A geomagnetic gradient tensor invariant fast matching navigation method fusing magcom and iccp algorithm

Abstract

The application provides a geomagnetic gradient tensor invariant fast matching navigation method combining a MAGCOM and an ICCP algorithm. The method is matched by using geomagnetic gradient tensor invariants through pre-matching, coarse matching, Hausdorff distance calculation, contour matching and multiple iteration steps. The method uses geomagnetic gradient tensor invariants as matching objects, combines a geomagnetic gradient tensor invariant reference map and a reference track output by an inertial navigation system to perform multiple iteration matching, and improves the real-time performance of the matching algorithm by using the principle of a digital register. The matching does not need the participation of a geomagnetic normal field model, and the matching accuracy is theoretically irrelevant to the accuracy of the normal field model.

Description

Technical Field

[0001] This invention belongs to the field of geomagnetic navigation, specifically involving a fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP. Background Technology

[0002] Controllable and high-precision passive autonomous navigation technology is one of the key technologies in modern aerospace, deep-sea, land-based platforms, and the Internet of Things (IoT) industries. Geomagnetic positioning and geomagnetic precise navigation technology is a type of non-active, source-free autonomous navigation method with advantages such as strong anti-interference capabilities and no cumulative error. It is a navigation system that can be relatively independent of the external environment. Magnetic gradient tensor invariants are scalars that do not change with coordinate system variations, obtained by performing certain operations on the magnetic gradient tensor. They are independent of the vehicle's attitude; therefore, the measurements of the magnetic gradient tensor invariants by the three-axis magnetometer cross array remain unchanged under different attitudes. Using such geomagnetic characteristics as matching quantities can reduce the impact of vehicle attitude changes on the accuracy of matching navigation. The Geomagnetic Contour Matching (MAGCOM) algorithm is an algorithm that relies on translational search for geomagnetic feature matching. Its algorithm process is relatively simple, its calculation speed is fast, its accuracy is high when the angular deviation between the actual track and the reference track is small, and it performs well in correcting large initial position errors. The Intermediate Closest Point (ICCP) algorithm can perform both translational and rotational searches, and it significantly corrects rotational deviations, but it is computationally complex and highly sensitive to initial errors. The MAGCOM algorithm has limited accuracy and cannot correct heading errors; while the ICCP algorithm is slow and may fail to match under conditions of large initial errors, getting trapped in local optima. Therefore, most common geomagnetic navigation matching methods are derived by improving upon the MAGCOM and ICCP algorithms or by combining other algorithms. For example, coarse matching is first performed over a large area to reduce the initial error, and then fine matching is performed using the ICCP algorithm, which provides a solution to the problem that the accuracy and running speed of traditional matching algorithms cannot be balanced (Wang Shengping, Zhang Hongmei, Zhao Jianhu, Tang Ping. Joint geomagnetic matching navigation using TERCOM and ICCP [J]. Journal of Wuhan University (Information Science Edition), 2011, 36(10): 1209-1212). However, the prerequisite for this algorithm to achieve high-precision navigation is that the background field accuracy is high and the measured geomagnetic sequence error is very small. Using the Hausdorff distance as a metric function, the ant colony algorithm is improved by using this function, and the chaotic optimization algorithm is integrated with the basic ant colony algorithm for geomagnetic MAGCOM matching (Wang Chongbing, Fan Rongshuang, Li Dawei et al. A geomagnetic matching algorithm with improved chaotic ant colony [J]. Journal of Navigation and Positioning, 2022, 10(03): 116-122). However, the inertial navigation track used is calculated from the real trajectory, and a small initial error is set. These navigation methods that use geomagnetic anomalies as the matching target require the participation of a geomagnetic normal field model, and the matching accuracy is related to the accuracy of the normal field model. Summary of the Invention

[0003] This invention relates to a fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP. Using geomagnetic gradient tensor invariants as the matching object, and employing a geomagnetic gradient tensor invariant baseline map and a reference track output by an inertial navigation system, multiple iterative matching steps are taken to obtain a matching track. The principle of digital registers is used to improve the real-time performance of the matching algorithm. By using geomagnetic gradient tensor invariants as the matching object, theoretically, the participation of a normal geomagnetic field model is unnecessary, thus solving the problems existing in the prior art.

[0004] A fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms includes the following steps: S100. Input the geomagnetic gradient tensor invariant baseline map and the reference track point sequence. Perform pre-matching of the geomagnetic gradient tensor invariant values ​​between the reference track point sequence and the measured value sequence, and filter out the track segments that need to be quickly matched and navigated using the geomagnetic gradient tensor invariant. S200, will refer to flight path Perform horizontal and vertical movements within the set error range; S300. Traverse the track sequence to be matched, calculate the Hausdorff distance between the geomagnetic gradient tensor invariant and the measured value of the geomagnetic gradient tensor invariant at the track point to be matched, and take the track to be matched with the smallest Hausdorff distance as the coarse matching track sequence. S400. Find the contour lines corresponding to the measured values ​​of the geomagnetic gradient tensor invariant, and then calculate the set of points on each contour line that are closest to the coarsely matched track sequence at the same moment. S500, Calculate the rotation matrix and translation vector; S600, through multiple iterations, satisfies the iterative convergence condition and achieves precise matching of the track sequence; S700 updates the track sequence and the measured value sequence of geomagnetic gradient tensor invariants output by S600 in a queue manner. The new reference track point and the measured value of geomagnetic gradient tensor invariant are enqueued, and the first element of the original sequence is dequeued, so that the sequence length remains unchanged. The next matching is performed by the assembled reference track point sequence and the measured value sequence.

