A cross-line based adaptive domain matching method

Abstract

The application relates to a cross-line adaptive domain matching method, which comprises the following steps: initially determining the nearest grid point position of the inertial navigation indicated position of an underwater vehicle on a gravity map; determining the half grid numbers in the horizontal direction and the vertical direction on the central cross-line with the nearest grid point position as the line center; if the best matching position and the best matching index value are not found on the central cross-line, determining the best matching index value on the four-way cross-line; if the best matching index value on the line is less than a set threshold value theta MSD during the period, jumping to step 10, otherwise, until the best matching index value is obtained; according to the best matching index value, determining the half grid numbers in the horizontal direction and the vertical direction of the adaptive domain; traversing the grid points in the domain to determine the best matching position in the domain, so as to correct the indicated position of the inertial navigation of the underwater vehicle. The application simultaneously improves the positioning efficiency and the out-of-domain matching performance of underwater gravity matching navigation.

Description

Technical Field

[0001] This invention relates to an adaptive domain matching method based on intersecting lines, belonging to the field of underwater navigation technology. Background Technology

[0002] Passive autonomous underwater navigation is a key technology for achieving long-duration, long-distance, and highly stealthy underwater navigation of submersibles. It primarily relies on a combination of inertial navigation and navigation based on matching information from geophysical fields (such as the Earth's magnetic or gravitational fields) or seabed geometry (such as seabed topography or landforms). In comparison, the Earth's gravitational field is less susceptible to the uncertainties of the marine environment and exhibits relative stability over long periods. Furthermore, gravity matching algorithms based on the gravity field have become a core research topic in underwater assisted inertial navigation.

[0003] Gravity matching algorithms are a core component of underwater passive navigation systems, and can be divided into single-point matching and sequence matching based on different sampling matching mechanisms. The TERCOM algorithm, as a representative of sequence matching, has received widespread attention and research due to its advantages such as insensitivity to initial position errors and strong matching robustness, aiming to improve the matching accuracy, efficiency, and reliability of underwater navigation. However, mismatches are sometimes unavoidable and significantly affect the matching accuracy and reliability of underwater navigation, while traversing and comparing a large number of grid points within the domain affects its positioning efficiency.

[0004] Existing research has found that intra-domain mismatches are relatively common and mainly caused by excessive initial inertial navigation errors, insufficient background matching features, or feature similarity. Out-of-domain mismatches, however, represent a new type of mismatch with even greater positioning errors. This refers to a phenomenon where the underwater vehicle's true position lies outside the effective matching domain boundary and is far from the optimal intra-domain matching position, severely impacting the underwater vehicle's actual navigation performance and even cumulatively leading to mission failure. Therefore, it is necessary to strengthen research on improving the out-of-domain matching performance of gravity matching algorithms to enhance their underwater navigation and positioning capabilities. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose an adaptive domain matching method based on cross lines to simultaneously improve the positioning efficiency and out-of-domain matching performance of underwater gravity matching navigation.

[0006] The solution of the present invention is:

[0007] An adaptive domain matching method based on intersecting lines includes:

[0008] Step 1: Initially determine the location of the nearest grid point on the gravity map for the inertial navigation indicator position of the underwater vehicle;

[0009] Step 2: Determine the number of half-grids in the horizontal and vertical directions on the center intersection line with the nearest grid point as the center.

[0010] Step 3: Calculate and determine the best matching position and its corresponding best matching index value on the horizontal line of the center intersection line, grid by grid.

[0011] Step 4, calculate the value i of the grid points on the horizontal line. Center The matching index value MSD corresponding to the horizontal grid point position;

[0012] Step 5: Update the best-match index value and best-match position on the horizontal line according to the MSD minimization principle. If the MSD value is updated, then compare the updated MSD value with the set threshold θ. MSD Compare sizes: If the updated MSD value is less than θ MSD If so, proceed to step 10; otherwise, i Center Increase by 1 and continue with step 3;

[0013] Step 6: Calculate and compare the best matching position and the best matching index value on the vertical line of the center intersection point by point;

[0014] Step 7, calculate the value j of the grid points on the vertical line. Center The matching index value MSD corresponding to the horizontal grid point position;

