A track association method based on improved topology

Abstract

The application discloses a track correlation method based on improved topology, which comprises the following steps: S1, converting two radar target tracks into a common coordinate system; S2, constructing a topology sequence of the radar target tracks; S3, combining historical topology information to calculate the topology average distance of the target at the current moment; S4, using the OSPA distance to measure the correlation degree of the target topology set to obtain a correlation matrix; and S5, using the Hungarian algorithm to perform optimal distribution on the correlation matrix to obtain a correlation result. The track correlation method based on the improved topology can effectively reduce the influence of random errors on the track correlation algorithm and improve the correlation performance.

Description

Technical Field

[0001] This invention relates to a multi-sensor data fusion technology, and more particularly to a trajectory association method based on improved topology. Background Technology

[0002] In a distributed radar fusion architecture, each radar uploads its local tracks to a fusion center, which then merges track information for the same target. A crucial issue is determining whether tracks from different radars correspond to the same target (i.e., track association).

[0003] In practical applications, due to the influence of radar errors (systematic errors and random errors), the track of the target detected by the radar deviates from the true track. Most traditional track association algorithms based on statistics and fuzzy logic use the absolute coordinate information between targets as the basis for association. When the radar has a large systematic error, the association performance of these traditional algorithms will be severely degraded.

[0004] To address the problem of track association under systematic errors, some scholars have proposed topology-based track association algorithms (RET). The topology method assumes that although radar systematic errors cause significant changes in the absolute positions of targets, they have little impact on the relative positions between targets. Therefore, the topology method constructs a topological structure based on the relative positions of targets and uses the comparison of the topological structures of different targets as the basis for association judgment, effectively reducing the impact of systematic errors on association.

[0005] However, in real-world environments, in addition to radar system errors, random errors also exist. Affected by random errors, target positions may deviate, and the topology may change, significantly reducing the correlation performance of topology-based methods. Therefore, when random errors are large, improving the performance of track correlation algorithms based on reference topology is crucial. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides a track association method based on improved topology. By utilizing historical topological information between targets, the method accumulates and averages the topological distances between targets at the current moment. The calculated average topological distance is used as a statistic, which can reduce the impact of random errors on the performance of the association algorithm. Simultaneously, in the association judgment, the OSPA distance is used to measure the topological sets of different targets to achieve track association.

[0007] To achieve the above objectives, this invention provides a track association method based on improved topology, comprising the following steps:

[0008] S1. Convert the tracks of the two radar targets to a common coordinate system;

[0009] S2. Construct the topological sequence of radar target tracks;

[0010] S3. Calculate the topological average distance of the target at the current moment by combining historical topological information;

[0011] S4. Use OSPA distance to measure the correlation of the target topology set and obtain the correlation matrix;

[0012] S5. The Hungarian algorithm is used to optimally allocate the correlation matrix to obtain the correlation result.

[0013] Preferably, step S1 specifically includes the following steps:

[0014] S1.1 Setting the target trajectory information X = [x, y, v] x ,v y ]; where x is the vertical distance, y is the horizontal distance, and v x Let v be the longitudinal velocity. y For lateral velocity;

[0015] S1.2. The radar's local coordinates are transformed to the common coordinate system using the following formula:

[0016]

[0017] Where [x,y] represents the target's value in the local coordinate system, [x',y'] represents the value in the common coordinate system, θ represents the angle between the radar coordinate system and the common coordinate system, and a and b represent the x and y coordinates of the vector from the origin of the common coordinate system to the origin of the radar coordinate system, respectively.

[0018] Preferably, step S2 specifically includes the following steps:

[0019] S2.1 At time k, the track sets of radar 1 and radar 2 are respectively:

[0020] U1={1,2,…,n1}, U2={1,2,…,n2}

[0021] n1 and n2 represent the number of targets detected by the two radars; and the state estimates of radar 1 and radar 2 at time k in the common coordinate system are respectively... and i∈U1, j∈U2;

[0022] S2.2 Construct the topology of each target:

[0023] Using the target as a reference point, the distance differences between other targets and this reference point are members of the topological sequence, and they are arranged in order of increasing azimuth.

