Method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small domain matching

Abstract

The application relates to a method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching. First, the optimal position of a grid line is determined, a new grid line is generated in the 'horizontal-to-vertical' direction alternately, and a new matching is performed until the pre-matching process on the self-adaptive termination line is terminated, and a line optimal matching position close to the real position of the underwater vehicle is obtained. Second, a small grid domain is formed with the line optimal matching position as the center, and the optimal matching position in the domain is determined according to the minimum matching index value principle, and finally, the sensor parameters of the inertial navigation system are calibrated to improve the positioning efficiency, matching reliability and other performances of underwater navigation. The experimental results verify that the algorithm has relatively excellent comprehensive matching performance in underwater gravity aided navigation, and three different gravity area track tests show that the positioning efficiency is improved by an average of 93% relative to TERCOM, and the relative reduction of the out-of-domain mismatching frequency is as high as 94%, and the algorithm has good positioning applicability in different gravity areas.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary fields of underwater navigation and artificial intelligence, and relates to a method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching. Background Technology

[0002] Underwater Gravity Aided Navigation (UGAN), as an alternative to inertial navigation systems (INS), is crucial for underwater vehicles to achieve long-endurance, long-distance, and high-precision underwater navigation missions. INS cannot independently meet the high requirements of underwater navigation missions due to the time-cumulative divergence of errors from inertial sensors (such as accelerometers and gyroscopes). Therefore, underwater assisted navigation technologies based on inherent Earth information (such as gravity, geomagnetism, and topography) have emerged. Benefiting from the long-term relative stability of the Earth's gravity (gradient) field, which is not easily affected by complex marine environments such as waves and tides, gravity-assisted navigation technology has become a hot research topic in the field of underwater passive navigation and positioning.

[0003] One of the key modules of gravity-assisted navigation is the gravity matching algorithm, whose performance affects the positioning reliability, efficiency, and accuracy of underwater navigation. Currently, gravity matching algorithms can be divided into two categories: single-point matching and sequence matching. In comparison, sequence matching determines the optimal calibration position of the submersible through the optimal correlation principle of a certain number of sampling points (not single points), exhibiting strong matching reliability; however, its high positioning time consumption problem remains to be solved. Typical examples of sequence matching algorithms include the Terrain Contour Matching (TERCOM) algorithm and the Iterative Nearest Contour Point (ICCP) algorithm. The TERCOM algorithm has good matching robustness and, compared to the ICCP algorithm, shows insensitivity to initial position errors. Therefore, gravity-assisted navigation technology based on the TERCOM algorithm has become an important component of underwater navigation and positioning. However, the TERCOM algorithm has two potential problems: 1) the inefficiency or time delay caused by traversing all points within its matching grid domain; 2) the limited features or smoothness within its matching domain lead to (within the domain) mismatches with large positioning errors between its optimal matching grid point and the submersible's true position, thus limiting its matching reliability. Therefore, improving the localization efficiency and matching reliability of the TERCOM algorithm has become two important research topics.

[0004] Mismatches are a major factor affecting the reliability of TERCOM underwater gravity-assisted navigation matching. Therefore, many scholars have conducted a series of studies on the causes and diagnostic analysis of mismatches. Wang S. et al. pointed out that the TERCOM algorithm has poor matching reliability in areas with similar feature distributions, believing that excessive initial inertial navigation error and insufficient background features are the two main reasons for mismatches. They proposed a similarity extreme value detection method for TERCOM mismatch diagnosis to improve TERCOM matching performance. Yan L. et al. pointed out that low gravity reference map resolution also leads to large positional errors in TERCOM. Wang K. et al., taking underwater terrain matching as an example, systematically analyzed the impact of terrain accuracy, map resolution, and initial inertial navigation error on TERCOM matching errors and gave verifiable conclusions regarding TERCOM mismatches. Wang J. et al. pointed out that the COR (Cross Correlation) index can lead to TERCOM mismatches to some extent, while MSD (Mean Squared Difference) is an effective matching index for determining the most relevant position, and its accuracy is slightly higher than MAD (Mean Absolute Difference) and COR. Wu L. et al. proposed a new underwater gravity-assisted navigation method by constructing a gravity pattern based on the relative positions between points indicated by the INS track and applying constraints during the matching process to eliminate the cumulative position error of the INS. Simulation results show that it significantly improves both positioning accuracy and matching success rate. Han Y. et al. pointed out that the large resolution of the reference map and the uncertainty of the gravity anomaly distribution can lead to TERCOM mismatches. They proposed a mismatch diagnosis method based on image registration (constrained spatial order constraint algorithm) by combining spatial order constraints with decision criterion constraints to improve TERCOM mismatch screening and matching accuracy. Dai T. et al. pointed out that the mismatch probability of matching algorithms such as TERCOM and ICCP is high when the features of the matching area are smooth. They proposed a real-time mismatch detection method by selecting a fitting model of the submersible navigation characteristics, mismatch detection by affine transformation between tracks, and track distance ratio constraints to achieve effective detection of mismatch points and improve the reliability of the matching algorithm. Wang R. et al. mentioned that TERCOM is susceptible to measurement errors in low-matching areas, resulting in false peaks or mismatches. They proposed a particle filter initialization method based on nonlinear multi-terrain assisted fusion positioning to improve positioning stability and accuracy.

[0005] However, these studies primarily focus on intra-domain mismatches, where the submersible's true location lies within the effective TERCOM matching domain. The causes of these mismatches include the limited features of flat (smooth) matching regions or small differences in neighboring evaluation index values ​​within the matching region. On the other hand, research on extra-domain mismatches is relatively scarce, where the submersible's true location lies outside the effective TERCOM matching domain. The main causes of extra-domain mismatches include the finiteness of the TERCOM matching grid domain boundaries or the proximity similarity of index values ​​within the domain (the causes of which are similar to those of intra-domain mismatches).

