A Reference Topology Robust Track Association Method for Implementing System Error Decoupling

Abstract

The present invention discloses a reference topology robust track association method for realizing system error decoupling, which relates to the technical field of signal processing. The specific steps are as follows: First, a hybrid reference topology is constructed based on the combination of the comprehensive reference topology and the nearest neighbor reference topology; Secondly, the robust influence of the reference topology is analyzed from two aspects of the distance system error and the angle system error respectively, and the analysis result that the reference topology and the distance system error are decoupled under polar coordinates is obtained; Then, based on the optimal sub-pattern assignment distance metric method, the reference topology distance is estimated from two aspects of the translation system error and the angle system error respectively; Finally, based on the results of the reference topology distance estimation of the angle system error and the translation system error, the optimal linear assignment algorithm is used to calculate and obtain the final estimation result of the robust track association. The reference topology robust track association method for realizing system error decoupling proposed by the present invention can effectively realize system error decoupling and improve the robustness of the algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a reference topology robust track association method for realizing system error decoupling. Background Art

[0002] The basic concept of system error decoupling is to reduce the interference of system error on track association as much as possible through some optimization processing algorithms, and improve the correctness of track association.

[0003] The basic concept of reference topology is to use a known target to be judged as the origin, draw a circle with a certain radius length, and form a reference track set for the adjacent track points falling within the circle. The pattern formed by all the reference track points in the set is called the reference topology of the target to be judged.

[0004] Regarding the reference topology track association problem for system error decoupling, on the one hand, there is a lack of accurate mathematical representation methods, making it difficult to effectively overcome the sensitivity problem of missing and false reporting of track information; on the other hand, the distance measurement between reference topologies mostly depends on subjective experience and lacks an objective quantification method, and it needs to be further improved in practicality in complex application scenarios.

[0005] Currently, researchers have proposed a variety of methods for robust track association estimation for system error decoupling, mainly based on the reference topology method, and proposed various forms of estimation algorithms such as reference topology sequences and topological probability matrices.

[0006] For example, in Example 1, in the journal paper "A Novel Fuzzy Pattern Recognition Data Association Method for Biased Sensor Data" by S Yue, W Yue, and X Shan in the International Conference on Information Fusion in 2006, the area around the target is discretely grid-divided, and track association estimation is performed through the target reference topology (RET) algorithm; this method lacks a mathematical representation method, the description process depends on subjective experience, and the calculation amount is too large in the case of dense targets, and the practicality is not strong.

[0007] For example, in Example 2, in the journal paper "Track Association Algorithm Based on Topological Sequence Method" in Acta Aeronautica et Astronautica Sinica in 2009, the concept of relative angle sorting is introduced to form a target topology sequence, and the similarity between the two sequences is measured for track association estimation; this method is relatively sensitive to false reporting and missing reporting phenomena, and the algorithm performance is greatly affected.

[0008] As in Example 3, in the journal paper "Track-to-track association using reference topology in the presence of sensor bias" by Xiongjie Du, Yue Wang, and Xiuming Shan in the Proceedings of Signal Processing, 10th International Conference on in 2010, a topological probability matrix is constructed from the probability distribution values of neighboring targets to measure the cross-correlation between the topological probability matrices of two targets for track association estimation. This method involves matrix calculations, has a high complexity, and is also sensitive to false alarms and missed detections, so the algorithm performance needs to be improved.

[0009] Therefore, the present invention proposes a robust track association method with reference topology for decoupling system errors to solve the deficiencies of the above-mentioned prior art. Summary of the Invention

[0010] The object of the present invention is to provide a robust track association method with reference topology for decoupling system errors, which solves the problem in the prior art that due to the system errors existing in the sensor itself, there are large deviations in obtaining the absolute position information of the target, and using this as an association criterion for robust track association estimation will further expand the errors, resulting in inaccurate optimization results.