[0005] Furthermore, in S100, the pre-matching step includes: S110, The geomagnetic gradient tensor invariant values ​​within the region to be matched, which contain the actual track point sequence and the reference track point sequence; S120. The similarity of the geomagnetic gradient tensor invariant values ​​at each track point in the matching area is measured by the correlation coefficient. When the correlation coefficient is less than 0.9, the two tracks are considered to be weakly correlated and need to be corrected; otherwise, no correction is needed. S130. Expand the edge of the region to be matched by an increment of one unit length, so that each of the two tracks adds one track point, and compare the similarity of the two sub-tracks in the new region to be matched. If the sub-tracks are strongly correlated, exit the search and display the track segments in the initial region to be matched. According to the principle of sliding time window, start from the end point of the current region to be matched and restart the search with the region to be matched of the initial size. S140. If the two track point sets are strongly correlated before and after edge expansion, then the entire region to be matched will be moved. This allows for the selection of track segments that require reference track correction, initiating a rapid matching navigation process using geomagnetic gradient tensor invariants.

[0006] Furthermore, in S200, the reference track output by the main navigation system... Perform horizontal and vertical movements to obtain multiple translated tracks to be matched. Then, obtain the corresponding geomagnetic gradient tensor invariant sequences from the track points of these tracks in the geomagnetic gradient tensor invariant reference map.

[0007] Furthermore, in S300, the Hausdorff distance is a measure of the similarity between two sets of points. It is a distance based on the maximum and minimum values. The definition of the Hausdorff distance between two finite set of points A and B is as shown in equation (1): (1) in, , , It is the Euclidean distance norm between the two point sets A and B.

[0008] Furthermore, in S400, based on the ICCP algorithm principle, the scalar field contour lines corresponding to the measured values ​​of the geomagnetic gradient tensor invariants at actual track points are identified. Then, calculate the coarsely matching track sequence on each contour line at the same time. The set of points with the closest Euclidean distance between them , Gradually expand the search area from the waypoint and identify the regions around the waypoint where contour lines appear. After finding the smallest area covered by contour lines, calculate the Euclidean distance to the reference waypoint for each point on the contour lines within this area: (2) The nearest point on the contour line within the search range is deduced from the minimum Euclidean distance. Expand the search area and calculate the Euclidean distance between points on the contour lines within the new search area and the reference track point. If a point exists... If the Euclidean distance is smaller, then update the nearest point. Then, continue expanding the search area until no point with a smaller Euclidean distance exists within the search area. Coordinates of the nearest point on the contour line Obtained by linear interpolation, as shown in equation (3): (3) Furthermore, in S500, a coarse-matched set of track sequence points is calculated. With the latest dot set The rotation matrix R and translation vector t of the rigid transformation between them cause the coarse-matched track sequence to undergo overall translation and rotation, including the following steps: S510, Calculate the point sets respectively and The centroid, weighted by the ratio of the length of the sub-segment between two track points to the length of the main segment. The calculation method is as follows: (4) (5) (6) S520. Using the quaternion method to perform rigid transformations, making the point set... and The sum of the Euclidean distances between the corresponding waypoints is minimized. The unit quaternion is , is represented as: (7) in, , , The rotation angle is determined by the fact that the quaternion method is used to process a two-dimensional reference map when matching the geomagnetic gradient tensor invariants, therefore the rotation axis is... Equation (7) simplifies to: (8) The rotation matrix R is: (9) S530, Construct the covariance matrix S: (10) in, This represents the number of sub-segments; S540. Construct a symmetric matrix W and solve for its largest eigenvalue. : (11) In the formula, These are the matrix elements of matrix S. Calculate the four real eigenvalues ​​of matrix W, where the largest eigenvalue is _____. : (12) (13) From equation (14) we get Corresponding feature vector ,in The rotation angle can be obtained from equation (15). : (14) (15) Will Substituting into equation (9), we obtain the rotation matrix R; S550, Solve for the translation vector t: (16) Since the rigid transformation process involves rotation followed by translation, the rotation matrix is ​​calculated first, and then the translation vector is calculated in the same order.

[0009] Furthermore, in S600, the track sequence is iterated multiple times to match the track point closest to the geomagnetic gradient tensor invariant, completing the fine matching and outputting the matched track sequence. (17) A threshold is set. When the sum of the Euclidean distances between corresponding track points on two adjacent iterations is less than the threshold, the iteration terminates. At this point, the matching algorithm is considered to have locally converged and terminates. A maximum number of iterations is also set. If, after reaching this number of iterations, the reference tracks on two adjacent iterations still differ significantly in angle and distance, and convergence is not possible, the loop is forcibly exited, and the final output track is used as the matching track. .