[0006] This research team proposes a soft-interval local semi-circular domain re-search method for underwater gravity-assisted navigation by utilizing the boundary determination of the 3σ soft circular domain and its single-time out-of-domain semi-circular domain re-search mechanism to improve the positioning reliability of the underwater vehicle's true position outside the domain. Furthermore, a domain center adaptive migration matching method (DAMM) is proposed, which constructs a domain center adaptive migration mechanism on the horizontal and vertical pre-matching lines and an adaptive domain generation mechanism based on the index value of the optimal line position to improve the positioning reliability and matching efficiency of the underwater vehicle's true position outside the domain. Test results show that the proposed algorithm achieves an average relative improvement in matching efficiency of approximately 70% in 10,000 tests on three simulated tracks, but the average improvement in efficiency for out-of-domain mismatch tests is only about 30%. The reason for this is that the optimal positions on the horizontal and vertical pre-matching lines are relatively far from the actual position of the submersible, and a larger matching grid domain is adaptively generated to cover its actual position, thus limiting the improvement of matching efficiency. At the same time, the DAMM algorithm limits the maximum half-side length (2.5σ) of the adaptive domain grid to control matching efficiency. Due to the randomness of the drift of the actual position outside the inertial navigation indication domain, a certain amount of mismatches outside the domain still occur. Therefore, there is an urgent need to propose new methods to improve the positioning efficiency and matching reliability of underwater gravity-assisted navigation. Summary of the Invention

[0007] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for improving underwater navigation efficiency and off-domain reliability based on alternating line small-domain matching.

[0008] The technical solution of this invention is:

[0009] This invention discloses a method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching, including:

[0010] Step 1: Determine the coordinates of the nearest neighbor grid point of the inertial navigation indicator's endpoint on the gravity reference map;

[0011] Step 2: Using the coordinates of the nearest neighbor grid point as the center starting point, and employing an alternating horizontal and vertical grid line generation mode, calculate the optimal position on the line that satisfies the pre-matching termination condition of the alternating line.

[0012] Step 3, at the optimal position on the line. Generate local small domains centered on the target;

[0013] Step 4: Calculate the number of horizontal and vertical half-grids in the local small region. and

[0014] Step 5: Calculate the coordinates of the grid points within the local sub-domain based on the number of horizontal and vertical half-grids.

[0015] Step 6: Calculate the grid points within the local small domain. Matching index value

[0016] Step 7: Select the grid point with the smallest matching index value within the local sub-domain as the optimal matching location within the local sub-domain.

[0017] Furthermore, in the aforementioned reliability method, the method employs an alternating horizontal and vertical grid line generation pattern to calculate the optimal position on the line that satisfies the pre-matching termination condition of the alternating lines. Specifically:

[0018] S11. Calculate the matching index value of the h-th horizontal grid line. Best match position online Where h is a positive integer;

[0019] S12. Determine the matching index value of the h-th horizontal grid line. Is it less than the matching metric threshold θ? MSD If yes, then the best matching position on the h-th horizontal grid line is the best position on the line, and the calculation is terminated; otherwise, proceed to step S13.

[0020] S13, using the best matching position on the h-th horizontal grid line. Given the center coordinates of the (h+1)th vertical grid line, calculate the matching index value and the optimal matching position on the (h+1)th vertical grid line.

[0021] S14. Determine whether the best matching position on the (h+1)th vertical grid line is equal to the best matching position on the (h)th horizontal grid line. If yes, the best matching position on the (h+1)th vertical grid line is the best position on the line, and exit the calculation. If no, repeat steps S11 to S13.

[0022] Furthermore, in the above reliability method, taking the coordinates of the nearest neighbor grid point as the center starting point specifically means that the center starting point is a horizontal grid line or a vertical grid line.

[0023] Furthermore, in the above reliability method, the calculation of the number of horizontal and vertical half-grids of the local small domain is... and Specifically:

[0024]

[0025] in, The half-side length regulation factor for the small domain; and These represent the accumulated lateral and longitudinal drift errors of the inertial navigation system during navigation, respectively. This indicates rounding up; R is the grid resolution of the gravity reference map.

[0026] Furthermore, in the above reliability method, the coordinates of the grid points within the domain Specifically:

[0027]

[0028]

[0029]

[0030] in, To meet the optimal position on the line that satisfies the pre-matching termination condition of the alternating line, and R represents the number of horizontal and vertical half-grids in a local small region, and R is the grid resolution of the gravity reference map.

[0031] Furthermore, in the above reliability method, the calculation of each grid point within the local small domain... Matching index value Specifically:

[0032]

[0033] in, This is a sequence of gravity extraction on a map, with each grid point within a local small region as the endpoint of the track. The gravity sequence G measured by the gravity sensor at the sampling point of the underwater vehicle's trajectory. Measured The reversed vector, L is the number of sampling points of the underwater vehicle track on the track S to be matched.

[0034] Furthermore, in the above reliability method, determining the coordinates of the nearest neighbor grid point of the inertial navigation indicator endpoint on the gravity reference map specifically involves:

[0035]

[0036] Where R represents the grid resolution of the gravity reference map, and [·] indicates rounding to the nearest integer. The inertial navigation system indicates the endpoint position.

[0037] Furthermore, in the aforementioned reliability method, the map gravity extraction sequence with each grid point within a local small domain as the trajectory endpoint specifically includes:

[0038] Determine the coordinates of L estimated positions on the reverse track S corresponding to each grid point within a local small domain;

[0039] Based on the coordinates of the calculated position, and following the nearest neighbor principle, determine the nearest neighbor grid point on the gravity map for each position point of the reverse trajectory S within the local small domain.

[0040] The gravity values ​​of the nearest neighbor grid points are extracted to obtain a gravity extraction sequence on the map with grid points in a local small domain as the endpoints of the track.

[0041] Furthermore, in the above reliability method, determining the coordinates of the L estimated positions on the reverse track S corresponding to each grid point within the local small domain specifically involves:

[0042]

[0043] Where i = 1, 2, ..., L, ε v and ε β These represent the disturbance deviations of the underwater vehicle's speed v and heading β, respectively. Let j and k be the coordinates of the grid points on the horizontal and vertical lines within a local small domain.