[0011] To achieve the above object, the present invention provides a robust track association method with reference topology for decoupling system errors. The system errors include range system error, angle system error, and translation system error. The specific steps are as follows:

[0012] Step 1: Construct a hybrid reference topology based on the combination of the comprehensive reference topology and the nearest neighbor reference topology.

[0013] Step 2: Analyze the influence of the robustness of the reference topology from the two aspects of range system error and angle system error respectively, and obtain the analysis result that the reference topology and the range system error are decoupled in polar coordinates.

[0014] Step 3: According to the analysis result of Step 2, perform reference topology distance estimation from the two aspects of translation system error and angle system error respectively based on the optimal sub-pattern assignment distance metric method OSPA.

[0015] Step 4: Based on the results of the reference topology distance estimation of the angle system error and the translation system error in Step 3, use the optimal linear assignment algorithm to calculate and obtain the final estimation result of the robust track association.

[0016] Preferably, in step 1, based on the combination of the comprehensive reference topology and the nearest neighbor reference topology, the process of constructing the hybrid reference topology is as follows:

[0017] S11. Determine the reference track set; with the target to be judged observed by sensor s as the center and R as the radius, screen out all track points within the circular area to form a point set, and form the reference track set, and the calculation expression is as follows:

[0018] (1)

[0019] In the formula, is the target to be judged, R is the reference radius, is the reference track set, is the j-th reference track point, the j-th track point falling within the reference radius R, N is the number of reference track points, represents the j-th track point observed by sensor s;

[0020] S12. Determine the comprehensive reference topology; according to all track points falling within the reference radius R and the target to be judged to form the reference topology, and the calculation expression is as follows:

[0021] (2)

[0022] In the formula, is the comprehensive reference topology, is the j-th reference topology element;

[0023] S13. Based on the nearest neighbor reference topology , balance the track association performance and the calculation complexity, and the calculation expression is as follows:

[0024] (3)

[0025] In the formula, is the number of topologies, indicating the upper limit of the number N of reference track points in;

[0026] S14. Considering the detection range and calculation complexity of sensor s, based on the comprehensive reference topology and the nearest neighbor reference topology , obtain a hybrid reference topology more suitable for engineering practice, and the calculation expression is as follows:

[0027] (4).

[0028] Preferably, the process of analyzing the robustness influence of the reference topology from two aspects of the distance system error and the angle system error in step 2 is as follows:

[0029] S21. Coordinate transformation; in polar coordinates, the target to be judged , the reference track point , and the reference topology element are subjected to the following coordinate transformation:

[0030] (5)

[0031] (6)

[0032] (7)

[0033] In the formula, 、 are respectively the radii of the target to be judged , the reference track point from the origin in polar coordinates, 、 are respectively the angles between the target to be judged , the reference track point and the polar axis in polar coordinates;

[0034] S22. Analyze the relationship between the reference topology and the distance system error in polar coordinates under the influence of the distance system error. Specifically, when the sensor s track set generates a distance system error , the expression of the reference topology element is as follows:

[0035] (8)

[0036] In the formula, are respectively the jth reference topology element, the reference track point, and the target to be judged after generating the distance system error, is the offset vector. According to formula (8), it can be seen that the offset vector data is small, is approximately equal to , and at this time, it is considered that the distance system error has little influence on the reference topology element . Therefore, in polar coordinates, the reference topology and the distance system error are decoupled;

[0037] S23. Analyze the relationship between the reference topology and the angle system error in polar coordinates under the influence of the angle system error. Specifically, when the sensor s track set generates an angle system error , the expression of the reference topology element is as follows:

[0038] (9)

[0039] In the formula, 、 、 are respectively the j-th reference topological element, reference track point, and target to be judged after the angular systematic error occurs; according to formula (9), it can be known that the angular systematic error causes the reference topological element to rotate counterclockwise by the same angle magnitude.

[0040] Preferably, in step 3, the process of estimating the reference topological distance based on the optimal sub-pattern assignment distance metric method OSPA from two aspects of translational systematic error and angular systematic error is as follows:

[0041] S31. Measure the distance between the reference topologies of the two tracks of sensors A and B and .