[0010] Furthermore, in S700, new reference track points and geomagnetic gradient tensor invariant measurements are enqueued, while the first element of the original sequence is dequeued, keeping the sequence length unchanged. The new reference track point sequence and geomagnetic gradient tensor invariant measurement sequence assembled in this way are then matched for the next time.

[0011] A storage medium storing a computer program, which, when executed by a processor, implements the above-described fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms.

[0012] A computer device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms.

[0013] The beneficial effects of this invention are as follows: This invention provides a fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms. First, the MAGCOM algorithm performs a large-scale scan search to select track segments requiring matching navigation. These track segments are then translated within an error range to find the path point set with the highest matching degree to the measured value sequence of geomagnetic gradient tensor invariants, which is used as a new reference track sequence. This reference track sequence is then used as input to the ICCP algorithm for high-precision matching, correcting the position of the reference track output by the inertial navigation system. This geomagnetic navigation method, which uses geomagnetic gradient tensor invariants as the matching object, theoretically eliminates the need for a geomagnetic normal field model. In this fusion algorithm, each run of the program typically relies on pre-stored track points and the acquisition of reference track points output by the inertial navigation system, reducing the real-time performance of the matching algorithm. To improve the real-time performance of the matching, this invention proposes an algorithm based on the principle of digital registers. This algorithm acquires track points in batches only during the initial track matching process. In subsequent matching processes, only one newly generated track point needs to be acquired to enable real-time track point matching. Furthermore, the geomagnetic gradient tensor invariant values ​​measured in two consecutive measurements differ by only one, eliminating the need to redraw the geomagnetic gradient tensor invariant contour map each time. This significantly improves the timeliness of the matching algorithm and thus enhances the efficiency of geomagnetic gradient tensor invariant matching. Attached Figure Description

[0014] Figure 1 This is an architecture diagram of a fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms according to the present invention. Figure 2 This is an architecture diagram of a register-based matching navigation real-time performance optimization algorithm. Figure 3 It is a track calibration map of a navigation method that uses a fusion algorithm to fast match navigation methods based on geomagnetic gradient tensor invariants. Figure 4 This is a magnified view of a portion of the track calibration map. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] In the accompanying drawings of specific embodiments of the present invention, in order to better and more clearly describe the working principle of each component in the system and show the connection relationship of each part in the device, only the relative positional relationship between each component is clearly distinguished. It does not constitute a limitation on the signal transmission direction, connection sequence, or size, dimension, and shape of each part within the component or structure.

[0017] Reference Figures 1-4 As shown, a fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms includes the following steps: S100. Input the geomagnetic gradient tensor invariant baseline map and the reference track point sequence. Perform pre-matching of the geomagnetic gradient tensor invariant values ​​between the reference track point sequence and the measured value sequence, and filter out the track segments that need to be quickly matched and navigated using the geomagnetic gradient tensor invariant. S200, will refer to flight path Perform horizontal and vertical movements within the set error range; S300. Traverse the track sequence to be matched, calculate the Hausdorff distance between the geomagnetic gradient tensor invariant and the measured value of the geomagnetic gradient tensor invariant at the track point to be matched, and take the track to be matched with the smallest Hausdorff distance as the coarse matching track sequence. S400. Find the contour lines corresponding to the measured values ​​of the geomagnetic gradient tensor invariant, and then calculate the set of points on each contour line that are closest to the coarsely matched track sequence at the same moment. S500, Calculate the rotation matrix and translation vector; S600, through multiple iterations, satisfies the iterative convergence condition and achieves precise matching of the track sequence; S700 updates the track sequence and the measured value sequence of geomagnetic gradient tensor invariants output by S600 in a queue manner. The new reference track point and the measured value of geomagnetic gradient tensor invariant are enqueued, and the first element of the original sequence is dequeued, so that the sequence length remains unchanged. The next matching is performed by the assembled reference track point sequence and the measured value sequence.

[0018] Specifically, by employing pre-matching and coarse matching steps, computational complexity can be reduced and the track segments most similar to measured values ​​can be selected, thereby improving matching efficiency. Using Hausdorff distance for coarse matching, along with contour line matching and multiple iterations for fine matching, the matching results can be progressively refined, improving accuracy and robustness. By adjusting the track, calculating rotation matrices and translation vectors, the position and attitude of the track sequence can be optimized, allowing for better matching with reference data. Using a queue approach for sequence updates and subsequent matching enables real-time track tracking, and the latest data is used for matching, improving both real-time performance and accuracy.