[0044] Furthermore, in the aforementioned reliability method, when the center starting point is simultaneously on both the horizontal and vertical grid lines, an alternating generation mode of the grid lines is adopted to calculate the optimal position on the line that satisfies the pre-matching termination condition of the alternating lines in parallel. The optimal position on the line that first satisfies the alternating line pre-matching termination condition in parallel computing. This is the final optimal position.

[0045] The advantages of this invention compared to the prior art are:

[0046] (1) This invention breaks the traditional traversal matching mode of all grid points in the TERCOM domain and constructs a pre-matching method based on alternating line grid points to quickly approximate the real position of the underwater vehicle, or even the real position outside the 3σ domain.

[0047] (2) This invention abandons the matching of a large number of invalid grid points in a large area, and takes the best matching position on the alternating line as the center and supplements the re-matching mechanism of small area grid points to effectively cover and accurately locate the real position of the underwater vehicle.

[0048] (3) This invention proposes a novel alternating line small-domain matching method that integrates alternating line pre-matching and small-domain rematching to improve the overall performance of underwater gravity-assisted navigation, such as positioning efficiency and reliability of out-of-domain matching.

[0049] (4) The simulation test results of the three tracks in different gravity zones of the present invention show that the positioning efficiency of the proposed algorithm is improved by 93% compared with the TERCOM algorithm, and the relative reduction in the number of mismatches outside the domain is as high as 94%. Attached image description:

[0050] Figure 1 This is a flowchart of the method of the present invention;

[0051] Figure 2 These are two examples of mismatches in the TERCOM matching principle of this invention: (a) intra-domain mismatch; (b) inter-domain mismatch.

[0052] Figure 3 The simulated sea area of ​​the South China Sea in this invention; (a) gravity anomaly map; (b) 3D topographic map;

[0053] Figure 4 This invention provides a comparative analysis of the ALSM algorithm's localization performance in the TERCOM out-of-domain mismatch test.

[0054] Figure 5 Examples of the positioning efficiency of the ALSM algorithm under different termination criteria of alternating lines in this invention: (a) small threshold type; (b) position invariant type;

[0055] Figure 6 To ensure high reliability of out-of-domain matching in the ALSM algorithm of this invention: (a) general matching type; (b) convex matching type; (c) migration matching type;

[0056] Figure 7 This is an example of the efficient and reliable out-of-domain matching of the ALSM algorithm of this invention;

[0057] Figure 8 This diagram illustrates the comparison of out-of-domain mismatch results based on different matching mechanisms under different flight paths according to the present invention. Detailed Implementation

[0058] The working principle and process of the present invention will be further explained and described below with reference to the accompanying drawings.

[0059] This invention discloses a method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching, including:

[0060] Step 1: Determine the coordinates of the nearest neighbor grid point of the inertial navigation indicator's endpoint on the gravity reference map;

[0061] Step 2: Using the coordinates of the nearest neighbor grid point as the starting point, and employing an alternating horizontal and vertical grid line generation pattern, calculate the optimal position on the line that satisfies the pre-matching termination condition of the alternating line.

[0062] Step 3, use the best online position Generate local small domains centered on the target;

[0063] Step 4: Calculate the number of horizontal and vertical half-grids in the local small region. and

[0064] Step 5: Calculate the coordinates of the grid points within the local sub-domain based on the number of horizontal and vertical half-grids.

[0065] Step 6: Calculate the grid points within the local small domain. Matching index value

[0066] Step 7: Select the grid point with the smallest matching index value within the local sub-domain as the optimal matching location within the local sub-domain.

[0067] Preferably, an alternating horizontal and vertical grid line generation pattern is used to calculate the optimal position on the line that satisfies the pre-matching termination condition of the alternating lines. Specifically:

[0068] S11. Calculate the matching index value of the h-th horizontal or vertical grid line. Best match position online Where h is a positive integer;

[0069] S12. Determine the matching index value of the h-th horizontal or vertical grid line. Is it less than the matching metric threshold θ? MSD If yes, then the best matching position on the h-th horizontal or vertical grid line is the best position on the line, and the calculation is terminated; otherwise, proceed to step S13.

[0070] S13, using the best matching position on the line of the h-th horizontal or vertical grid point. Given the center coordinates of the (h+1)th vertical or horizontal grid point, calculate the matching index value and the optimal matching position on the (h+1)th vertical or horizontal grid point.

[0071] S14. Determine whether the best matching position on the (h+1)th vertical or horizontal grid line is equal to the best matching position on the (h)th horizontal or vertical grid line. If yes, the best matching position on the (h+1)th vertical or horizontal grid line is the best position on the line, and exit the calculation. If no, repeat steps S11 to S13.

[0072] Preferably, the center starting point is on the horizontal grid line, or on the vertical grid line, or simultaneously on both the horizontal and vertical grid lines.

[0073] Preferably, the number of horizontal and vertical half-grids in the local small region is calculated. and Specifically:

[0074]

[0075] in, The half-side length regulation factor for the small domain; and These represent the accumulated lateral and longitudinal drift errors of the inertial navigation system during navigation, respectively. This indicates rounding up; R is the grid resolution of the gravity reference map.

[0076] Preferably, the coordinates of the grid points within the domain Specifically:

[0077]

[0078]

[0079]

[0080] in, To meet the optimal position on the line that satisfies the pre-matching termination condition of the alternating line, and R represents the number of horizontal and vertical half-grids in a local small region, and R is the grid resolution of the gravity reference map.

[0081] Preferably, each grid point within a local small domain is calculated. Matching index value Specifically:

[0082]

[0083] in, This is a sequence of gravity extraction on a map, with each grid point within a local small region as the endpoint of the track. The gravity sequence G measured by the gravity sensor at the sampling point of the underwater vehicle's trajectory. Measured The reversed vector, L is the number of sampling points of the underwater vehicle track on the track S to be matched.

[0084] Preferably, the coordinates of the nearest neighbor grid point of the inertial navigation indicator endpoint on the gravity reference map are determined as follows:

[0085]

[0086] Where R represents the grid resolution of the gravity reference map, and [·] indicates rounding to the nearest integer. The inertial navigation system indicates the endpoint position.