[0015] Step 8: Compare and update the best matching index value and best matching position on the vertical line according to the MSD minimization principle. If the MSD value is updated, then compare the updated MSD value with the set threshold θ. MSD Compare sizes: If the updated MSD value is less than θ MSD Then proceed to step 10; otherwise, j Center Increase by 1 and continue with step 6;

[0016] Step 9: If no optimal matching position or optimal matching index value is found on the central intersection line, then determine the optimal matching index value on the four-way intersection line; if an updated optimal matching index value exists during this period that is less than the set threshold θ. MSD If the result is positive, proceed to step 10; otherwise, continue until the best matching index value is obtained.

[0017] Step 10: Determine the number of half-grid points in the horizontal and vertical directions of the adaptive domain based on the best matching index value;

[0018] Step 11: Traverse the grid points within the domain to determine the best matching position within the domain, so as to correct the indicated position of the underwater vehicle's inertial navigation system.

[0019] Furthermore, the inertial navigation system indicates the coordinates of the nearest grid point on the gravity map as the endpoint. Its calculation formula is:

[0020]

[0021] In the formula, and represents the horizontal and vertical positions of the underwater vehicle's endpoint indicated by the inertial navigation system, respectively; R represents the grid resolution of the gravity map; and [·] represents rounding to the nearest integer.

[0022] Furthermore, the number of half-grids in the horizontal and vertical directions along the central intersection line with the nearest grid point as the line center. and Its calculation formula is:

[0023]

[0024] In the formula, σ x and σ y These represent the lateral and longitudinal drift errors of the inertial navigation system at the end of the trajectory, respectively. This indicates rounding up to the nearest integer.

[0025] Furthermore, the optimal matching position on the horizontal line of the center intersection is determined by calculating and comparing points grid by grid. and its corresponding best matching index value The value i of the grid point on the line. Center by Starting with and To terminate, when If necessary, proceed to step 6.

[0026] Furthermore, calculate the value i of the grid point on this line. Center Horizontal grid position The corresponding matching index value MSD is used to calculate the x-coordinate of the grid point.

[0027]

[0028] Furthermore, the best matching position on the vertical line of the center intersection is calculated and updated grid-by-grid for comparison. and best matching index value The value j of the grid point on the vertical line is... Center by Starting with and To terminate, when If necessary, continue with step 9.

[0029] Furthermore, in step 7, the value j of the grid points on the vertical line is calculated. Center Horizontal grid position The corresponding matching index value MSD is used to calculate the ordinate of the grid point.

[0030]

[0031] Calculation based on this grid point A reverse sequence of track positions ending at a specific point in time;

[0032] Calculate this grid point Approximate gravity sequence corresponding to gravity reference diagram With simulated gravity value sequence The matching index value MSD between them.

[0033] Furthermore, in step 9, the center position coordinates and the number of half-grids in the horizontal and vertical directions are redefined. Based on the order of steps 2-8, the optimal online matching position and its optimal matching index value on the upper right intersection line are determined, and the optimal matching index value is compared with the set threshold θ. MSD Compare the sizes; if it is less than θ MSD If the online matching terminates, proceed to step 10; otherwise, continue comparing the grid points on the upper right cross line until the last grid point on the upper right cross line. If step 10 is not executed yet, proceed in the order of lower right, lower left, and upper left. If, during this process, the updated best online matching index value is less than the set threshold θ, the process continues. MSD If the result is positive, proceed to step 10; otherwise, continue until the optimal online matching position and the optimal matching index value are obtained.

[0034] Furthermore, calculations are performed using this grid point. The reverse sequence of track positions with the endpoint as the k-th reverse position (x) on the northeast-bound track of the underwater vehicle. k ,y k The formula for calculating ) is

[0035]

[0036] Where v and θ represent the speed and heading on the underwater vehicle's track, respectively, and ε v and ε θ The speed error and heading error of the track are respectively defined, where L represents the total number of sampling points on the track, and Δt represents the time interval between sampling points on the track.