[0019] Furthermore, for S100, the matching algorithm performs better in areas where the geomagnetic gradient tensor field changes drastically, i.e., in regions with dense geomagnetic gradient tensor invariant contour maps. Therefore, before the vehicle begins operation, a geomagnetic gradient tensor invariant reference map is drawn for local areas with dense geomagnetic gradient tensor invariant contour maps on the pre-planned track. When the vehicle travels to this area, the reference track point output by the inertial navigation system and other main navigation equipment is used to measure the geomagnetic gradient tensor invariant value at the track point in real time by the triaxial magnetometer cross array carried by the vehicle, and it is matched with the geomagnetic gradient tensor invariant value at the reference track point. The pre-matching process is accelerated based on the principle of the sliding time window algorithm. The pre-matching steps include: S110, The geomagnetic gradient tensor invariant values ​​within the region to be matched, which contain the actual track point sequence and the reference track point sequence; S120. The similarity of the geomagnetic gradient tensor invariant values ​​at each track point in the matching area is measured by the correlation coefficient. When the correlation coefficient is less than 0.9, the two tracks are considered to be weakly correlated and need to be corrected; otherwise, no correction is needed. S130. Expand the edge of the region to be matched by an increment of one unit length, so that each of the two tracks adds one track point, and compare the similarity of the two sub-tracks in the new region to be matched. If the sub-tracks are strongly correlated, exit the search and display the track segments in the initial region to be matched. According to the principle of sliding time window, start from the end point of the current region to be matched and restart the search with the region to be matched of the initial size. S140. If the two track point sets are strongly correlated before and after the edge expansion, the entire area to be matched will be moved to select the track segments that need to be corrected for reference track, and the geomagnetic gradient tensor invariant fast matching navigation process will be started.

[0020] Specifically, this invention improves matching accuracy by pre-drawing a reference map of the geomagnetic gradient tensor invariant and a localized area with dense geomagnetic gradient tensor invariant contour maps on the flight track, and by real-time measuring the geomagnetic gradient tensor invariant values ​​at flight track points. Utilizing a sliding time window algorithm and a similarity metric (correlation coefficient), flight track segments requiring reference track correction can be quickly selected within a predetermined area, accelerating the matching process. The correlation of flight track segments is assessed based on the similarity metric results, allowing for track correction as needed. This enhances the adaptability of the matching algorithm to areas with drastic changes in the geomagnetic gradient tensor field, strengthening its robustness. Real-time measurement of the geomagnetic gradient tensor invariant values ​​at flight track points, combined with track correction and searching using the sliding time window algorithm, offers advantages in real-time flight track tracking.

[0021] Furthermore, in S200, the reference track output by the main navigation system... Perform horizontal and vertical movements to obtain multiple translated tracks to be matched. Then, obtain the corresponding geomagnetic gradient tensor invariant sequences from the track points of these tracks in the geomagnetic gradient tensor invariant reference map.

[0022] Specifically, in S200, multiple translated tracks to be matched are obtained at different positions and attitudes by horizontally and vertically shifting the reference track. This provides flexibility to adapt to matching requirements under different positions and attitudes. Horizontal and vertical shifts allow adjustment of the position and attitude of the tracks to be matched to better adapt to the characteristics of the geomagnetic gradient tensor invariant reference map. This improves the accuracy and robustness of the matching. By obtaining multiple translated tracks to be matched, diverse matching strategies can be employed, such as comparing the corresponding geomagnetic gradient tensor invariant sequences in the geomagnetic gradient tensor invariant reference map. In this way, the optimal matching scheme can be selected using different matching results.

[0023] Furthermore, in S300, the Hausdorff distance is a measure of the similarity between two sets of points. It is a distance based on the maximum and minimum values. The definition of the Hausdorff distance between two finite set of points A and B is as shown in equation (1): (1) in, , , It is the Euclidean distance norm between the two point sets A and B.

[0024] The bidirectional Hausdorff distance H(A, B) is the larger of the unidirectional Hausdorff distances d(A, B) and d(B, A), and is used to measure the maximum mismatch between two point sets. Within the error range, for each movement of the reference track, the Hausdorff distance between the geomagnetic gradient tensor invariant values ​​and the measured values ​​of the geomagnetic gradient tensor invariant at all track points in the track sequence is calculated and stored. The track with the smallest Hausdorff distance is the best-matched track, which is the coarse-matched track sequence. .

[0025] Specifically, in S300, the Hausdorff distance is used as a measure of similarity for the matching operation. The Hausdorff distance is a distance based on maxima and minima used to describe the similarity between two sets of points. Specifically, the steps in S300 involve calculating the Hausdorff distance between the geomagnetic gradient tensor invariant values ​​and the measured values, and finding the track sequence with the smallest Hausdorff distance as the coarse matching track sequence.

[0026] In S300, the Hausdorff distance is used to measure the similarity between the geomagnetic gradient tensor invariant values ​​and the measured values. A smaller Hausdorff distance indicates a higher similarity between the two sets of points, which is beneficial for accurate matching. The Hausdorff distance describes the maximum degree of mismatch between two sets of points. By selecting the track to be matched with the smallest Hausdorff distance as the coarse matching track, matching errors can be reduced and matching accuracy can be improved. The Hausdorff distance is used to calculate the distance between the geomagnetic gradient tensor invariant values ​​and the measured values ​​at all track points in the reference track. This allows for matching on a per-track-point basis and control over the range of matching errors, improving matching accuracy and robustness.