[0042] S32. Judge the relationship between the distance between the reference topologies of the two tracks and and the penalty cost of isolated elements. If the distance between the reference topologies of the two tracks and is not greater than the penalty cost of isolated elements, it is determined that there are no paired element singularities in the system; if the distance between the reference topologies of the two tracks and is less than the penalty cost of isolated elements, it is determined that there are paired element singularities in the system, and then calculate the reference topological distance in the case of only translational systematic error or only angular systematic error respectively.

[0043] Preferably, in S31, the process of measuring the distance between the reference topologies of the two tracks of sensors A and B and is as follows:

[0044] S311. Calculate the metric distance between the sets of the reference topologies of the two tracks of sensors A and B and , where , , , and the specific calculation expression is as follows:

[0045] (10)

[0046] In the formula, is the metric distance between the two set elements , is the penalty cost of isolated elements, is the basic metric;

[0047] S312. Calculate the metric distance between two track reference topologies based on the optimal sub-pattern assignment distance metric method OSPA and the metric distance between sets, and the expression is as follows:

[0048] (11)

[0049] In the formula, is the order parameter of the OSPA distance, is the OSPA distance between the two reference topologies and ; Under the condition of , it is considered that all m elements in set are successfully paired, is the sum of the distances of the paired elements between the two sets, which reflects the state difference between the elements of different sets, is the set the distance corresponding to the remaining isolated elements; Under the condition of , it is considered that all n elements in set are successfully paired; At the same time, the OSPA distance satisfies the following conditions:

[0050] (12)

[0051] In the formula, is the OSPA distance between set and when their elements are completely paired.

[0052] Preferably, when there are paired element outliers in the system in S32, the calculation expression of the reference topology distance under the condition of only translational system error is as follows:

[0053] (13)

[0054] In the formula, are the numbers of reference track points of sensors A and B respectively, is the pairing matrix between sensors A and B, is the number of paired elements, is the pairing matrix the (u, v)th element in, is the total number of remaining isolated points in the two sets except the pairing matrix , is the sum of the pairing matrix and the isolated points in the two sets, Is the reference topological element The basic distance between them.

[0055] Preferably, when there are paired element singularities in the system in S32, the calculation expression of the reference topological distance in the case of only angular system error is as follows:

[0056] (14)

[0057] (15)

[0058] In the formula, Is the relative angular system error of sensors A and B, Are the reference topological elements respectively The angular estimates in polar coordinates; when Is a fixed value, Is obtained by solving through formula (15); when Is a fixed value, formula (14) is equivalent to formula (13); when Is a fixed value, .

[0059] Preferably, in step 4, the process of calculating the final estimated result of robust track association using the optimal linear assignment algorithm based on the results of reference topological distance estimation of angular system error and translation system error in step 3 is as follows:

[0060] S41. Input the local detection track sets of sensors A and B 、 , set the reference radius R, the number of topologies And the correlation gate threshold ;

[0061] S42. According to formula (4), calculate the hybrid reference topology of each target to be judged Respectively ;

[0062] S43. Judge whether the difference between the targets to be judged of sensors A and B Is greater than the correlation gate threshold , if , then calculate Through formula (16), and execute S45, otherwise execute the next step; the calculation expression is as follows:

[0063] (16);

[0064] S44. When only translational system error is generated in the two track sets of sensors A and B, solve , and execute S45; when only angular systematic errors are generated in the two track sets of sensors A and B, solve and obtain using Equation (14) , and execute S45;

[0065] S45. Based on the above calculations, obtain , and use the optimal linear assignment algorithm to calculate and obtain the final estimation result of robust track association .