[0087] Preferably, the gravity extraction sequence on the map, with each grid point within a local small region as the endpoint of the track, is as follows:

[0088] Determine the coordinates of L estimated positions on the reverse track S corresponding to each grid point within a local small domain;

[0089] Based on the coordinates of the calculated position, and following the nearest neighbor principle, determine the nearest neighbor grid point on the gravity map for each position point of the reverse trajectory S within the local small domain.

[0090] Gravity values ​​of the nearest neighbor grid points are extracted to obtain a gravity extraction sequence on the map with grid points within a local small domain as the endpoints of the track.

[0091] Preferably, the coordinates of the L calculated positions on the reverse track S corresponding to each grid point within the local small domain are determined, specifically as follows:

[0092]

[0093] Where i = 1, 2, ..., L, ε v and ε β These represent the disturbance deviations of the underwater vehicle's speed v and heading β, respectively. Let j and k be the coordinates of the grid points on the horizontal and vertical lines within a local small domain.

[0094] Preferably, when the center starting point is simultaneously on both the horizontal and vertical grid lines, an alternating generation mode of the grid lines is adopted, and the optimal position on the line that satisfies the pre-matching termination condition of the alternating lines is calculated in parallel. The optimal position on the line that first satisfies the alternating line pre-matching termination condition in parallel computing. This is the final optimal position.

[0095] Example

[0096] 1. Principle of underwater gravity-assisted navigation based on TERCOM

[0097] Underwater gravity-assisted navigation technology comprises four parts: an inertial navigation system, a gravity reference map, gravity sensors, and a gravity matching algorithm. Figure 1As shown, these are used to calculate and output the underwater vehicle's position and navigation information, extract gravity values ​​from a position-based reference map, measure real-time position-based gravity values, and perform fusion calculations to output the optimal matching position to calibrate the inertial navigation system's position information and continue assisting navigation. The gravity matching algorithm is a key technology in underwater gravity-assisted navigation, ultimately determining the underwater vehicle's actual navigation performance and the level of mission completion.

[0098] Currently, gravity matching algorithms mainly include sequence matching algorithms represented by TERCOM and Iterative Closest Contour Point (ICP) algorithms, and single-point matching algorithms represented by Sandia Inertial Terrain Aided Navigation (SITAN). In comparison, the TERCOM algorithm has better insensitivity to initial position errors and better matching robustness, and has become an effective underwater gravity-assisted navigation algorithm.

[0099] 1.1 TERCOM Matching Principle

[0100] The TERCOM algorithm is a matching algorithm that determines the optimal grid point within a domain based on the principle of optimal sequence correlation. It typically uses the submersible's endpoint position indicated by the inertial navigation system (INS) as the domain center, and then re-grids the matching domain using three times the INS error (σ) as half the grid length. The optimal matching position is determined by comparing the index values ​​of all grid points within the domain, thus calibrating the INS parameters and continuing to guide the underwater vehicle's navigation. Underwater gravity-assisted navigation based on TERCOM can be summarized in the following six steps.

[0101] 1) Determine the coordinates of the nearest neighbor grid point of the inertial navigation system's indicated endpoint on the gravity (anomaly) reference map. Assume the underwater vehicle is traveling at a speed v along a north-northeast direction β, and sequentially sample L position points on the track at time intervals Δt. Then when i = L, the sampling position For inertial navigation to indicate the endpoint position At this time, the coordinates of its nearest grid points The calculation formula is

[0102]

[0103] Where R represents the grid resolution of the gravity (anomaly) baseline map, and [·] represents rounding to the nearest integer.

[0104] 2) Calculate the number of horizontal and vertical half-grids in the TERCOM matching domain. The TERCOM algorithm uses 3σ as the domain half-side length; therefore, the number of horizontal half-grids with a gravity map grid resolution R as the grid interval is calculated. and vertical half-grid number The calculation formulas are respectively

[0105]

[0106] in, and These represent the accumulated lateral and longitudinal drift errors of the inertial navigation system during navigation, respectively. This indicates rounding up to the nearest integer.

[0107] 3) Calculate the coordinates of each grid point within the TERCOM matching domain. All grid points within the matching domain are... Centered on the grid, the grid points with values ​​j and k on the horizontal and vertical lines are respectively located. The calculation formula is

[0108]

[0109] in, The total number of all grid points within the TERCOM domain is

[0110] 4) Determine the coordinates of the L estimated positions on the reverse track corresponding to each grid point within the domain. Based on the underwater vehicle's speed v and heading β, calculate the coordinates of the L estimated positions on the reverse track corresponding to each grid point within the domain. For a track S to be matched with a destination of length L, the coordinates of the i-th reverse position on S are... The calculation formula is

[0111]

[0112] Where i = 1, 2, ..., L, ε v and ε β These represent the disturbance deviations of the underwater vehicle's speed v and heading β, respectively.

[0113] 5) Calculate the matching index values ​​between the nearest neighbor grid points on the gravity map and the measured gravity sequence of the underwater vehicle, based on the nearest neighbor principle for each position point of the reverse track S within the domain. Gravity extraction (replacement) sequence on the map for the end point of the flight path Then compare the gravity sequence with the gravity sensor measured at the sampling point of the underwater vehicle's trajectory. Calculate the matching index value between the two. Its calculation formula is:

[0114]

[0115] in, G represents the measured gravity sequence from the gravity sensor. Measured The reversed vector.

[0116] 6) Determine the optimal matching position within the domain based on the principle of minimizing the matching index. Calculate all grid points within the matching domain according to equation (5). Corresponding matching index value Then, determine the optimal matching position within the TERCOM domain based on the principle of minimizing the matching index. Its calculation formula is:

[0117]

[0118] 1.2 Problems with TERCOM

[0119] As analyzed above regarding the TERCOM matching principle, a significant problem is the inefficiency in positioning caused by the traversal and comparison of all grid points within the rectangular domain. This inefficiency significantly decreases as the domain half-side length increases with the factor of the inertial navigation error (σ). Another deeper potential problem is TERCOM mismatch, a matching phenomenon where the distance between the optimal position obtained by the matching algorithm and the actual position of the underwater vehicle exceeds a predetermined threshold. This mainly includes intra-domain mismatches caused by limited features in the matching domain or the proximity similarity of index values, and extra-domain mismatches caused by the finite boundaries of the matching domain.