[0027] Furthermore, in S400, based on the ICCP algorithm principle, the scalar field contour lines corresponding to the measured values ​​of the geomagnetic gradient tensor invariants at actual track points are identified. Then, calculate the coarsely matching track sequence on each contour line at the same time. The set of points with the closest Euclidean distance between them , The contour lines of the geomagnetic gradient tensor invariant appear as irregular, smooth curves. However, when magnified to a certain extent, these contour lines can be considered as being composed of many small straight line segments. Starting from the trackpoint, the search range is gradually expanded, and the areas around the trackpoint where contour lines appear are identified. After finding the smallest area covered by contour lines, the Euclidean distance from each point on the contour lines within this area to the reference trackpoint is calculated: (2) The nearest point on the contour line within the search range is deduced from the minimum Euclidean distance. Expand the search area and calculate the Euclidean distance between points on the contour lines within the new search area and the reference track point. If a point exists... If the Euclidean distance is smaller, then update the nearest point. Then, continue expanding the search area until no point with a smaller Euclidean distance exists within the search area. Coordinates of the nearest point on the contour line Obtained by linear interpolation, as shown in equation (3): (3).

[0028] Specifically, S400 finds the nearest point by calculating the Euclidean distance between points on the geomagnetic gradient tensor invariant contour lines and the reference track point, and then uses linear interpolation to determine the coordinates of the nearest point on the contour line. This improves the matching accuracy and enhances the precision of the matched points. By progressively expanding the search range and identifying the areas around the track point where contour lines appear, the smallest area covered by contour lines can be found. This selective search range saves computational resources and reduces unnecessary calculations. Since the geomagnetic gradient tensor invariant contour lines exhibit irregular smooth curves, using the nearest Euclidean distance point for matching effectively suppresses the influence of outliers on the matching results, enhancing the robustness of the algorithm.

[0029] Furthermore, in S500, a coarse-matched set of track sequence points is calculated. With the latest dot set The rotation matrix R and translation vector t of the rigid transformation between them cause the coarse-matched track sequence to undergo overall translation and rotation, including the following steps: S510, Calculate the point sets respectively and The centroid, weighted by the ratio of the length of the sub-segment between two track points to the length of the main segment. The calculation method is as follows: (4) (5) (6); S520. Using the quaternion method to perform rigid transformations, making the point set... and The sum of the Euclidean distances between the corresponding waypoints is minimized, and the unit quaternion is... , is represented as: (7) in, , , The rotation angle is determined by the fact that the quaternion method is used to process a two-dimensional reference map when matching the geomagnetic gradient tensor invariants, therefore the rotation axis is... Equation (7) simplifies to: (8) The rotation matrix R is: (9) S530, Construct the covariance matrix S: (10) in, This represents the number of sub-segments; S540. Construct a symmetric matrix W and solve for its largest eigenvalue. : (11) In the formula, These are the matrix elements of matrix S.

[0030] Calculate the four real eigenvalues ​​of matrix W, where the largest eigenvalue is _____. : (12) (13) From equation (14) we get Corresponding feature vector ,in The rotation angle can be obtained from equation (15). : (14) (15) Will Substituting into equation (9), we obtain the rotation matrix R; S550, Solve for the translation vector t: (16) Since the rigid transformation process involves rotation followed by translation, the rotation matrix is ​​calculated first, and then the translation vector is calculated in the same order.

[0031] Specifically, in the S500, translation and rotation operations allow adjustment of the position and attitude of the coarse-matched track sequence based on the nearest point set, ensuring a better correspondence with the nearest point. This helps to accurately match track sequences and improve the accuracy of the navigation system. The optimal translation vector and rotation matrix can be found by minimizing the sum of the Euclidean distances between the coarse-matched track sequence point set after rigid transformation and the corresponding track points in the nearest point set. This makes the distances between matched point pairs closer to reality, improving the matching quality. The center position of the two point sets can be determined by calculating the centroids of the coarse-matched track sequence point set and the nearest point set. This helps to focus the coarse-matched track sequence near the nearest point, reducing unnecessary matching errors. A quaternion method is used for rigid transformation, and the optimal rotation matrix is ​​obtained by solving a least-squares problem. This method optimizes the results of the rigid transformation, improving the accuracy and stability of the matching.

[0032] Furthermore, in S600, the track sequence is iterated multiple times to match the track point closest to the geomagnetic gradient tensor invariant, completing the fine matching and outputting the matched track sequence. (17) A threshold is set. When the sum of the Euclidean distances between corresponding track points on two adjacent iterations is less than the threshold, the iteration terminates. At this point, the matching algorithm is considered to have locally converged and terminates. A maximum number of iterations is also set. If, after reaching this number of iterations, the reference tracks on two adjacent iterations still differ significantly in angle and distance, and convergence is not possible, the loop is forcibly exited, and the final output track is used as the matching track. .

[0033] Specifically, in S600, through multiple iterations, the matching track sequence can be continuously optimized to make it closer to the geomagnetic gradient tensor invariant, thereby improving the matching accuracy. By setting termination conditions, including limits on the Euclidean distance between track points and the number of iterations, it is possible to detect whether the matching algorithm has locally converged or reached the maximum number of iterations, and to terminate the iteration appropriately to obtain the final matching track sequence.