[0024] It can be seen that, for track i of radar 1, the coordinate sequence of the target and the adjacent n1-1 targets is: The topological sequence of track i is obtained by calculating the distance difference vectors from other targets to the reference point:

[0025]

[0026] Similarly, the coordinate sequence of radar 2's track j and its adjacent n²-1 targets can be obtained as follows: The topological sequence of track j is:

[0027]

[0028] Preferably, step S3 specifically includes the following steps:

[0029] S3.1. Traverse the topological sequence elements of target i and target j, and then calculate the distance between the elements in the two topological sequences using the following formula:

[0030]

[0031] Where m and n are the indices of the elements in the topological sequences i and j, respectively, m∈1,2…,n1-1, n∈1,2…,n2-1;

[0032] S3.2. Combining the historical topological information of targets i and j, accumulate the distances in the current topological sequence and calculate the average value:

[0033]

[0034] After traversing all elements of the topological sequence, the topological distance matrix r between target i and target j at time k can be obtained. ij (k), the matrix dimension is (n1-1)*(n2-1).

[0035] Preferably, step S4 specifically includes the following steps:

[0036] S4.1 Calculate the OSPA distance between the two topological sets of target i and target j using the following formula:

[0037]

[0038] in, and Let h be the number of elements in the topological sequence of target i and j, and h be two sets. The allocation matrix between; q h The number of elements matched between two topological sets, i.e. This indicates the number of unmatched elements in the two sets; The distance between elements of the set is the topological distance matrix r in step S3.2. ijThe corresponding element in (k); p is the order of the OSPA distance; c is the cutoff distance;

[0039] And the dimension is and Any element h of the matrix lm The following conditions must be met:

[0040]

[0041]

[0042] S4.2 Calculate the OSPA range of all targets on Radar 1 and Radar 2 to obtain the correlation matrix D:

[0043]

[0044] Preferably, in step S4.1, p is set to 2; c is set according to the systematic error and random error.

[0045] Preferably, in step S5, the following Hungarian algorithm is used to solve the correlation matrix D to obtain the correlation result:

[0046]

[0047] in, And satisfy the following constraints:

[0048] st

[0049] Preferably, the optimal allocation principle in step S5 is: each row and each column of the matrix has at most one element allocated; if that element is allocated, then x ij =1, otherwise, x ij =0, and the value of the assigned element is the smallest.

[0050] Therefore, the present invention adopts the above-mentioned track association method based on improved topology. By accumulating the historical topological distance information of the target, the average topological distance of the target at the current moment is calculated. The OSPA distance is used to measure the correlation of the target topology set. This can overcome the influence of random error on the track association algorithm based on reference topology and improve the association accuracy.

[0051] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0052] Figure 1 This is a flowchart of the improved topology-based track association method described in this invention;

[0053] Figure 2 This is a flight path distribution map in an embodiment of the present invention;

[0054] Figure 3 The figure shows a comparison of the association accuracy of the improved RET algorithm and the traditional RET algorithm in the embodiments of the present invention.

[0055] Figure 4 The figure shows a comparison of the correlation accuracy of the improved RET algorithm and the traditional RET algorithm as a function of the standard deviation of the ranging random error in the embodiments of the present invention.

[0056] Figure 5 The figure shows a comparison of the correlation accuracy of the improved RET algorithm and the traditional RET algorithm as a function of the standard deviation of the angle measurement random error in the embodiments of the present invention.

[0057] Figure 6 This is a simulation result comparing the correlation accuracy of the improved RET algorithm and the traditional RET algorithm as a function of ranging system error in an embodiment of the present invention.

[0058] Figure 7 This is a simulation result comparing the correlation accuracy of the improved RET algorithm and the traditional RET algorithm as a function of the angle measurement system error in the embodiments of the present invention;

[0059] Figure 8 This is a simulation result comparing the association accuracy of the improved RET algorithm and the traditional RET algorithm as a function of target spacing in an embodiment of the present invention. Detailed Implementation

[0060] The present invention will be further described below with reference to the accompanying drawings. It should be noted that this embodiment is based on the present technical solution and provides detailed implementation methods and specific operation processes, but the protection scope of the present invention is not limited to this embodiment.