[0120] This invention's research on TERCOM mismatches shows that the positioning error of mismatches within its domain is generally several grid resolutions. The corresponding optimal position is relatively close to the submersible's true position and located near the center of the contour lines of the matching index value. Figure 2 (a); however, the positioning error of out-of-domain mismatches can be as high as tens of grid resolutions, and the corresponding optimal position is relatively far from the actual position of the submersible, and the center of the contour line of the matching index value is even located outside the boundary of the matching domain, such as Figure 2 (b)

[0121] To address these two issues with TERCOM, the circular distribution characteristic of the matching index values ​​can be utilized. Iterative pre-matching of grid lines can be used to approximate the center position of the matching index domain, and the optimal positioning of the underwater vehicle's endpoint position can be obtained through the re-matching of its local grid small domains. This aims to achieve high positioning efficiency and matching reliability for underwater gravity-assisted navigation by employing fewer matching grid points.

[0122] 2. A method for matching small regions using alternating lines is proposed.

[0123] 2.1 Alternating Line Pre-matching Mechanism

[0124] The high computational complexity and inefficient positioning of the traditional TERCOM algorithm, which relies on indiscriminate traversal of a large number of grid points within the 3σ matching domain, is a key reason for its high computational complexity. Based on the circular distribution characteristics of the matching index values ​​of grid points within the domain, this paper replaces the time-consuming method of traversing a large number of grid points in the matching domain with grid line pre-matching. Furthermore, it constructs an alternating horizontal and vertical generation pattern for grid lines to efficiently obtain coordinates near the center of the contour lines of the index values ​​within the domain, approximating the actual position of the submersible, using fewer matching grid points. This is known as the alternating line pre-matching mechanism.

[0125] To facilitate a mathematical expression of the alternating line pre-matching mechanism without loss of generality, the horizontal grid lines are used as the initial pre-matching, and the optimal position on the line is determined alternately in the order of "horizontal → vertical → ..." until the optimal position on the adjacent horizontal and vertical lines remains unchanged or the index value of the optimal position on the line is less than a set threshold, at which point the alternating matching process terminates.

[0126] Let the midpoint of the first grid pre-matching line (i.e., the initial lateral matching line) be denoted as . And let it be equal to the center coordinates of the TERCOM matching domain, that is, the position of the nearest grid point on the map indicating the endpoint of the inertial navigation system for the submersible. Using the TERCOM matching domain half-side length 3σ as the half-side length of this horizontal grid line, the number of half-side grid points on its line is: Therefore, using the gravity map grid resolution R as the grid interval on the line, the position coordinates of the j-th grid point on the line can be obtained. Its calculation formula is:

[0127]

[0128] in,

[0129] Calculate each grid point on the line according to formulas (4)-(6). Matching index value It follows the principle of minimizing the matching index value to compare points one by one and finally obtain the best matching position on the line.

[0130] The optimal position on the first horizontal grid line The center coordinates of the second vertical grid line are denoted as... Right now If the half-side length of the TERCOM domain is 3σ, then the number of half-side grid points on the line with a grid spacing of R is: The coordinates of the kth grid point on the vertical line can then be derived. Its calculation formula is:

[0131]

[0132] in,

[0133] Similarly, calculate each grid point on the line according to equations (4)-(6). Matching index value It follows the principle of minimizing the matching index value to compare points one by one and finally obtain the best matching position on the line.

[0134]

[0135] Similarly, the optimal position of the h-th pre-matched grid line ∈ {1,2,…} The center coordinates of the (h+1)th grid line are denoted as... The coordinates of each grid point on the line are calculated using Equation (7) or Equation (8) in an alternating manner of "horizontal → vertical → ...". Then, the optimal matching position on the line is obtained by following Equations (4)-(6) and adhering to the principle of minimizing the matching index value.

[0136] To achieve adaptive termination of the alternating line pre-matching process, the condition is whether the optimal matching positions on two adjacent pre-matching lines are the same: if they are the same, the pre-matching process terminates; otherwise, the number of pre-matching lines h is incremented by 1, and the pre-matching process continues. Furthermore, to ensure the efficiency of the alternating line pre-matching process, a matching index threshold θ for stopping traversal of grid points on the line is set using the domain center statistical index value. MSD That is, each comparative update of the online grid point best matching index value The time must be related to the threshold θ MSD Compare sizes: if less than the threshold θ MSD If the condition is met, the alternating line pre-matching process is terminated; otherwise, the matching comparison of the next grid point continues. Therefore, the adaptive termination condition of the alternating line pre-matching process can be expressed as follows:

[0137]

[0138] Where h = 1, 2, ...

[0139] 2.2 Small Domain Rematching Mechanism

[0140] Let the optimal position on the line that satisfies the pre-matching termination condition of the alternating line be denoted as . It is highly probable that it is located in a small neighborhood of the underwater vehicle's actual location, therefore it can Centered on a small local grid domain, the underwater vehicle's true location is effectively and reliably located by matching and comparing grid points within the domain. This is known as the small-domain rematching mechanism.

[0141] To calculate the number of horizontal and vertical half-grids in the generated local small domain. and Let the half-side length control factor of this small domain be... but and The calculation formulas are respectively

[0142]

[0143] Then, the coordinates of the grid points within this small domain, with a grid spacing of R equal to the gravity map grid, and horizontal and vertical values ​​of j and k respectively. The calculation formula is

[0144]

[0145] in,

[0146] Calculate each grid point within the small domain according to equations (4)-(6). Matching index value By adhering to the principle of minimizing the matching index value, the optimal matching position within a small domain can be obtained.

[0147] 2.3 Implementation of the proposed model

[0148] The alternating line small-field matching method submitted in this invention integrates two parts: the alternating line pre-matching mechanism and the small-field re-matching mechanism. Its implementation pseudocode is shown in Algorithm 1.