[0037] Furthermore, extract track sampling points (x) k ,y k The approximate gravity sequence of the track sampling points is obtained by taking the gravity values ​​of the nearest neighbor grid points on the gravity reference map. And compared with the corresponding gravity value sequence of the simulated gravimeter. The MSD (Mean Score) is calculated using the following formula:

[0038]

[0039] The beneficial effects of this invention compared to the prior art are:

[0040] This invention improves the positioning efficiency and matching accuracy of underwater gravity matching navigation, calibrates the sensor parameters of the inertial navigation system, and assists in completing long-term, long-distance, high-precision navigation missions for underwater vehicles. Attached Figure Description

[0041] Figure 1 The flowchart shows the execution process of the cross-line adaptive domain matching method.

[0042] Figure 2 Gravity reference map (a) and water depth map (b) for a simulated area of ​​the South China Sea;

[0043] Figure 3 Comparison of localization performance for out-of-domain mismatch testing (a) and location matching (b);

[0044] Figure 4 This illustrates the matching efficiency of the CADM algorithm.

[0045] Figure 5 This is a schematic diagram of high-precision out-of-domain positioning using the CADM algorithm. Detailed Implementation

[0046] The present invention will be further described below with reference to the embodiments.

[0047] An adaptive domain matching method based on cross lines, such as Figure 1 As shown, it includes:

[0048] Step 1: Determine the coordinates of the nearest grid point on the gravity (anomaly) map for the inertial navigation indicator endpoint. Its calculation formula is:

[0049]

[0050] In the formula, and represents the horizontal and vertical positions of the underwater vehicle's endpoint indicated by the inertial navigation system, respectively; R represents the grid resolution of the gravity (anomaly) map; and [·] represents rounding to the nearest integer.

[0051] Step 2, calculate with The number of half-grids in the horizontal and vertical directions on the center intersection line of the line center. and Its calculation formula is:

[0052]

[0053] In the formula, σ x and σ y These represent the lateral and longitudinal drift errors of the inertial navigation system at the end of the trajectory, respectively. This indicates rounding up to the nearest integer.

[0054] Step 3: Calculate and compare the grid points on the horizontal line of the center intersection to determine the best matching position on the line. and its corresponding best matching index value The value i of the grid point on the line. Center by Starting with and To terminate, when If necessary, proceed to step 6.

[0055] Step 4, calculate the value i Center Horizontal grid position The corresponding matching index value MSD. Specifically, (1), the formula for calculating the x-coordinate of this grid point is:

[0056]

[0057] (2) Calculate using this grid point The sequence of reverse track positions ending at a point in time, taking the northeastward course of an underwater submersible as an example, shows the reverse position (x) of its k-th track. k ,y k The formula for calculating ) is

[0058]

[0059] Where v and θ represent the speed and heading (north-east) of the underwater vehicle along its track, respectively, and ε v and ε θ The speed error and heading error of the track are respectively defined, where L represents the total number of sampling points on the track, and Δt represents the time interval between sampling points on the track.

[0060] (3) Extract track sampling points (x k ,y k The approximate gravity sequence of track sampling points is obtained by taking the gravity values ​​of the nearest neighbor grid points on the gravity (anomaly) baseline map. And compared with the corresponding gravity value sequence of the simulated gravimeter. The MSD (Mean Score) is calculated using the following formula:

[0061]

[0062] Step 5: Compare and update the best-matching index value at this horizontal line according to the MSD minimization principle. and best matching position If MSD value is updated Then, with the set threshold θ MSD =0.1 Compare sizes: If the updated Less than θ MSD Then proceed to step 11; otherwise, iCenter Increase by 1 and continue with step 3.

[0063] Step 6: Calculate and update the best matching position on the vertical line of the center intersection point by point and compare the results. and best matching index value The value j of the grid point on the vertical line is... Center by Starting with and To terminate, when If necessary, continue with step 9.

[0064] Step 7, calculate the value j Center Horizontal grid position The corresponding matching index value MSD is used to calculate the ordinate of the grid point.

[0065]

[0066] Similar to step 4(2), the calculation is performed using this grid point. The reverse sequence of track positions for the endpoint; similar to step 4(3), calculate the grid point. Approximate gravity sequence corresponding to gravity (anomaly) baseline map With simulated gravity value sequence The matching index value MSD between them.