[0061] Figure 1 The flowchart of the track association method based on improved topology described in this invention is as follows: Figure 1 As shown, a track association method based on improved topology includes the following steps:

[0062] S1. Convert the tracks of the two radar targets to a common coordinate system;

[0063] Preferably, step S1 specifically includes the following steps:

[0064] S1.1 Setting the target trajectory information X = [x, y, v] x ,v y ]; where x is the vertical distance, y is the horizontal distance, and v x Let v be the longitudinal velocity. y For lateral velocity;

[0065] S1.2. The radar's local coordinates are transformed to the common coordinate system using the following formula:

[0066]

[0067] Where [x,y] represents the target's value in the local coordinate system, [x',y'] represents the value in the common coordinate system, θ represents the angle between the radar coordinate system and the common coordinate system, and a and b represent the x and y coordinates of the vector from the origin of the common coordinate system to the origin of the radar coordinate system, respectively.

[0068] S2. Construct the topological sequence of radar target tracks;

[0069] Preferably, step S2 specifically includes the following steps:

[0070] S2.1 At time k, the track sets of radar 1 and radar 2 are respectively:

[0071] U1={1,2,…,n1}, U2={1,2,…,n2}

[0072] n1 and n2 represent the number of targets detected by the two radars; and the state estimates of radar 1 and radar 2 at time k in the common coordinate system are respectively... and i∈U1, j∈U2;

[0073] S2.2 Construct the topology of each target:

[0074] Using the target as a reference point, the distance differences between other targets and this reference point are members of the topological sequence, and they are arranged in order of increasing azimuth.

[0075] It can be seen that, for track i of radar 1, the coordinate sequence of the target and the adjacent n1-1 targets is: The topological sequence of track i is obtained by calculating the distance difference vectors from other targets to the reference point:

[0076]

[0077] Similarly, the coordinate sequence of radar 2's track j and its adjacent n²-1 targets can be obtained as follows: The topological sequence of track j is:

[0078]

[0079] S3. Calculate the topological average distance of the target at the current moment by combining historical topological information;

[0080] Preferably, step S3 specifically includes the following steps:

[0081] S3.1. Traverse the topological sequence elements of target i and target j, and then calculate the distance between the elements in the two topological sequences using the following formula:

[0082]

[0083] Where m and n are the indices of the elements in the topological sequences i and j, respectively, m∈1,2…,n1-1, n∈1,2…,n2-1;

[0084] S3.2. Combining the historical topological information of targets i and j, accumulate the distances in the current topological sequence and calculate the average value:

[0085]

[0086] After traversing all elements of the topological sequence, the topological distance matrix r between target i and target j at time k can be obtained. ij (k), the matrix dimension is (n1-1)*(n2-1).

[0087] S4. Use OSPA distance to measure the correlation of the target topology set and obtain the correlation matrix;

[0088] Preferably, step S4 specifically includes the following steps:

[0089] S4.1 Calculate the OSPA distance between the two topological sets of target i and target j using the following formula:

[0090]

[0091] in, and Let h be the number of elements in the topological sequence of target i and j, and h be two sets. The allocation matrix between; q h The number of elements matched between two topological sets, i.e. This indicates the number of unmatched elements in the two sets; The distance between elements of the set is the topological distance matrix r in step S3.2. ij The corresponding element in (k); p is the order of the OSPA distance; c is the cutoff distance;

[0092] And the dimension is and Any element h of the matrix lm The following conditions must be met:

[0093]

[0094] S4.2 Calculate the OSPA range of all targets on Radar 1 and Radar 2 to obtain the correlation matrix D:

[0095]

[0096] Preferably, in step S4.1, p is set to 2; c is set according to the systematic error and random error.

[0097] S5. The Hungarian algorithm is used to optimally allocate the correlation matrix to obtain the correlation result.