[0149]

[0150]

[0151]

[0152] 3. Experimental Results

[0153] This invention presents and discusses the numerical results of three sets of experiments. The first two experiments aimed to study the high efficiency and reliability of ALSM-based underwater gravity-assisted navigation. On one hand, they verified the effectiveness of ALSM underwater gravity-assisted navigation; on the other hand, they analyzed the reasons for ALSM's excellent matching performance and tested the good applicability of ALSM under different trajectories.

[0154] The simulated sea area is the South China Sea (113°E–115°E, 8°N–10°N), and gravity and topographic data were downloaded from the University of California, San Diego website. http: / / topex.ucsd.edu / The resolution of the gravity anomaly data was changed from the original 1'×1' bilinear interpolation to 100m×100m (e.g. Figure 3 (a)) provides a good platform for rapid simulation testing and analysis of matching navigation. Meanwhile, the simulated sea area topography, such as... Figure 3(b) Areas less than 200m from the sea surface are designated as unsuitable terrain zones to ensure the navigation safety of underwater vehicles.

[0155] The simulated flight path must not be traversed Figure 3 (b) shows the terrain misfit area, and 120 track points were sampled with a sensor sampling period of 20 seconds. Furthermore, the simulated submersible was effectively calibrated before underwater navigation sampling, meaning its initial position error was reset to 0m. The experimental platform was programmed using MATLAB 2018a software on a personal laptop (Windows 10, Intel(R) Core(TM) I7-8565U CPU).

[0156] To ensure the validity and fairness of the experimental results, each simulation test was conducted independently 10,000 times, and the ALSM algorithm matching index threshold θ was used. MSD The accuracy was set to 0.1, and the traditional TERCOM algorithm was selected as the comparison algorithm. The metrics for evaluating underwater navigation performance included the average (Ave), standard deviation (STD), worst value, and best value of multiple matching accuracies, the average positioning time (τ), and the positioning success rate (η). The positioning success rate represents the percentage of valid matches with matching accuracy less than the judgment threshold in the total number of tests (the judgment threshold for matching accuracy in this paper is set to the diagonal length of a unit grid resolution, i.e., ...). ).

[0157] 3.1 Verifying the effectiveness of ALSM underwater gravity-assisted navigation

[0158] The simulated track starting point (TSP) was selected from the grid point (1100, 300) on the gravity anomaly baseline map, and a simulated track was generated according to relevant parameter settings. To ensure the fairness of the comparative test under the same experimental conditions, 10,000 repeated experiments were conducted using the TERCOM algorithm. The baseline condition data of each experiment was saved and used as the import data for the proposed ALSM algorithm. The corresponding experiments were then completed according to the ALSM matching mechanism. The results of each experiment were recorded. Based on the relative position between the TERCOM 3σ domain boundary and the actual position of the submersible, and whether a mismatch occurred, the experiment was divided into three categories: in-domain mismatch (In-domain mismatch), out-domain mismatch (Out-domain mismatch), and non-mismatch (Non-mismatch), with the corresponding numbers denoted as NIM, NOM, and NNM, respectively. Among them, the optimal position based on the TERCOM domain boundary was determined. Intra-domain mismatch judgment expression

[0159]

[0160] Under the same experimental baseline conditions, the proposed ALSM algorithm outperforms the TERCOM algorithm in 10,000 experiments, achieving superior positioning statistics, particularly with a 92% reduction in average positioning time. Simultaneously, its out-of-domain mismatch count is reduced by 98% compared to the TERCOM algorithm. These results demonstrate that the novel gravity-assisted navigation algorithm proposed in this invention significantly improves underwater navigation and positioning efficiency while also noticeably enhancing the matching reliability of the TERCOM algorithm in out-of-domain mismatch tests. Stratified comparative statistical results by experimental category show that the proposed ALSM algorithm achieves (approximately) equal matching accuracy statistical values ​​to both the non-mismatch and in-domain mismatch tests of the TERCOM algorithm, and its average positioning time is significantly shorter than that of the TERCOM algorithm, i.e., a 92% reduction. This suggests that the algorithm proposed in this invention can achieve rapid and high-precision positioning of the underwater vehicle's true location using fewer grid points along alternating lines and within small domains. For the TERCOM out-of-domain mismatch test, the ALSM algorithm's four matching accuracy indicators are significantly better than the comparison algorithms and closely approximate the matching accuracy indicators of the non-mismatch test; at the same time, it still maintains a relatively high positioning efficiency (i.e., τ index), which is 91% higher than the TERCOM algorithm, verifying the excellent positioning effect of the proposed new matching mechanism on the true position of the submersible outside the domain.

[0161] Figure 4 The proposed ALSM algorithm is visually demonstrated to improve its localization performance in the TERCOM out-of-domain mismatch test. Line graphs and frequency statistics of matching accuracy, along with scatter plots of the optimal matching location, are presented. Figure 4 Analysis shows that the ALSM algorithm significantly outperforms the comparative algorithms in successive matching accuracy for TERCOM out-of-domain mismatch tests, and almost all meet the effective matching threshold (i.e., 50 / 51). The frequency statistics show that most matching accuracies fall between one and one unit diagonal grid resolution, and it even achieves effective relocation for TERCOM out-of-domain mismatch tests exceeding ten grid resolutions. These results effectively demonstrate the high matching reliability of the proposed ALSM algorithm for the submersible's true out-of-domain location. Furthermore, the comparative position scatter plot further visually demonstrates that the ALSM algorithm's optimal matching positions effectively cover small errors in the submersible's true location and are tightly clustered within a small neighborhood of the submersible's true location, while the TERCOM optimal matching positions are scattered over large error ranges far from the submersible's true location. This verifies the high-precision positioning performance of the proposed algorithm for large errors in the submersible's true location outside the TERCOM domain. The above comparative statistical results effectively verify the high efficiency and reliability of the proposed ALSM algorithm in locating the submersible's true location and its effectiveness in underwater gravity-assisted navigation.