[0067] Step 8: Compare and update the best matching index value on the vertical line according to the MSD minimization principle. and best matching position If MSD value is updated Then, with the set threshold θ MSD Compare sizes: If new Less than θ MSD Then proceed to step 11; otherwise, j Center Increase by 1 and continue with step 6.

[0068] Step 9: Determine the optimal matching position on the upper right cross line of the four-way cross line. and its best matching index value (1) Calculate the coordinates of the center position of the upper right intersection line. Its calculation formula is:

[0069]

[0070] (2), Calculate Number of half-grids in the horizontal and vertical directions on the four-way intersection line centered on the grid and Its calculation formula is:

[0071]

[0072] (3) Similar to steps 3 to 5, determine the optimal matching index value on the horizontal line of the upper right cross line. and best matching position And compare the threshold θ in a timely manner MSD Jump to step 11.

[0073] (4) Similar to steps 6 to 8, determine the optimal matching index value on the vertical line of the upper right intersection line. and best matching position And compare the threshold θ in a timely manner MSD Jump to step 11.

[0074] Step 10, similar to step 9, involves taking the value of the vertical grid point of the upper right intersection line. Then, continue to determine the optimal matching index value of the four-way crossover in the order of "bottom right → bottom left → top left". and best matching position And compare the threshold θ in a timely manner MSD Jump to step 11.

[0075] Step 11: Determine the number of half-grid points in the horizontal and vertical directions of the adaptive domain. and Its calculation formula is:

[0076]

[0077] in, and Let these represent the horizontal and vertical half-side lengths of the adaptive domain, respectively. The horizontal half-side length of the adaptive domain is... The calculation formula is

[0078]

[0079] Similarly, with σ y Substitute σ x The length of the half-side of the adaptive domain in the vertical direction can be obtained.

[0080] Step 12, determine the best matching position (x) within the domain. Best ,y Best The x-coordinate of its grid point is i. Domain by Starting with and The terminator is defined as the ordinate with value j. Domain by Starting with and To terminate, the best online match position will be used. With i as the center of the domain Do m and j Domain The grid positions for the horizontal and vertical grid points are respectively. Its calculation formula is:

[0081]

[0082] Step 13, similar to steps 4(2) and (3), calculates the grid point. The corresponding matching index value MSD.

[0083] Step 14: Compare and update according to the minimum principle to obtain the best matching position (x) within the domain. Best ,y Best This is used to correct the inertial navigation system's indicated position for the underwater vehicle.

[0084] Example

[0085] The simulation test area is the South China Sea, encompassing its latitude and longitude. Gravity data with a resolution of 1'×1' was downloaded from the University of California, San Diego website (http: / / topex.ucsd.edu / ), and then proportionally scaled down to a 100m×100m gravity map using bilinear interpolation, as shown below. Figure 2 As shown in (a), it has been proven to provide a test platform for rapid simulated navigation. Furthermore, to ensure the navigation safety of the underwater vehicle, a water depth threshold of 200m is used as the navigable depth threshold. The water depth at sampling points on the simulated trajectory should not be lower than this threshold. A 3D water depth diagram of the simulated sea area is shown below. Figure 2 As shown in (b).

[0086] The number of sampling points for the simulated underwater trajectory was 110, and the sampling period of the gravity sensor was 20s. Other simulated sensor and trajectory parameter settings are shown in Table 1. To ensure the fairness of the test results, the traditional TERCOM algorithm (3σ) was used as the comparison algorithm. Each experimental group independently conducted 10,000 tests, and the matching accuracy and positioning time of each test were recorded. The mean, standard deviation, worst, and best values ​​of the matching accuracy of all tests, as well as the average positioning time (T), were used as evaluation indicators for the matching navigation performance.