[0034] Through multiple iterations in S600, the matching track sequence can be gradually optimized, ensuring that the final output matching track has high accuracy and reliability. This helps improve the positioning accuracy and robustness of the navigation system.

[0035] Furthermore, in S700, new reference track points and geomagnetic gradient tensor invariant measurements are enqueued, while the first element of the original sequence is dequeued, keeping the sequence length unchanged. The new reference track point sequence and geomagnetic gradient tensor invariant measurement sequence assembled in this way are then matched for the next time.

[0036] Specifically, in S700, newly measured reference track points are added to the end of the queue. This ensures that the latest reference track point is added to the queue with each update. New geomagnetic gradient tensor invariant measurements are also added to the end of the queue. This ensures that the queue contains geomagnetic gradient tensor invariant measurements corresponding to the reference track points. To maintain the sequence length, the oldest reference track point and its corresponding geomagnetic gradient tensor invariant measurement are removed from the front of the queue. Based on the reference track points and geomagnetic gradient tensor invariant measurements in the queue, a new sequence of reference track points and a new sequence of measured geomagnetic gradient tensor invariant values ​​are constructed for the next matching operation.

[0037] In this way, the S700 maintains the unchanged lengths of the reference track point sequence and the measured sequence of geomagnetic gradient tensor invariants. Each match uses the latest reference track point and the corresponding geomagnetic gradient tensor invariant measurement, thus ensuring that the match result matches the latest measurement data.

[0038] A storage medium storing a computer program, which, when executed by a processor, implements the above-described fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms.

[0039] Specifically, a computer program stored on a storage medium enables a fast matching navigation method based on geomagnetic gradient tensor invariants, integrating MAGCOM (Geomagnetic Track Matching) and ICCP (Stiff Transformation and Multiple Iterations) algorithms. This method combines MAGCOM and ICCP algorithms, utilizing geomagnetic gradient tensor invariants for track matching navigation. The stability and uniqueness of geomagnetic gradient tensor invariants provide accurate track matching results. By fusing these two algorithms, fast and accurate navigation can be achieved. Using the MAGCOM algorithm, a coarse matching of the track can be performed in the initial matching stage to quickly determine possible matching candidate points. Subsequently, the rigid transformation and multiple iterations using the ICCP algorithm further improve the accuracy and reliability of the matching. This fusion method overcomes noise and interference in track matching, providing more stable and accurate navigation results. By storing this computer program on a programmable storage medium, it can be modified and extended as needed to meet different application scenarios and requirements. This makes the algorithm flexible and adaptable to various navigation systems and devices.

[0040] In summary, by using a computer program stored on a storage medium, this fast matching navigation method based on geomagnetic gradient tensor invariants, which integrates MAGCOM and ICCP algorithms, can provide a fast, accurate, and reliable navigation solution with broad application potential and adaptability. This geomagnetic navigation method, which uses geomagnetic gradient tensor invariants as the matching object, theoretically does not require the participation of a geomagnetic normal field model.

[0041] A computer device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms.

[0042] Specifically, the computer device includes a memory, a processor, and computer programs stored in the memory. By executing these programs, the processor is able to implement a fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms.

[0043] Because computer equipment is equipped with processors and memory, it can efficiently execute computer programs. This enables navigation methods integrating MAGCOM and ICCP algorithms to perform rapid calculations and provide navigation results instantly in scenarios with high real-time requirements. By running a computer program integrating MAGCOM and ICCP algorithms on a computer device, the processor's computing power can be fully utilized to achieve rapid matching navigation of geomagnetic gradient tensor invariants. This method combines multiple algorithms and technologies to provide efficient matching navigation, thereby improving the accuracy and practicality of navigation. The navigation algorithm can be modified and upgraded as needed to adapt to different application scenarios and requirements. This allows computer equipment to be continuously optimized and improved with technological advancements and changing application needs. Computer equipment is equipped with processors, possessing powerful data processing and computing capabilities. This enables navigation methods integrating MAGCOM and ICCP algorithms to efficiently process and calculate large amounts of track data and geomagnetic gradient tensor invariants, providing fast and accurate navigation solutions.

[0044] In summary, a computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor can realize a fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms, bringing beneficial effects such as real-time computation, efficient matching navigation, algorithm flexibility and scalability, and powerful data processing capabilities.

[0045] The following is an embodiment of the present invention: Experiment: Introducing a correction rate As one of the evaluation metrics for algorithm simulation results, the smaller the value of r, the stronger the matching algorithm's ability to correct track errors; conversely, the larger the value of r, the weaker the correction ability. When the extreme case is reached, where the tracks completely overlap, the correction rate will be 0.