[0098] Preferably, in step S5, the following Hungarian algorithm is used to solve the correlation matrix D to obtain the correlation result:

[0099]

[0100] in, And satisfy the following constraints:

[0101] st

[0102] Preferably, the optimal allocation principle in step S5 is: each row and each column of the matrix has at most one element allocated; if that element is allocated, then x ij =1, otherwise, x ij =0, and the value of the assigned element is the smallest.

[0103] Example

[0104] Furthermore, this embodiment conducted the following simulation experiments based on the above method:

[0105] Assume there are two radars, and eight targets moving at uniform linear velocity in a common coordinate system. The initial positions of the targets are (0m, 0m, 4m / s, 0m / s), (0m, 2m, 4m / s, 0m / s), (0m, 4m, 4m / s, 0m / s), (0m, 6m, 4m / s, 0m / s), (0m, 8m, 4m / s, 0m / s), (0m, 10m, 4m / s, 0m / s), (0m, 12m, 4m / s, 0m / s), and (0m, 14m, 4m / s, 0m / s). The systematic errors of radars 1 and 2 are Δr1 = 1m, Δθ1 = 0.2°, Δr2 = 1m, and Δθ2 = 0.2°, respectively. The random errors follow a Gaussian distribution with a mean of 0, and the standard deviations of the random errors are σ. r1 =0.2m, σ θ1 =0.2°, σ r2 =0.2m, σ θ2 =0.2°. The Kalman filter algorithm was used to track the target. The simulation time was 50s and the measurement period was T=1s. To avoid randomness, 50 Monte Carlo simulation experiments were conducted.

[0106] Figure 2 This is a flight path distribution map in an embodiment of the present invention; Figure 3 This is a simulation result comparing the association accuracy of the improved RET algorithm and the traditional RET algorithm in the embodiments of the present invention. Figure 2 and Figure 3 It can be seen that the RET algorithm improved by this invention has a higher association accuracy than the original RET algorithm.

[0107] To verify the algorithm's adaptability to random errors, the standard deviation of the ranging error and the standard deviation of the angle measurement error were varied.

[0108] Change the standard deviation of the ranging error of radar 1, and change σ r1 The simulation parameters were varied at equal intervals from 0.2m to 2m, while other simulation parameters remained constant, resulting in the following: Figure 4 The results show that as the standard deviation of the ranging error increases, the association accuracy of the RET algorithm gradually decreases from 100% to 75%, while the accuracy of the improved RET algorithm of this invention is above 95%, which is higher than that of the traditional RET algorithm.

[0109] Change the standard deviation of the angle measurement error of radar 1, and change σ θ1 The temperature is varied at equal intervals from 0.2° to 2°, while other simulation parameters remain constant, resulting in the following: Figure 5 The results show that as the standard deviation of the angle measurement error increases, the correlation accuracy of the RET algorithm drops sharply, while the accuracy of the improved RET algorithm of this invention remains relatively high. Therefore... Figure 4 , Figure 5 The improved RET algorithm of this invention has been verified to effectively overcome the influence of random errors on track association.

[0110] To verify that the algorithm also has good performance for systematic errors, the range measurement systematic error scale and the angle measurement systematic error scale were changed.

[0111] The simulation results show that the trajectory association accuracy of the two algorithms varies with the ranging system error when the ranging system error of radar 1 is varied at equal intervals from 1m to 5m. Figure 6 As shown; the angular measurement system error Δθ1 of radar 1 is varied at equal intervals from 0.1° to 1°, and the simulation results are as follows. Figure 7 As shown. By Figure 6 , Figure 7 It can be seen that as the systematic errors in ranging and angle measurement increase, the correlation accuracy of the two algorithms remains basically stable without significant decrease. The algorithm of this invention is slightly better than the RET algorithm. This indicates that the increase in systematic error does not have a significant impact on the performance of RET-related algorithms.