[0162] 3.2 Analysis of the reasons for the excellent matching performance of the ALSM algorithm

[0163] This invention focuses on exploring and analyzing the reasons for the superior matching performance of the proposed ALSM algorithm in underwater gravity-assisted navigation. To investigate the high positioning efficiency of the ALSM algorithm in underwater gravity-assisted navigation, based on two iteration termination criteria in the alternating line pre-matching mechanism, examples are drawn for adaptive iteration termination: one based on the optimal matching index value on the line being less than a decision threshold (referred to as the small threshold type), and the other based on the unchanged positions of two optimal matches on adjacent lines (referred to as the position-invariant type). Figure 5 As shown.

[0164] Depend on Figure 5 Analysis shows that the proposed ALSM algorithm's alternating line pre-matching mechanism quickly approximates the true position of the underwater vehicle through finite grid point matching on the line and selective adaptive termination. Then, it achieves efficient and high-precision positioning of the vehicle's true position through re-matching of fewer grid points in its local neighborhood. At the same time, it avoids the traversal matching calculation and comparison of a large number of invalid grid points in the TERCOM domain. That is, the combination of iterative line grid point matching and local small-domain matching proposed in this invention to replace the traversal matching of multiple grid points in the large matching domain is the key reason for ensuring the high positioning efficiency of underwater gravity-assisted navigation. To a certain extent, it also verifies the feasibility of improving the positioning efficiency of underwater navigation.

[0165] To further explore the high reliability performance of the proposed ALSM algorithm in underwater gravity-assisted navigation, examples of high reliability and high efficiency based on out-of-domain mismatch testing of the TERCOM algorithm, representing different out-of-domain matching patterns, are presented, such as... Figure 6 and Figure 7 As shown.

[0166] Depend on Figure 6 Analysis shows that the proposed ALSM algorithm approximates different forward movement patterns of the submersible's true position through pre-matched alternating lines and is supplemented by re-matching with fewer local grid points, thereby adaptively achieving high-precision and high-reliability positioning of the submersible's true position outside the domain. Figure 6 (a) represents the general matching pattern for high-reliability localization of real locations outside the domain using the proposed algorithm. Figure 6 (b) and Figure 6 (c) is to achieve high reliability in covering and locating the actual location outside the submersible's domain by iteratively protruding and migrating the best position in each online iteration. Depending on the different modes of approximating the actual location of the submersible, it can be called protrusion matching type and migration matching type, respectively. Figure 7This further demonstrates that the ALSM algorithm achieves high efficiency and reliability in matching the submersible's true location outside the domain by using fewer online grid point matches instead of traversing and matching a large number of worthless grid points within the TERCOM domain. The adaptive alternating grid line iterative approximation of the submersible's true location is key to the algorithm's high matching reliability, and to some extent, it also verifies the feasibility of improving the matching reliability of underwater navigation.

[0167] In summary, the above results analyze and verify the excellent matching performance of the proposed ALSM algorithm in underwater gravity-assisted navigation, including high-efficiency and high-precision positioning and high-reliability out-of-domain matching. This invention will further verify the good applicability of the proposed ALSM algorithm in underwater navigation using track lines in different gravity zones.

[0168] 3.3 Testing the applicability of ALSM under different flight paths

[0169] To further test the applicability of the proposed ALSM algorithm to track lines in different gravity zones, grid coordinates A(600,400), B(1700,1400), and C(1700,500) on the gravity anomaly map were used as the new starting points for each simulated track. Simulated tracks were generated according to relevant parameter settings and 10,000 tests were conducted independently. The ALSM algorithm outperformed the comparative algorithms in almost all aspects, including matching accuracy statistics, average positioning time, matching success rate, and out-of-domain matching reliability, especially in positioning efficiency (τ index), number of out-of-domain false matches (NOM index), and worst-case matching accuracy (Worst index). In terms of positioning efficiency, the proposed algorithm improved upon TERCOM by 94%, 92%, and 93%, respectively, with an average improvement of 93%. Regarding out-of-domain mismatches, the ALSM algorithm significantly reduced TERCOM's dozens of out-of-domain mismatches to only a few, with relative improvements of 97%, 94%, and 91%, all exceeding 91%. In terms of Worst accuracy, the proposed algorithm reduced the extreme values ​​of matching accuracy from TERCOM's 1524.88m, 2239.59m, and 1978.34m to 269.26m, 269.26m, and 354.67m, respectively, representing improvements of approximately 82%, 88%, and 82%. This demonstrates that the proposed ALSM algorithm maintains high positioning efficiency, high out-of-domain matching reliability, high matching success rate, and excellent matching accuracy for underwater gravity-assisted navigation across different gravity zones.

[0170] The ALSM algorithm significantly improved all six matching performance metrics of the TERCOM out-of-domain mismatch test on three tracks. Among them, the average positioning time (τ) maintained high matching efficiency in all tests, improving by 92%, 90%, and 91% respectively compared to TERCOM (with an average of 91%). The average reduction in the number of out-of-domain mismatches was also as high as 94%. This verifies that it can still maintain high positioning efficiency and high matching reliability for underwater navigation in the TERCOM out-of-domain mismatch test. In terms of matching accuracy statistics, the average Ave index of the ALSM algorithm decreased from more than 5.5 grid resolutions in TERCOM to less than 1 grid resolution, with an average accuracy improvement of 84%, demonstrating the high average out-of-domain positioning accuracy of the proposed algorithm. Its out-of-domain accuracy standard deviation (STD) and best accuracy are both less than half a grid resolution, indicating that the proposed ALSM algorithm has relatively stronger matching robustness and optimal positioning value. Its worst-case matching accuracy also decreased from more than 15 or about 20 grid resolutions in the comparison algorithm to only about 2 grid resolutions, with an average reduction of about 90%, suggesting that the proposed ALSM algorithm can still find the best matching position with relatively smaller errors even in extremely poor scenarios, and maintains good potential application prospects in underwater navigation in different gravity zones. To further intuitively analyze the excellent matching performance of the ALSM algorithm in the TERCOM out-of-domain mismatch test, a comparative diagram of the matching accuracy polygon-frequency statistics and the optimal position dispersion is drawn, such as... Figure 8 As shown.

