Fracture track association method based on track release and GM-PHD

Abstract

The invention discloses a fracture track association method based on track release and GM-PHD, and aims to solve the problem that track prediction of a traditional TSA algorithm is inaccurate due to dynamic generation and disappearance of targets in a multi-target scene and solve the problem that information cannot be effectively utilized during track fracture. The new and old tracks are released as trace point data, and the data in the fracture period is integrated to form a new data set, so that the track re-association effect is remarkably improved. And a GM-PHD filter is used for dynamically estimating the multi-target state, so that the accuracy of track prediction is improved. And through global optimal distribution and polynomial fitting, realizing re-association and splicing of the broken track, and constructing a complete target track after association of the broken track.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and further relates to a method for associating broken tracks based on track release and Gaussian mixture probability density algorithm GM-PHD (Gaussian Mixture Probability Hypothesis Density) in the field of target tracking technology. The present invention can be used for target ships monitored by shore-based sea radar in real time, and there is track misassociation, resulting in track breakage for reassociation. Background Art

[0002] Broken track association technology is a technology used in multi-target tracking systems to effectively re-associate broken track segments after target tracks are interrupted for various reasons. Track association not only involves associating different state points of the same target at the same time, but also includes effectively associating the previous and next track segments after the target track is broken. In the target tracking process, the track may be broken due to factors such as high maneuvering targets, false alarms, large measurement errors, close-range target formations, low detection probability or long sampling intervals. When the track is interrupted, traditional association technology cannot accurately identify and connect these broken track segments, thus affecting the performance of the entire tracking system. In order to ensure the continuity and correctness of the target trajectory, these broken tracks must be re-associated. At present, the track segment association algorithm TSA (Track Segment Association) has been widely used in a variety of tracking systems. When dealing with track breaks, the association of the broken tracks is usually achieved by predicting the old track segments and tracing the new track segments back to a common time point for two-dimensional allocation.

[0003] Hangzhou Dianzi University disclosed a method for associating interrupted track fragments of marine vessels based on Gaussian process in its patent document "A method for associating interrupted tracks based on Gaussian process" (application number CN 202011410712.2 application publication number CN 117233745A). The implementation steps of this method are: 1) classify the interrupted tracks and obtain the initial track set; 2) use the Gaussian process to learn the unknown function of the target motion, and predict and reversely predict the new and old tracks in the initial track pair; 3) perform speed screening, binary hypothesis testing and two-dimensional allocation on the obtained track fragments to solve the ambiguity problem, and obtain the optimal allocation track set; 4) The interrupted track prediction value of the obtained optimal allocation track set is fused using Gaussian process to obtain the complete track. Although this method uses the method of associating interrupted tracks using Gaussian process to improve the accuracy of track association, it also obtains the track at the interruption point and improves the average track life. However, this method still has three shortcomings: First, this method uses Gaussian process to recursively infer the target motion track, which has too high computational complexity and cannot meet the real-time requirements in actual scenarios. Second, there is useful real track information during the track break period, but this algorithm does not use this part of information, resulting in the track reassociation cannot be changed in time according to the information during the break period, resulting in incorrect reassociation.

[0004] The patent document “Method for associating interrupted tracks of maritime targets using high-orbit optical satellites” (application number: CN201911036959.X application publication number CN 110686679A) discloses a method for re-associating interrupted tracks of maritime targets based on optical satellites. The method is implemented by the following steps: 1) extrapolating the first track backward and the second track forward to obtain the state estimation of the first track and the second track at the same time; 2) performing preliminary association between the first track and the second track whose state estimation at the same time satisfies the constraint condition, and obtaining a preliminary association set; 3) further associating the tracks in the preliminary association set by adopting the hypothesis test method of χ2 distribution, and obtaining a further association set; solving the further association set by adopting the two-dimensional optimal allocation principle, and obtaining the association set with the minimum global cost as the first-stage association set; 4) solving the possible association fragment pairs by adopting the distance two-dimensional optimal allocation for the complement of the first-stage association set in the preliminary association set, and obtaining the intermediate association set; 5) screening the intermediate association set by adopting the amplitude relationship detection, and obtaining the second-stage association set; 6) fitting the association track pairs in the first-stage association set and the second-stage association set by adopting the N-order polynomial, and obtaining the continuous track. The disadvantage of this method is that the recursive algorithm used in this method is the Kalman recursive algorithm, which is only applicable to linear situations, while there are many nonlinear situations in the sea environment. In nonlinear situations, the Kalman recursive algorithm cannot correctly perform broken track association. This is because there are two main reasons for track breakage: first, the signal loss caused by obstacle blocking, the tracking system does not have correct input data, resulting in track breakage; second, in a multi-target environment, when the distance between multiple targets is close, the target signals may overlap or confuse each other, and the sensor cannot distinguish between different targets, resulting in the tracking system being unable to accurately associate with the correct target track, resulting in track interruption or wrong association; and the traditional re-association method after track interruption only solves the track breakage caused by obstacle blocking. For the situation where the track is interrupted or wrongly associated due to the close distance between multiple targets, the tracking system cannot accurately associate with the correct target track.

