h(i,j) represents the water depth data at the position (i,j) in the prior nautical chart;

[0060] According to the error range of the inertial navigation system at the current moment obtained in step 1, determine the initial value R0 of the search radius, according to (x * ,y * ) is the normalized value of the terrain relief in the area The search radius R is set to:

[0061] Step 5: Within the search range of the prior chart, taking into account the error of the water depth measurement value, all the isobaths within the error range are extracted, and the extracted isobaths are discretized into isobath points; grid search is used to extract the center point of the grid within the error range;

[0062] Step 6: Outsource the extracted depth contour points and grid center points to constrained fully symmetric polytopes, and construct a constrained fully symmetric polytope with the smallest corresponding volume while ensuring that all depth contour points and grid center points are fully included.

[0063] Step 7: Calculation and The intersection of Will The geometric position center coordinates are used as the estimated value of the horizontal position coordinates of the underwater vehicle at the current moment;

[0064]

[0065] Where R is a matrix that satisfies

[0066] The center of the holosymmetric polytope is given by However, there are constraints on the fully symmetric polytope, which means that the center of the geometric position is no longer the center in the formula. Therefore, it is necessary to calculate the combined center coordinates based on the vertex coordinates. Given an example of a fully symmetric polytope and a constrained fully symmetric polytope, where the center is c Z =[1;1], the generator matrix is ​​G Z =[0 2 0 1; 0 0 2 1], constraint A Z =[-1 -1-1 1], b Z = [2]. At this time, the geometric center of the constrained fully symmetric polytope is c g =[2 / 3,2 / 3], so it is necessary to calculate the geometric center of the constrained fully symmetric polyhedron as the estimated position.

[0067] However, as the motion update proceeds, the order and dimension of the constrained fully symmetric polytope are gradually increasing, resulting in a large amount of computational consumption. Therefore, it is necessary to perform dimensionality and complexity reduction on the constrained fully symmetric polytope to reduce the computational consumption of the algorithm.

[0068] Dimensionality reduction is a two-step process. The first step is to eliminate constraints until constraint n c Reach the specified target and eliminate n c The process will also be accompanied by the elimination of an n g, so the complexity order is o d remains unchanged, and then the generator n g Perform dimensionality reduction to convert o d Reduce to the specified index range.

[0069] Calculate the system order and system dimension of the constrained fully symmetric polytope at this time. If the system complexity is greater than the set system order threshold and dimension threshold Rescaling is used to transfer information from the constraints to the generator. Without changing the fully symmetric polytope of the constraints, the unit hypercube is changed and linear changes are made on the unit hypercube to achieve the scaling of the unit hypercube, thereby reducing the constraint information. The complexity order calculation formula is as follows:

[0070] o d =(n g -n c ) / n

[0071] Among them, n g is the dimension of the generator, n c is the dimension of the constraint, and n is the dimension of the constrained fully symmetric polytope.

[0072] After rescaling, dimensionality reduction is performed on the high-dimensional constrained fully symmetric polytope, and the generated matrix is ​​reduced in dimensionality until it meets the threshold requirement;

[0073] Step 8: Obtain the water depth value at the current estimated value of the horizontal position coordinate of the underwater vehicle in the priori nautical chart, calculate the error between the water depth value and the water depth measurement value; and compare the error with Z xt The volume of is input into the validity evaluation function to obtain the validity evaluation result of the navigation result; if the navigation result at the current moment is determined to be valid, the estimated value of the horizontal position coordinate of the underwater vehicle at the current moment is fed back to the inertial navigation system for correction;

[0074] Single-beam sonar has limited single-shot measurement information and cannot evaluate the effectiveness of navigation results. As a result, although the terrain-assisted navigation output results are obtained, the effectiveness of the output position information cannot be known. The present invention uses twin support vector machines to evaluate the effectiveness of navigation results, completes the effectiveness evaluation of each matching result, and improves the effectiveness of terrain-assisted navigation methods in practical applications.

[0075] A training data set is constructed, and the difference between the water depth values ​​and the volume of the constrained fully symmetric polytope are used as the input of the twin support vector machine, and the navigation error is used as the output of the twin support vector machine. After training, the regression relationship between the difference between the volume of the constrained fully symmetric polytope and the water depth value and the effectiveness of the navigation result is obtained. The regression function is the effectiveness evaluation function.