[0171] Depend on Figure 8 Analysis shows that the proposed ALSM algorithm significantly reduces the successive matching accuracy for TERCOM out-of-domain mismatches on three different tracks, with some reductions reaching approximately twenty grid resolutions. Furthermore, its frequency statistics show a dominance of about half a grid resolution, rather than TERCOM's nearly ten grid resolutions, indicating that the proposed algorithm maintains strong high-precision and high-reliability positioning capabilities even for large-error out-of-domain mismatches. Its optimal matching position is closely within a small range of the underwater vehicle's true location, rather than TERCOM's large-scale, imprecise positioning, verifying the effective coverage and high reliability of the proposed ALSM algorithm for the underwater vehicle's true location. These experimental results demonstrate that the proposed ALSM algorithm can effectively improve underwater gravity-assisted navigation performance, exhibiting excellent positioning efficiency, high out-of-domain matching reliability, robustness, and outstanding matching accuracy.

[0172] The above embodiments are merely explanations of the present invention and should not be construed as limiting the present invention. Therefore, any implementation methods similar to the present invention or implementation methods used in other similar structures but with similar concepts to the present invention are within the protection scope of the present invention.

[0173] The above description is only the best specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the protection scope of the present invention.

[0174] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for improving underwater navigation efficiency and off-domain reliability based on alternating line small-domain matching, characterized in that, include: Determine the coordinates of the nearest neighbor grid point on the gravity reference map to indicate the endpoint position of the inertial navigation system; Using the coordinates of the nearest neighbor grid point as the center starting point, and employing an alternating horizontal and vertical grid line generation pattern, the optimal position on the line that satisfies the pre-matching termination condition of the alternating line is calculated. ; With the aforementioned optimal online position Generate local small domains centered on the target; Calculate the number of horizontal and vertical half-grids in the local small region. and ; Calculate the coordinates of the grid points within the local sub-domain based on the number of horizontal and vertical half-grids. ; Calculate each grid point within the local small domain Matching index value ; The grid point with the smallest matching index value within the local minima is selected as the optimal matching location within that local minima. ; The method employs an alternating horizontal and vertical grid line generation pattern to calculate the optimal position on the line that satisfies the pre-matching termination condition of the alternating lines. Specifically: S11. Calculate the matching index value of the h-th horizontal grid line. Best match position online Where h is a positive integer; S12. Determine the matching index value of the h-th horizontal grid line. Is it less than the matching indicator threshold? If yes, then the best matching position on the line of the h-th horizontal grid point is the best position on the line, and the calculation is terminated; otherwise, proceed to step S13. S13, using the best matching position on the line of the h-th horizontal grid point. Given the center coordinates of the (h+1)th vertical grid point line, calculate the matching index value and the optimal matching position on the line for the (h+1)th vertical grid point line. ; S14. Determine whether the best matching position on the (h+1)th vertical grid line is equal to the best matching position on the (h)th horizontal grid line. If yes, the best matching position on the (h+1)th vertical grid line is the best position on the line, and exit the calculation. If no, repeat steps S11 to S13.

2. The method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching according to claim 1, characterized in that: The center starting point may be on a horizontal grid line, or on a vertical grid line, or simultaneously on both horizontal and vertical grid lines.

3. The method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching according to claim 1, characterized in that: The calculation of the number of horizontal and vertical half-grids in the local small region. and Specifically: in, The half-side length regulation factor for the small domain; and These represent the accumulated lateral and longitudinal drift errors of the inertial navigation system during navigation, respectively. This indicates rounding up; R is the grid resolution of the gravity reference map.

4. The method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching according to claim 1, characterized in that: The coordinates of the grid points within the domain Specifically: in, To meet the optimal position on the line that satisfies the pre-matching termination condition of the alternating line, and R represents the number of horizontal and vertical half-grids in a local small region, and R is the grid resolution of the gravity reference map.

5. The method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching according to claim 1, characterized in that: The calculation of each grid point within the local small region Matching index value Specifically: in, This is a sequence of gravity extraction on a map, with each grid point within a local small region as the endpoint of the track. Gravity sequence measured by gravity sensor at sampling point of underwater vehicle track. The reversed vector, L is the track to be matched. Number of sampling points on the track of the submersible.

6. The method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching according to claim 1, characterized in that: The determination of the coordinates of the nearest neighbor grid point of the inertial navigation indicator endpoint on the gravity reference map specifically involves: in, This indicates the grid resolution of the gravity reference map. This indicates rounding to the nearest integer. The inertial navigation system indicates the endpoint position.

7. The method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching according to claim 5, characterized in that: The image gravity extraction sequence, which uses grid points within a local small region as the endpoints of the track, is specifically as follows: Determine the reverse-order trajectory S corresponding to each grid point within the local small domain. The coordinates of the calculated location; Based on the calculated coordinates of the location, and following the nearest neighbor principle, the inverse flight path is determined for each grid point within the local small domain. The nearest neighbor grid point of each location on the gravity map; The gravity values ​​of the nearest neighbor grid points are extracted to obtain a gravity extraction sequence on the map with grid points in a local small domain as the endpoints of the track.

8. The method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching according to claim 7, characterized in that: The reverse trajectory S corresponding to each grid point within the local small domain is determined. The coordinates of the calculated location are as follows: in, , and These represent the speeds of the underwater vehicle. and heading The disturbance deviation; The values ​​on the horizontal and vertical lines within a local small domain are respectively and The coordinates of the grid point positions.

9. The method for improving underwater navigation efficiency and out-of-domain reliability based on alternating line small-domain matching according to claim 2, characterized in that: When the central starting point is simultaneously on both a horizontal and a vertical grid line, an alternating generation mode of the grid lines is adopted, and the optimal position on the line that satisfies the pre-matching termination condition of the alternating lines is calculated in parallel. The optimal position on the line that first satisfies the alternating line pre-matching termination condition in parallel computing. This is the final optimal position.

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