[0005] In summary, there are two main problems in the association of interrupted tracks using the TSA algorithm:

[0006] First, traditional TSA algorithms cannot dynamically handle track disruptions caused by the generation and disappearance of targets. Traditional TSA algorithms usually assume that the number of targets is fixed and only focus on associating and repairing existing tracks. These algorithms rely on a fixed number of targets and perform data association through parameters such as position and speed, but when targets suddenly appear or disappear, the algorithm cannot flexibly adjust the number of targets. This results in the system being unable to update the track in a timely manner when targets appear or disappear, and the track cannot be correctly re-associated after being interrupted.

[0007] Second, traditional algorithms cannot utilize data during track breaks, while there is some useful information during track breaks. Assuming that the ship made a turning operation during the break, if this part of the broken information is directly discarded, it will lead to serious mismatches before and after the break, and ultimately cause the failure of broken track association. Summary of the invention

[0008] The purpose of the present invention is to address the shortcomings of the above-mentioned prior art and propose a broken track association method based on track release and GM-PHD, aiming to solve the problem of inaccurate track prediction of traditional TSA algorithm due to dynamic generation and disappearance of targets in multi-target scenarios, while effectively utilizing the data during the track fragmentation period to improve the effect of track reassociation.

[0009] The technical idea for achieving the purpose of the present invention is: the present invention releases the received new and old tracks as point track data, and introduces the data during the break period for integration to form a new data set containing the break information. This process solves the problem that the prior art cannot effectively utilize data during the track break period, so that even when the track undergoes a large change, the present invention can still successfully integrate the information during the break period, significantly improving the effect of track reassociation. In addition, the present invention uses the Gaussian probability mixture density algorithm GM-PHD to filter the new data set, and uses the probability hypothesis density PHD (Probability Hypothesis Density) to estimate the status of multiple targets, which not only avoids the complex data association problem of traditional filters, but also can dynamically handle the generation and disappearance of targets. This improvement solves the limitations of the traditional TSA algorithm in multi-target scenarios, especially when targets are dynamically generated and disappear, the GM-PHD algorithm can maintain the accuracy of track prediction, effectively solving the limitation of the TSA algorithm on the fixed number of targets. The present invention divides the tracks into new tracks and old tracks by time classification for the data processed by GM-PHD, and performs speed matching on the new and old tracks, and calculates the time and distance difference to infer the speed of the track during the break, so as to preliminarily screen out the track pairs that may be associated. For the screened track pairs, further recursion and prediction processing are performed, and the new track is recursively forward and the old track is predicted backward to improve the association accuracy. Then, hypothesis testing is performed on the predicted data to screen out track pairs with a higher matching possibility again. For the track pairs that pass the test, a global optimal allocation method is used to solve the many-to-many matching problem, and the optimal pairing combination is found to minimize the matching cost. Finally, the associated track segments are re-associated, and the track in the break interval is processed by polynomial fitting, which is spliced ​​with the new and old tracks to form a complete target track after the broken track is associated.

[0010] The steps of the present invention include the following:

[0011] Step 1: input the track segment to be associated, extract the target position at each time point in the track segment, form a point track set of the track segment, release the data in the point track set, and merge the released point track data with the clutter and target point track data obtained by the radar during the break period into a point track data set;

[0012] Step 2: Use GM-PHD to track and filter the point track data set to obtain the track set containing label information after tracking;

[0013] Step 3, perform speed matching on the track set to obtain a candidate track set;

[0014] Step 4, reverse or predict the new and old track segments in the candidate track set to obtain a recursive candidate track set;

[0015] Step 5, performing a chi-square test on the candidate track set, and re-screening the candidate tracks that do not meet the association conditions to obtain a screened candidate track set;

[0016] Step 6, optimally allocating the screened candidate track set to obtain a track set to be associated;

[0017] Step 7: fuse the track segments.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] First, the present invention introduces a track release step, integrates the released data with the data during the track break, and then re-tracks and filters, thereby overcoming the defect of the prior art that the data cannot be effectively utilized during the track break. This allows the present invention to successfully achieve track reassociation even when the track changes significantly during the break, significantly improving the effect of track break processing.