[0066] Therefore, the present invention adopts the above-mentioned reference topology robust track association method for realizing systematic error decoupling, and has the following beneficial effects:

[0067] (1) Using the absolute position of the target as the association criterion improves the robustness of the association estimation; on this basis, a hybrid reference topology is proposed, which reduces the computational complexity and increases the practicality of the algorithm;

[0068] (2) Based on the results of the reference topology distance estimation of angular and translational systematic errors, use the optimal linear assignment algorithm to calculate and obtain the final estimation result of robust track association, thereby effectively reducing the phenomenon of track information omission and false alarm.

[0069] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is the overall flowchart of a reference topology robust track association method for realizing systematic error decoupling according to the present invention;

[0071] Figure 2 is a schematic diagram of the reference track set of an embodiment of the present invention;

[0072] Figure 3 is the flowchart of obtaining the final estimation result of robust track association in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0073] The following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0074] Please refer to Figures 1 - 3 , a reference topology robust track association method for realizing systematic error decoupling, where the systematic errors include range systematic error, angular systematic error, and translational systematic error; the specific steps are as follows:

[0075] Step 1: Based on the combination of the comprehensive reference topology and the nearest neighbor reference topology, construct a hybrid reference topology. The specific process is as follows:

[0076] S11. Determine the reference track set: With the target to be judged observed by sensor s as the center and R as the radius, screen out all track points within the circular area to form a point set, thus forming the reference track set, and the calculation expression is as follows:

[0077] (1)

[0078] In the formula, is the target to be judged, R is the reference radius, is the reference track set, is the j-th reference track point of, the j-th track point falling within the reference radius R, N is the number of reference track points, represents the j-th track point observed by sensor s;

[0079] S12. Determine the comprehensive reference topology: According to all track points falling within the reference radius R and the target to be judged to form the difference vector between them to form the reference topology of, and the calculation expression is as follows:

[0080] (2)

[0081] In the formula, is the comprehensive reference topology of, is the j-th reference topology element of;

[0082] S13. Based on the nearest neighbor reference topology , balance the track association performance and the computational complexity. Since the larger the reference radius R, the more the number of reference track points and the better the track association performance, but at the same time the computational complexity also increases significantly. Therefore, the nearest neighbor reference topology is introduced, and the calculation expression is as follows:

[0083] (3)

[0084] In the formula, is the number of topologies, representing the upper limit of the number of reference track points N in;

[0085] S14. Considering the detection range of sensor s and the computational complexity, based on the comprehensive reference topology and the nearest neighbor reference topology , obtain a hybrid reference topology that is more suitable for engineering practice , the calculation expression is as follows:

[0086] (4).

[0087] Step 2: Analyze the robustness influence of the reference topology from two aspects of the distance system error and the angle system error respectively, and obtain the analysis result that the reference topology and the distance system error are decoupled in the polar coordinate; the specific process is as follows:

[0088] S21. Coordinate transformation; in the polar coordinate, transform the target to be judged , the reference track point , and the reference topology element as follows:

[0089] (5)

[0090] (6)

[0091] (7)

[0092] In the formula, 、 are respectively the radii of the target to be judged , the reference track point from the origin in the polar coordinate, 、 are respectively the angles between the target to be judged , the reference track point and the polar axis in the polar coordinate;

[0093] S22. Analyze the relationship between the reference topology and the distance system error in the polar coordinate under the influence of the distance system error, specifically: when the distance system error occurs in the track set of the sensor s, the expression of the reference topology element is as follows:

[0094] (8)

[0095] In the formula, are respectively the j-th reference topology element, the reference track point, and the target to be judged after the distance system error occurs, is the offset vector. According to formula (8), it can be seen that the offset vector data is small, is approximately equal to , and at this time, it is considered that the distance system error has little influence on the reference topology element . Therefore, in the polar coordinate, the reference topology and the distance system error are decoupled;

[0096] S23. Analyze the relationship between the reference topology and the angular systematic error in polar coordinates under the influence of the angular systematic error. Specifically: When there is an angular systematic error in the track set of sensor s the expressions of the reference topology elements are as follows:

[0097] (9)

[0098] In the formula, 、 、 are the j-th reference topology element, the reference track point, and the target to be judged after the angular systematic error occurs, respectively. According to formula (9), it can be seen that the angular systematic error causes the reference topology element to rotate counterclockwise by the same angle magnitude.