[0087] Table 1 Parameter settings for simulated flight paths

[0088]

[0089] 3.2 Results and Analysis

[0090] Using the grid point (700, 1800) on the gravity map as the starting point of the trajectory, a simulated underwater vehicle trajectory was generated using the sensor and trajectory parameters set in Table 1. To ensure the fairness of the comparative evaluation, TERCOM was used to independently perform 10,000 matching runs, and its simulated measured gravity sequence, INS indication of the endpoint position, and other original test data were used as inputs to the CADM algorithm to ensure that both had the same environmental configuration. The comparison results were recorded and statistically analyzed, as shown in Table 2.

[0091] Table 2 Comparative statistics of all matching tests

[0092]

[0093]

[0094] As shown in Table 2, the proposed CADM algorithm outperforms the TERCOM algorithm in matching accuracy and average localization time across all tests. In particular, its overall worst-case localization accuracy and matching efficiency are improved by 74.42% and 82.57% respectively compared to TERCOM. Analyzing from different test categories, the CADM algorithm significantly reduces the number of out-of-domain false matches by TERCOM (36→1), a reduction of 97.22%. All four out-of-domain matching accuracy metrics of CADM show significant improvements, with relative increases of 82.52%, 85.84%, 82.57%, and 68.93% respectively. Figure 3 The diagram visually demonstrates the high positioning accuracy and excellent matching position of the CADM algorithm; its corresponding matching efficiency is improved by 56.89%. In tests of both intra-domain mismatches and non-mismatches, the CADM algorithm not only maintains relatively equivalent matching index values ​​but also significantly improves the matching efficiency of underwater navigation, with relative improvements of 74.48% and 74.67%, respectively. These results fully validate the high positioning efficiency and excellent extra-domain matching accuracy of the CADM algorithm in underwater gravity-matching navigation.

[0095] Note: In non-mismatch tests, the Mean and STD values ​​of the CADM algorithm are slightly improved because the algorithm proposed in this paper can adaptively break the boundary restrictions of the TERCOM matching domain. For the true position of the submersible outside the TERCOM matching domain but where no mismatch occurs, the positioning accuracy can be improved to a certain extent according to probability.

[0096] To further analyze the reasons for the high efficiency of CADM algorithm in matching and the high accuracy of out-of-domain positioning, the following diagrams are drawn: Figure 4 and Figure 5 .

[0097] Depend on Figure 4Analysis shows that the proposed CADM algorithm achieves high efficiency in matching the true position of the underwater vehicle by pre-matching the limited grid points of the intersecting lines and performing a decisional jump to re-match the relatively few grid points in the adaptive domain. It effectively avoids the problem of excessively long underwater navigation matching time caused by the indiscriminate traversal search of a large number of grid points in a large matching domain. Figure 5 This indicates that the proposed CADM algorithm can break the inherent boundary limitations of TERCOM and achieve efficient and high-precision positioning of the underwater vehicle's real location outside the domain by generating and re-matching adaptive matching domain grid points.

[0098] The above results and analysis effectively verify the high matching efficiency, high out-of-domain positioning reliability, and excellent matching accuracy of the CADM algorithm proposed in this invention.

[0099] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A cross-line adaptive domain matching method, characterized in that, include: Step 1: Initially determine the location of the nearest grid point on the gravity map for the inertial navigation indicator position of the underwater vehicle; Step 2: Determine the number of half-grids in the horizontal and vertical directions on the center intersection line with the nearest grid point as the center. Step 3: Calculate and determine the best matching position and its corresponding best matching index value on the horizontal line of the center intersection line, grid by grid. Step 4, calculate the value i of the grid points on the horizontal line. Center The matching index value MSD corresponding to the horizontal grid point position; Step 5: Update the best-match index value and best-match position on the horizontal line according to the MSD minimization principle. If the MSD value is updated, then compare the updated MSD value with the set threshold θ. MSD Compare sizes: If the updated MSD value is less than θ MSD If so, proceed to step 10; otherwise, i Center Increase by 1 and continue with step 3; Step 6: Calculate and compare the best matching position and the best matching index value on the vertical line of the center intersection point by point; Step 7, calculate the value j of the grid points on the vertical line. Center The matching index value MSD corresponding to the horizontal grid point position; Step 8: Compare and update the best matching index value and best matching position on the vertical line according to the MSD minimization principle. If the MSD value is updated, then compare the updated MSD value with the set threshold θ. MSD Compare sizes: If the updated MSD value is less than θ MSD Then proceed to step 10; otherwise, j Center Increase by 1 and continue with step 6; Step 9: If no optimal matching position or optimal matching index value is found on the central intersection line, then determine the optimal matching index value on the four-way intersection line; if an updated optimal matching index value exists during this period that is less than the set threshold θ. MSD If the result is positive, proceed to step 10; otherwise, continue until the best matching index value is obtained. Step 10: Determine the number of half-grid points in the horizontal and vertical directions of the adaptive domain based on the best matching index value; Step 11: Traverse the grid points within the domain to determine the best matching position within the domain, so as to correct the indicated position of the underwater vehicle's inertial navigation system.