[0046] Select actual flight path Reference flight path The maximum number of iterations is 8, the sampling interval T=5, the number of sampling points N=6, and zero mean and standard deviation are added to the geomagnetic gradient tensor invariant baseline plot. Gaussian noise. First, obtain the Gaussian noise using a triaxial magnetometer cross array in the matching navigation region. The measured values ​​of the geomagnetic gradient tensor invariants at the track points [m1, m2, m3, m4, m5, m6], corresponding to... The geomagnetic gradient tensor invariant sequence of the track points is [I1, I2, I3, I4, I5, I6]. The matched track sequence after the first match is [A1, A2, A3, A4, A5, A6]. After the first match, the new geomagnetic gradient tensor invariant measurement value m7 is enqueued, and the first measurement value m1 of the original sequence is dequeued, generating a new measurement value sequence of [m2, m3, m4, m5, m6, m7]. The newly output reference track point I7 is enqueued in the matched track sequence, generating a new reference track sequence of [A2, A3, A4, A5, A6, I7], and a second match is performed. This process continues, generating two sequences in queue form for each match. The simulation results of the matching algorithm are as follows: Figure 3 and 4 As shown, the initial error before correction was 1550 meters, and the final error after correction was 356.57 meters, with a correction rate of [missing information]. Compared to the standalone ICCP or MAGCOM algorithms, the fusion matching navigation algorithm exhibits improved operational stability. The fast matching navigation method using magnetic gradient tensor invariants, which integrates MAGCOM and ICCP algorithms, takes approximately 3 seconds for two matches, about 5 seconds less than without register optimization, thus improving the real-time performance of the matching algorithm.

[0047] A fast matching navigation method based on geomagnetic gradient tensor invariants, integrating MAGCOM and ICCP algorithms, leverages the independence of geomagnetic gradient tensor invariants from vehicle attitude to reduce the impact of vehicle attitude changes on matching navigation accuracy. By incorporating a pre-matching step, the algorithm selects track segments for matching, enhancing its efficiency. Based on register principles, only one point needs to be calculated for each match, improving real-time performance. Multiple iteration termination conditions are set to reduce the probability of negative optimization. Simulation results demonstrate that the algorithm can correct track errors even in noisy environments. The fusion algorithm combines the advantages of high matching accuracy of the ICCP algorithm and good matching robustness of the MAGCOM algorithm. It leverages the characteristics of the MAGCOM algorithm, such as wide search area, fast speed, stable operation over long flight time, good real-time performance, and low computational load. First, the MAGCOM algorithm is used for coarse matching, and then the ICCP algorithm is used for fine matching. This narrows the search range and enables the aircraft to quickly determine the initial state of the ICCP algorithm in areas with drastic changes in the geomagnetic gradient tensor field. This avoids the shortcomings of the ICCP algorithm, which is prone to getting trapped in local optima, and the MAGCOM algorithm, which cannot correct for heading errors.

Claims

1. A fast matching navigation method for geomagnetic gradient tensor invariants integrating MAGCOM and ICCP algorithms, characterized in that, Includes the following steps: S100. Input the geomagnetic gradient tensor invariant baseline map and the reference track point sequence. Perform pre-matching of the geomagnetic gradient tensor invariant values ​​between the reference track point sequence and the measured value sequence, and filter out the track segments that need to be quickly matched and navigated using the geomagnetic gradient tensor invariant. S200, will refer to flight path Perform horizontal and vertical movements within the set error range; S300. Traverse the track sequence to be matched, calculate the Hausdorff distance between the geomagnetic gradient tensor invariant and the measured value of the geomagnetic gradient tensor invariant at the track point to be matched, and take the track to be matched with the smallest Hausdorff distance as the coarse matching track sequence. S400. Find the contour lines corresponding to the measured values ​​of the geomagnetic gradient tensor invariant, and then calculate the set of points on each contour line that are closest to the coarsely matched track sequence at the same moment. S500, Calculate the rotation matrix and translation vector; S600, through multiple iterations, satisfies the iterative convergence condition and achieves precise matching of the track sequence; S700 updates the track sequence and the measured value sequence of geomagnetic gradient tensor invariants output by S600 in a queue manner. The new reference track point and the measured value of geomagnetic gradient tensor invariant are enqueued, and the first element of the original sequence is dequeued, so that the sequence length remains unchanged. The next matching is performed by the assembled reference track point sequence and the measured value sequence.

2. The fast matching navigation method for geomagnetic gradient tensor invariants integrating MAGCOM and ICCP algorithms according to claim 1, characterized in that, In S100, the pre-matching step includes: S110, The geomagnetic gradient tensor invariant values ​​within the region to be matched, containing the actual track point sequence and the reference track point sequence; S120. The similarity of the geomagnetic gradient tensor invariant values ​​at each track point in the matching area is measured by the correlation coefficient. When the correlation coefficient is less than 0.9, the two tracks are considered to be weakly correlated and need to be corrected; otherwise, no correction is needed. S130. Expand the edge of the region to be matched by an increment of one unit length, so that each of the two tracks adds one track point, and compare the similarity of the two sub-tracks in the new region to be matched. If the sub-tracks are strongly correlated, exit the search and display the track segments in the initial region to be matched. According to the principle of sliding time window, start from the end point of the current region to be matched and restart the search with the region to be matched of the initial size. S140. If the two track point sets are strongly correlated before and after the edge expansion, the entire area to be matched will be moved to select the track segments that need to be corrected for reference track, and the geomagnetic gradient tensor invariant fast matching navigation process will be started.