[0099] Step 3. According to the analysis results of Step 2, estimate the reference topology distance from two aspects of the translational systematic error and the angular systematic error respectively based on the optimal sub-pattern assignment distance metric method OSPA; since and describe the distance metric method between points, the reference topology needs to be solved through the distance metric method between sets. To reduce the sensitivity to the state difference and the number difference between different set elements, an algorithm for measuring the distance consistency of sets is proposed, that is, the optimal sub-pattern assignment distance metric method; the specific process is as follows:

[0100] S31. Measure the distance between the reference topologies and of the tracks of sensors A and B; the specific process is as follows:

[0101] S311. Calculate the metric distance between the sets of the reference topologies and of the tracks of sensors A and B, where 、 , The specific calculation expression is as follows:

[0102] (10)

[0103] In the formula, is the metric distance between the two set elements , is the penalty cost for isolated elements, is the basic metric;

[0104] S312. Calculate the reference topologies of the two tracks based on the optimal sub-pattern assignment distance metric method OSPA and The metric distance between sets is expressed as follows:

[0105] (11)

[0106] Wherein, is the order parameter of the OSPA distance, is the OSPA distance between the two reference topologies and ; Under the condition of , it is considered that all m elements in the set are successfully paired, is the sum of the distances of the paired elements between the two sets, which reflects the state difference between the elements of different sets, is the set the distance corresponding to the remaining isolated elements; Under the condition of , it is considered that all n elements in the set are successfully paired; At the same time, the OSPA distance satisfies the following conditions:

[0107] (12)

[0108] Wherein, is the set and the OSPA distance between them when the elements are completely paired.

[0109] S32. Judge the relationship between the distance between the two track reference topologies and and the penalty cost of isolated elements. If the distance between the two track reference topologies and is not greater than the penalty cost of isolated elements, it is determined that there are no isolated points of paired elements in the system; If the distance between the two track reference topologies and is less than the penalty cost of isolated elements, it is determined that there are isolated points of paired elements in the system, and then calculate the reference topology distance in the case of only translational systematic error or only angular systematic error; Among them, when there are isolated points of paired elements in the system, the calculation expression of the reference topology distance in the case of only translational systematic error is as follows:

[0110] (13)

[0111] Wherein, are the numbers of reference track points of sensors A and B respectively, is the pairing matrix between sensors A and B, is the number of paired elements, is the pairing matrix The (u, v)-th element in is the total number of remaining isolated points in the two sets except for the pairing matrix ; is the sum of the pairing matrix and the isolated points in the two sets; is the basic distance between the reference topological elements .

[0112] When there are paired element isolated points in the system, the calculation expression of the reference topological distance in the case of only angular systematic error is as follows:

[0113] (14)

[0114] (15)

[0115] In the formula, is the relative angular systematic error of sensors A and B; are the angular estimates of the reference topological elements in polar coordinates respectively; when is a fixed value, is obtained by solving through formula (15); when is a fixed value, formula (14) is equivalent to formula (13); when is a fixed value, .

[0116] Step 4: Based on the angular systematic error and translational systematic error in Step 3, use the optimal linear assignment algorithm to calculate the final estimated result of robust track association according to the reference topological distance estimation result; the specific process is as follows:

[0117] S41. Input the local detection track sets , of sensors A and B, and set the reference radius R, the number of topologies and the correlation gate threshold ;

[0118] S42. According to formula (4), calculate the hybrid reference topology of each target to be judged respectively;

[0119] S43. Judge whether the difference between the targets to be judged of sensors A and B is greater than the correlation gate threshold . If , then calculate through formula (16) and execute S45; otherwise, execute the next step. The calculation expression is as follows:

[0120] (16);

[0121] S44. When only translational systematic errors occur in the two track sets of sensors A and B, solve and obtain using Equation (13) , and execute S45; when only angular systematic errors occur in the two track sets of sensors A and B, solve and obtain using Equation (14) , and execute S45;

[0122] S45. According to the obtained from the above calculations, use the optimal linear assignment algorithm to calculate and obtain the final estimation result of robust track association .