2. The method for adaptive domain matching based on intersecting lines according to claim 1, characterized in that, The inertial navigation system indicates the coordinates of the nearest grid point on the gravity map. Its calculation formula is: In the formula, and represents the horizontal and vertical positions of the underwater vehicle's endpoint indicated by the inertial navigation system, respectively; R represents the grid resolution of the gravity map; and [·] represents rounding to the nearest integer.

3. The method for adaptive domain matching based on intersecting lines according to claim 1, characterized in that, The number of half-grids in the horizontal and vertical directions on the center intersection line with the nearest grid point as the center. and Its calculation formula is: In the formula, σ x and σ y These represent the lateral and longitudinal drift errors of the inertial navigation system at the end of the trajectory, respectively. This indicates rounding up to the nearest integer.

4. The method for adaptive domain matching based on intersecting lines according to claim 1, characterized in that, The best matching position on the horizontal line of the center intersection is determined by calculating and comparing points grid by grid. and its corresponding best matching index value The value i of the grid point on the line. Center by Starting with and To terminate, when If necessary, proceed to step 6.

5. The method for adaptive domain matching based on intersecting lines according to claim 1, characterized in that, Calculate the value i of the grid point on the line. Center Horizontal grid position The corresponding matching index value MSD is used to calculate the x-coordinate of the grid point.

6. The method for adaptive domain matching based on intersecting lines according to claim 1, characterized in that, Calculate and compare the best matching position on the vertical line of the center intersection point by point and update it accordingly. and best matching index value The value j of the grid point on the vertical line is... Center by Starting with and To terminate, when If necessary, continue with step 9.

7. The method for adaptive domain matching based on intersecting lines according to claim 1, characterized in that, In step 7, the value j of the grid point on the vertical line is calculated. Center Horizontal grid position The corresponding matching index value MSD is used to calculate the ordinate of the grid point. Calculation based on this grid point A reverse sequence of track positions ending at a specific point in time; Calculate this grid point Approximate gravity sequence corresponding to gravity reference diagram With simulated gravity value sequence The matching index value MSD between them.

8. The method for adaptive domain matching based on intersecting lines according to claim 1, characterized in that, In step 9, the center position coordinates and the number of half-grids in the horizontal and vertical directions are redefined. Based on the order of steps 2-8, the optimal online matching position and its optimal matching index value on the upper right intersection line are determined, and the optimal matching index value is compared with the set threshold θ. MSD Compare the sizes; if it is less than θ MSD If the online matching terminates, proceed to step 10; otherwise, continue comparing the grid points on the upper right cross line until the last grid point on the upper right cross line. If step 10 is not executed yet, proceed in the order of lower right, lower left, and upper left. If, during this process, the updated best online matching index value is less than the set threshold θ, the process continues. MSD If the result is positive, proceed to step 10; otherwise, continue until the optimal online matching position and the optimal matching index value are obtained.

9. The adaptive domain matching method based on intersecting lines according to claim 5, characterized in that, Calculation based on this grid point The reverse sequence of track positions with the endpoint as the k-th reverse position (x) on the northeast-bound track of the underwater vehicle. k ,y k The formula for calculating ) is Where v and θ represent the speed and heading on the underwater vehicle's track, respectively, and ε v and ε θ The speed error and heading error of the track are respectively defined, where L represents the total number of sampling points on the track, and Δt represents the time interval between sampling points on the track.

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