[0076] The method for calculating the volume of a constrained fully symmetric polytope is as follows: the constrained fully symmetric polytope is used as a convex polyhedron to calculate the volume. The vertex coordinates corresponding to the convex polyhedron are obtained according to the constrained fully symmetric polytope, and the convex polyhedron is divided by Delaunay triangulation to obtain multiple triangles. After obtaining multiple triangles after triangulation, the area of ​​each triangle is calculated to obtain the area of ​​the convex polyhedron, which is the volume of the constrained fully symmetric polytope.

[0077] Step 9: If the underwater vehicle has not completed the mission, return to step 2 and continue navigation.

[0078] Combination Figure 1 The overall implementation method is explained. First, the water depth data is obtained through single-beam sonar and depth meter, and the inertial navigation system is used to provide attitude and reference trajectory. The appropriate search area is selected in the prior nautical chart according to the reference position provided by the inertial navigation, and the appropriate water depth data points are extracted through isobath / grid point extraction to constrain the fully symmetric polyhedral terrain-assisted navigation, and the matched corrected position is fed back to the inertial navigation system to correct the accumulated error of the inertial navigation system.

[0079] Combination Figure 2 The overall algorithm flow chart is described. The present invention first completes the initialization and motion update of the constrained fully symmetric polytope through the initial conditions and motion update information provided by the inertial navigation system, and uses the water depth information measured by the single-beam sonar and the depth meter to extract the isobath points / grid points that meet the measurement error range within the search range, and outsources the water depth points through the constrained fully symmetric polytope, calculates the intersection of the observed constrained fully symmetric polytope and the constrained fully symmetric polytope after the motion update, and outsources it with the new constrained fully symmetric polytope, calculates the order and complexity of the constrained fully symmetric polytope at this time, determines whether to execute the order and complexity reduction, calculates the geometric position center of the constrained fully symmetric polytope, estimates the matching position, evaluates the effectiveness of the navigation result, and determines whether to reach the end point.

[0080] Combination Figure 3 The implementation method of evaluating the effectiveness of navigation results is described. The volume of the constrained fully symmetric polytope and the water depth difference at the center of the geometric position are calculated based on the obtained motion-updated constrained fully symmetric polytope. The volume and water depth difference are used as the input of the twin support vector machine, and the navigation error is used as the output of the twin support vector machine. Data regression is performed to obtain the regression relationship between the constrained fully symmetric polytope parameters and the navigation results, and the effectiveness evaluation of the navigation results is completed.

[0081] Combination Figure 4Explain how to implement the complexity and dimensionality reduction of constrained fully symmetric polytopes. Calculate the order of the constrained fully symmetric polytope after the observation update, determine whether the order is greater than the set threshold, and if so, perform rescaling. Next, determine whether the dimension of the constrained fully symmetric polytope is greater than the set threshold. If so, perform system dimensionality reduction to generate a new constrained fully symmetric polytope.

[0082] In the seabed terrain-assisted navigation method, single-beam sonar is used as a measurement sensor to reduce system energy consumption, but the resulting lack of measurement information leads to poor robustness of the navigation results. Currently, particle filtering can achieve robust positioning results under poor information measurement, but the resulting computational burden makes it difficult to operate.

[0083] The present invention introduces the constrained fully symmetric polytope in the set membership filter into the seabed terrain assisted navigation method, reduces the operation consumption of the algorithm and can process the measurement noise of the unknown distribution of the low-resolution priori nautical chart. In the constrained fully symmetric polytope seabed terrain assisted navigation method, the appropriate water depth data is extracted by using isobaths and grid points in the priori nautical chart, and outsourced by the constrained fully symmetric polytope, so that the real water depth data is in the constrained fully symmetric polytope, without increasing the system calculation consumption, the robustness of the navigation method is improved, and the order and dimension of the system are calculated, and the complexity of the system is judged, so as to reduce the execution complexity and dimension, and further improve the operation efficiency of the algorithm. And the effectiveness of the navigation result is evaluated by the water depth difference and volume of the geometric position center of the constrained fully symmetric polytope, so as to improve the feasibility of the navigation method in practical applications.

[0084] The present invention fully considers the problems existing in the seabed terrain assisted navigation method using single-beam sonar as a measurement sensor and low-resolution priori nautical charts, and proposes corresponding solutions to improve the robustness of navigation results and complete the effectiveness evaluation of navigation results while maintaining low computing consumption.