[0112] The spacing between targets is varied from 1m to 5m at equal intervals, that is, the target environment changes from dense to sparse. Figure 8It can be seen that when the target becomes denser, both the improved RET algorithm and the RET algorithm of this invention decrease, but the association accuracy of the improved RET algorithm of this invention is still higher than that of the RET algorithm.

[0113] Therefore, the present invention adopts the above-mentioned track association method based on improved topology. By accumulating the historical topological distance information of the target, the average topological distance of the target at the current moment is calculated. The OSPA distance is used to measure the correlation of the target topology set. This can overcome the influence of random error on the track association algorithm based on reference topology and improve the association accuracy.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A track association method based on improved topology, characterized in that: Includes the following steps: S1. Convert the tracks of the two radar targets to a common coordinate system; S2. Construct the topological sequence of radar target tracks; S3. Calculate the topological average distance of the target at the current moment by combining historical topological information; S4. Use OSPA distance to measure the correlation of the target topology set and obtain the correlation matrix; S5. The Hungarian algorithm is used to optimally allocate the correlation matrix to obtain the correlation result; Step S2 specifically includes the following steps: S2.1 At time k, the track sets of radar 1 and radar 2 are respectively: and Let be the number of targets detected by the two radars; and let the state estimates of radar 1 and radar 2 at time k in the common coordinate system be respectively... and , ; S2.2 Construct the topology of each target: Using the target as a reference point, the distance differences between other targets and this reference point are members of the topological sequence, and they are arranged in order of increasing azimuth. For track i of radar 1, the target and its adjacent... The coordinate sequence of the targets is The topological sequence of track i is obtained by calculating the distance difference vectors from other targets to the reference point: Similarly, the trajectory j of radar 2 and its adjacent... The coordinate sequence of the targets is The topological sequence of track j is: ； Step S3 specifically includes the following steps: S3.

1. Traverse the topological sequence elements of target i and target j, and then calculate the distance between the elements in the two topological sequences using the following formula: Where m and n are the indices of the elements in the topological sequences i and j, respectively. ; S3.

2. Combining the historical topological information of targets i and j, accumulate the distances in the current topological sequence and calculate the average value: After traversing all elements of the topological sequence, the topological distance matrix between target i and target j at time k can be obtained. The matrix dimension is .

2. The track association method based on improved topology according to claim 1, characterized in that: Step S1 specifically includes the following steps: S1.1 Information on setting the target trajectory Where x is the vertical distance and y is the horizontal distance. For longitudinal velocity, For lateral velocity; S1.

2. The radar's local coordinates are transformed to the common coordinate system using the following formula: Where [x,y] represents the target's value in local coordinates, , ] represents the value in the common coordinate system, θ is the angle between the radar coordinate system and the common coordinate system, and a and b are the x and y coordinates of the vector from the origin of the common coordinate system to the origin of the radar coordinate system, respectively.

3. The track association method based on improved topology according to claim 2, characterized in that: Step S4 specifically includes the following steps: S4.1 Calculate the OSPA distance between the two topological sets of target i and target j using the following formula: in, and Let h be the number of elements in the topological sequence of target i and j, and h be two sets. The allocation matrix between them; The number of elements matched between two topological sets, i.e. ; This indicates the number of unmatched elements in the two sets; The distance between elements in the set is the topological distance matrix in step S3.

2. The corresponding element in the table; p is the order of the OSPA distance; c is the cutoff distance; And the dimension is and Any element of the matrix The following conditions must be met: ； S4.2 Calculate the OSPA range of all targets on Radar 1 and Radar 2 to obtain the correlation matrix D: 。 4. The track association method based on improved topology according to claim 3, characterized in that: In step S4.1, p is set to 2; c is set according to the systematic error and random error.

5. The track association method based on improved topology according to claim 3, characterized in that: In step S5, the following Hungarian algorithm is used to solve the correlation matrix D to obtain the correlation result: in, And satisfy the following constraints: 。 6. The track association method based on improved topology according to claim 5, characterized in that: The optimal allocation principle described in step S5 is: each row and each column of the matrix has at most one element allocated; if that element is allocated, then... ,otherwise, And the value of the assigned element is the smallest.

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