[0123] Therefore, the present invention adopts the above-mentioned reference topology robust track association method for decoupling systematic errors. By using the relative position of the target instead of the absolute position for robust track association estimation, it can effectively achieve decoupling of systematic errors, effectively reduce the phenomenon of missing and false reporting of track information, and thus improve the robustness of the algorithm.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A reference topology robust track association method for achieving system error decoupling, characterized by: System errors include distance system error, angle system error and translation system error; the specific steps are as follows: Step 1: Based on the combination of comprehensive reference topology and nearest neighbor reference topology, a hybrid reference topology is constructed; Step 2: Analyze the influence of the reference topology on the robustness from the two aspects of distance system error and angle system error, and obtain the analysis result that the reference topology and the distance system error are decoupled in polar coordinates; Step 3: According to the analysis results of step 2, the reference topological distance is estimated from two aspects, namely, the translation system error and the angle system error, based on the optimal sub-mode allocation distance measurement method OSPA; Step 4: Based on the results of the angular system error and the translation system error in step 3 and referring to the topological distance estimation, the optimal linear assignment algorithm is used to calculate the final estimation result of the robust track association.

2. A reference topology robust track association method for achieving system error decoupling according to claim 1, characterized in that: The process of constructing a hybrid reference topology based on the combination of the comprehensive reference topology and the nearest neighbor reference topology in step 1 is as follows: S11, determine the reference track set; the target to be judged observed by sensor s With R as the radius and R as the center, all track points in the circular area are selected to form a point set. The reference track set is calculated as follows: (1) In the formula, is the target to be judged, R is the reference radius, for The reference track set, for The jth reference track point falls within the reference radius R, N is the number of reference track points, represents the j-th track point observed by sensor s; S12, determine the comprehensive reference topology; according to all track points falling within the reference radius R With the target to be judged The difference vector between The reference topology is calculated as follows: (2) In the formula, for The comprehensive reference topology, is the j-th reference topological element; S13, based on the nearest neighbor reference topology , balancing the track association performance and computational complexity, the calculation expression is as follows: (3) In the formula, is the topological number, indicating The upper limit of the number of reference track points N; S14, based on comprehensive reference topology and nearest neighbor reference topology , obtain the hybrid reference topology , the calculation expression is as follows: (4)。 3. A reference topology robust track association method for achieving system error decoupling according to claim 2, characterized in that: The process of analyzing the influence of the reference topology on robustness from the perspectives of distance system error and angle system error in step 2 is as follows: S21, coordinate conversion: In polar coordinates, the target to be judged , Reference track point , reference topology elements Perform the following coordinate transformation: (5) (6) (7) In the formula, 、 They are the targets to be judged in polar coordinates. , Reference track point The radius from the origin, 、 They are the targets to be judged in polar coordinates. , Reference track point Angle with the polar axis; S22. Under the influence of the range system error, the relationship between the reference topology and the range system error in polar coordinates is analyzed. Specifically, when the sensor s track set produces a range system error When , the expression referring to the topological element is as follows: (8) In the formula, , , are the jth reference topological element, reference track point, and target to be judged after the distance system error is generated, respectively. is the offset vector. According to formula (8), the offset vector data is small. Approximately , at this time, the distance system error is considered Reference topology elements The influence of is small, so the reference topology and distance system error are decoupled in polar coordinates; S23. Under the influence of the angle system error, the relationship between the reference topology and the angle system error in polar coordinates is analyzed. Specifically, when the sensor s track set generates an angle system error When , the expression referring to the topological element is as follows: (9) In the formula, 、 、 are the jth reference topological element, reference track point, and target to be judged after the angle system error is generated. According to formula (9), the angle system error Reference topological elements Rotated counterclockwise by the same angle.