[0085] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for assisting navigation based on seabed terrain, characterized in that: The following steps are involved: Step 1: At the initial moment, the horizontal position coordinates (x * ,y * ) and error range; (x * ,y * ) as the center, under the premise of ensuring that the horizontal position coordinates of the underwater vehicle within the error range are all included, a constrained fully symmetric polytope with the smallest corresponding volume is constructed Step 2: According to the inertial navigation system, obtain the motion vector of the underwater vehicle from the previous moment to the current moment, and update the constrained fully symmetric polytope at the previous moment The center position and generating vector of the constrained fully symmetric polytope after motion update are obtained Step 3: Obtain the water depth measurement value of the underwater vehicle's current location based on the single-beam sonar and depth meter carried by the underwater vehicle; Step 4: In the prior chart, set the search radius to (x * ,y * ) as the center to determine the search range and ensure that the actual position of the underwater vehicle is within the search range; Step 5: Within the search range of the prior chart, taking into account the error of the water depth measurement value, all the isobaths within the error range are extracted, and the extracted isobaths are discretized into isobath points; grid search is used to extract the center point of the grid within the error range; Step 6: Outsource the extracted depth contour points and grid center points to constrained fully symmetric polytopes, and construct a constrained fully symmetric polytope with the smallest corresponding volume while ensuring that all depth contour points and grid center points are fully included. Step 7: Calculation and The intersection of Will The geometric position center coordinates are used as the estimated value of the horizontal position coordinates of the underwater vehicle at the current moment; Step 8: Obtain the water depth value at the current time of the estimated horizontal position coordinate value of the underwater vehicle in the priori nautical chart, calculate the error between the water depth value and the water depth measurement value; and compare the error with The volume of is input into the validity evaluation function to obtain the validity evaluation result of the navigation result; if the navigation result at the current moment is determined to be valid, the estimated value of the horizontal position coordinate of the underwater vehicle at the current moment is fed back to the inertial navigation system for correction; Step 9: If the underwater vehicle has not completed the mission, return to step 2 and continue navigation.

2. The method for assisting navigation based on seabed terrain according to claim 1, characterized in that: The step 2 is specifically as follows: Among them, u t-1 Represents the motion vector of the underwater vehicle from the previous moment to the current moment provided by the inertial navigation system; Represents the constrained fully symmetric polytope corresponding to the motion noise.

3. The method for assisting navigation based on seabed terrain according to claim 1, characterized in that: The method for setting the search radius in step 4 is: The terrain relief of each area is pre-calculated in the prior nautical chart, and the values ​​of the terrain relief of all areas are normalized to the range of 0.5-1; According to the error range of the inertial navigation system at the current moment obtained in step 1, determine the initial value R0 of the search radius, according to (x * ,y * ) is the normalized value of the terrain relief in the area The search radius R is set to:

4. The method for assisting navigation based on seabed terrain according to claim 3, characterized in that: The calculation method of the terrain relief is: Where M and N are the length and width of the calculation area respectively; h(i,j) represents the water depth data at the position (i,j) in the prior nautical chart.

5. The method for assisting navigation based on seabed terrain according to claim 1, characterized in that: The calculation in step 7 and The intersection of Specifically: The constrained fully symmetric polytope is constructed as follows: Z=<c,G,A,b> Among them, c represents the center of the constrained fully symmetric polytope Z, G is the generating vector, and A and b are the constraints; and The intersection of The calculation method is: Where R is a matrix that satisfies 6. The method for assisting navigation based on seabed terrain according to claim 1, characterized in that: The method for obtaining the effectiveness evaluation function in step 8 is: A training data set is constructed, and the difference between the water depth values ​​and the volume of the constrained fully symmetric polytope are used as the input of the twin support vector machine, and the navigation error is used as the output of the twin support vector machine. After training, the regression relationship between the difference between the volume of the constrained fully symmetric polytope and the water depth value and the effectiveness of the navigation result is obtained. The regression function is the effectiveness evaluation function.

7. The method for assisting navigation based on seabed terrain according to claim 1, characterized in that: In step 7, we obtain the constrained fully symmetric polytope Z xt After that, the dimension and complexity are reduced to reduce the algorithm computational cost.

8. A computer device / equipment / system comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

Citation Information

Patent Citations

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