3. The fast matching navigation method for geomagnetic gradient tensor invariants integrating MAGCOM and ICCP algorithms according to claim 2, characterized in that, In S200, the reference track output by the main navigation system Perform horizontal and vertical movements to obtain multiple translated tracks to be matched. Then, obtain the corresponding geomagnetic gradient tensor invariant sequences from the track points of these tracks in the geomagnetic gradient tensor invariant reference map.

4. The fast matching navigation method for geomagnetic gradient tensor invariants integrating MAGCOM and ICCP algorithms according to claim 3, characterized in that, In S300, the Hausdorff distance is a measure of the similarity between two sets of points. It is a distance based on the maximum and minimum values. The definition of the Hausdorff distance between two finite set of points A and B is as shown in equation (1): （1） in, , , It is the Euclidean distance norm between the two point sets A and B.

5. The fast matching navigation method for geomagnetic gradient tensor invariants integrating MAGCOM and ICCP algorithms according to claim 4, characterized in that, In S400, based on the ICCP algorithm principle, the scalar field contour lines corresponding to the measured values ​​of the geomagnetic gradient tensor invariants at actual track points are identified. Then, calculate the coarsely matching track sequence on each contour line at the same time. The set of points with the closest Euclidean distance between them , Gradually expand the search area from the waypoint and identify the regions around the waypoint where contour lines appear. After finding the smallest area covered by contour lines, calculate the Euclidean distance to the reference waypoint for each point on the contour lines within this area: （2） The nearest point on the contour line within the search range is deduced from the minimum Euclidean distance. Expand the search area and calculate the Euclidean distance between points on the contour lines within the new search area and the reference track point. If a point exists... If the Euclidean distance is smaller, then update the nearest point. Then, continue expanding the search area until there are no points within the search area with a distance smaller than the Euclidean distance. Coordinates of the nearest point on the contour line Obtained by linear interpolation, as shown in equation (3): （3）。 6. The fast matching navigation method for geomagnetic gradient tensor invariants integrating MAGCOM and ICCP algorithms according to claim 5, characterized in that, In S500, the coarse-matched track sequence point set is calculated. With the latest dot set The rotation matrix R and translation vector t of the rigid transformation between them cause the coarse-matched track sequence to undergo overall translation and rotation, including the following steps: S510, Calculate the point sets respectively and The centroid, weighted by the ratio of the length of the sub-segment between two track points to the length of the main segment. The calculation method is as follows: （4） （5） （6） S520. Using the quaternion method to perform rigid transformations, making the point set... and The sum of the Euclidean distances between the corresponding waypoints is minimized, and the unit quaternion is... , is represented as: （7） in, , , The rotation angle is determined by the fact that the quaternion method is used to process a two-dimensional reference map when matching the geomagnetic gradient tensor invariants, therefore the rotation axis is... Equation (7) simplifies to: （8） The rotation matrix R is: （9） S530, Construct the covariance matrix S: （10） in, This represents the number of sub-segments; S540. Construct a symmetric matrix W and solve for its largest eigenvalue. : （11） In the formula, These are the matrix elements of matrix S. Calculate the four real eigenvalues ​​of matrix W, where the largest eigenvalue is _____. : （12） （13） From equation (14) we get Corresponding feature vector ,in The rotation angle can be obtained from equation (15). : （14） （15） Will Substituting into equation (9), we obtain the rotation matrix R; S550, Solve for the translation vector t: （16） Since the rigid transformation process involves rotation followed by translation, the rotation matrix is ​​calculated first, and then the translation vector is calculated in the same order.

7. A fast matching navigation method for geomagnetic gradient tensor invariants integrating MAGCOM and ICCP algorithms according to claim 6, characterized in that, In S600, the track sequence is iterated multiple times to match the track point closest to the geomagnetic gradient tensor invariant, completing the fine matching and outputting the matched track sequence. （17） A threshold is set. When the sum of the Euclidean distances between corresponding track points on two adjacent iterations is less than the threshold, the iteration terminates. At this point, the matching algorithm is considered to have locally converged and terminates. A maximum number of iterations is also set. If, after reaching this number of iterations, the reference tracks on two adjacent iterations still differ significantly in angle and distance, and convergence is not possible, the loop is forcibly exited, and the final output track is used as the matching track. .

8. The fast matching navigation method for geomagnetic gradient tensor invariants integrating MAGCOM and ICCP algorithms according to claim 7, characterized in that, In S700, new reference track points and geomagnetic gradient tensor invariant measurements are enqueued, while the first element of the original sequence is dequeued, keeping the sequence length unchanged. The new reference track point sequence and geomagnetic gradient tensor invariant measurement sequence assembled in this way are then matched for the next time.

9. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms as described in any one of claims 1-8.

10. A computer device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, the processor executing the program to implement the fast matching navigation method for geomagnetic gradient tensor invariants that integrates MAGCOM and ICCP algorithms as described in any one of claims 1-8.

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