4. A reference topology robust track association method for achieving system error decoupling according to claim 3, characterized in that: In step 3, the process of estimating the reference topological distance from the two aspects of translation system error and angle system error based on the optimal sub-pattern assignment distance metric method OSPA is as follows: S31, measurement sensor A, B two track reference topology and distance; S32, judging the reference topology of two tracks and The relationship between the distance and the penalty cost of isolated elements, if the two tracks refer to the topology and If the distance between the two tracks is not greater than the isolated element penalty time, it is determined that there is no paired element isolated point in the system; if the two tracks refer to the topology and When the distance is less than the isolated element penalty, it is determined that the system has an isolated point of paired elements, and the reference topological distance is calculated separately when only the translation system error exists or only the angle system error exists.

5. A reference topology robust track association method for achieving system error decoupling according to claim 4, characterized in that: Reference topology of two tracks of measurement sensors A and B in S31 and The distance process is as follows: S311, calculate the reference topology of the two tracks of sensors A and B and The metric distance between sets, where , , , the specific calculation expression is as follows: (10) In the formula, For two set elements The metric distance between Penalize costs for isolated elements, is the basic measure; S312, Calculate the reference topology of two tracks based on the optimal sub-mode allocation distance measurement method OSPA and The metric distance between sets is expressed as follows: (11) In the formula, is the order parameter of the OSPA distance, Reference topology for both , The OSPA distance between Under these conditions, it is considered that the set All m elements are paired successfully. Pair elements between two sets The distance and reflects the state difference between elements of different sets. For collection Remaining The distance corresponding to an isolated element; Under these conditions, it is considered that the set All n elements are paired successfully; at the same time, the OSPA distance satisfies the following conditions: (12) In the formula, For collection and The OSPA distance between the two elements when they are perfectly paired.

6. A reference topology robust track association method for achieving system error decoupling according to claim 5, characterized in that: In S32, when there are paired element isolated points in the system, the calculation expression of the reference topological distance in the case of only translation system errors is as follows: (13) In the formula, are the number of reference track points of sensors A and B respectively, is the pairing matrix between sensors A and B, is the number of paired elements, is the pairing matrix The (u, v)th element in In addition to the pairing matrix The total number of remaining isolated points in the other two sets, is the pairing matrix between the two sets and the sum of isolated points, For reference topological elements The basic distance between.

7. A reference topology robust track association method for achieving system error decoupling according to claim 6, characterized in that: In S32, when there are paired element isolated points in the system, the calculation expression of the reference topological distance in the case of only angular system errors is as follows: (14) (15) In the formula, is the relative angle system error of sensors A and B, , To refer to the topological elements , Angle estimation in polar coordinates; when is a fixed value, By solving equation (15), we can get: is a fixed value, formula (14) is equivalent to formula (13); when is a fixed value, .

8. A reference topology robust track association method for achieving system error decoupling according to claim 7, characterized in that: In step 4, the process of using the optimal linear assignment algorithm to calculate the final estimation result of robust track association based on the angle system error and translation system error in step 3 with reference to the result of topological distance estimation is as follows: S41, local detection track set of input sensors A and B , , set the reference radius R, the number of topologies and associated gate threshold ; S42, according to formula (4), calculate and obtain each target to be judged , Hybrid Reference Topology ; S43, judging the target to be judged by sensors A and B , Is the difference between the two greater than the associated wave gate threshold? ,like , then we can calculate it through formula (16): , and execute S45, otherwise execute the next step; the calculation expression is as follows: (16)； S44. When the track sets of sensors A and B only produce translational system errors, equation (13) is used to solve , and execute S45; when the two track sets of sensors A and B only produce angle system errors, use formula (14) to solve and obtain , and execute S45; S45, obtained according to the above calculation , the optimal linear assignment algorithm is used to calculate the final estimation result of robust track association .

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