[0020] Second, the present invention introduces the Gaussian mixture probability density algorithm GM-PHD, which estimates the states of multiple targets through the probability hypothesis density PHD, can dynamically handle the generation and disappearance of targets, and adapt to the complex changes of multi-target scenes. It overcomes the problem of inaccurate track prediction of the traditional TSA algorithm due to the dynamic generation and disappearance of targets in the existing technology in solving multi-target scenes, so that the present invention effectively solves the limitation of the traditional TSA algorithm requiring a fixed number of targets, and improves the ability to associate broken tracks in a multi-target environment.

[0021] Third, the present invention combines the data during the fracture period and GM-PHD filtering through track release, which not only improves the accuracy of fracture track association, but also enhances the adaptability and robustness of the algorithm in a multi-target dynamically changing environment, fully demonstrating the superiority of processing multi-target scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a flow chart of the present invention;

[0023] Figure 2 It is a simulation diagram of the present invention, wherein, Figure 2 (a) is the actual motion trajectory diagram of the target in the simulation experiment of the present invention, Figure 2 (b) is the original data diagram of the simulation experiment of the present invention, Figure 2 (c) is the track diagram after tracking using the GM-PHD algorithm in the simulation experiment of the present invention, Figure 2 (d) is the track diagram after correlation of the simulation experiment of the present invention. DETAILED DESCRIPTION

[0024] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0025] Reference Figure 1 , further describing the implementation steps of the embodiment of the present invention.

[0026] Step 1: Input the track segment to be associated, extract the target position at each time point in the track segment, form a point track set of the track segment, release the data in the point track set, and merge the released point track data with the clutter and target point track data obtained by the radar during the break period into a point track data set.

[0027] Track breakage may be caused by the following reasons: first, signal loss due to obstacle blocking, and the tracking system does not have the correct input data, resulting in track breakage; second, in a multi-target environment, when the distance between multiple targets is close, the target signals may overlap or confuse each other, and the sensor cannot distinguish between different targets, resulting in the tracking system being unable to accurately associate with the correct target trajectory, resulting in track interruption or incorrect association. The traditional reassociation method after track interruption only solves the track breakage caused by obstacle blocking, and does not consider the track breakage caused by track misassociation. In response to this situation, the present invention releases the broken data and does not directly use the wrongly associated track, thus avoiding the track breakage caused by wrong track association.

[0028] Traditional algorithms cannot use data during track breaks, but there is also some useful information during track breaks. Assuming that the ship makes a turn during the break, if this part of the information is directly discarded, it will lead to serious mismatches before and after the break, and eventually make the broken track association fail. Therefore, the present invention adds the data during the break to the initial data, making full use of this part of the data.

[0029] The steps of releasing the data in the point trace set are as follows:

[0030] In the first step, according to the start time of each track, the track start time before the break is set as the old track, and the track start time after the break is set as the new track.

[0031] The second step is to restore the estimated or measured positions of all tracks in the point track set to independent points to obtain a restored point track data set.

[0032] The third step is to clean and filter the restored point trace data, remove abnormal points that are obviously deviated from other points, and use the processed point trace set as the input point trace data set.

[0033] Step 2: Use GM-PHD to track and filter the point track data set to obtain the track set containing label information.

[0034] Traditional tracking algorithms usually assume that the number of targets is fixed and only focus on associating and repairing existing tracks. These algorithms rely on a fixed number of targets and perform data association through parameters such as position and speed, but when targets suddenly appear or disappear, the algorithm cannot flexibly adjust the number of targets. This results in the system being unable to update the track in a timely manner when the target appears or disappears, resulting in incorrect track association. The present invention uses GM-PHD to track and filter the point track data set to obtain a track information data set containing label information after tracking.

[0035] The GM-PHD filter dynamically models the changing process of multi-target states, including the appearance of new targets and the disappearance of existing targets, by recursively inferring the probability hypothesis density function of the target, so that the filter can flexibly adapt to the dynamic changes in the number of targets and effectively solve the appearance and disappearance problems in multi-target tracking. The specific steps are as follows:

[0036] The first step is to predict the probability density of the point trace at each time according to the following formula:

[0037] v k|k-1 (x) = ∫p S ·φ k|k-1 (x|ξ)v k-1 (ξ)dξ+v γ,k (x)

[0038] Among them, v k|k-1 (x) represents the probability density of the point state at the kth moment predicted based on the point state at the k-1th moment, p S represents the survival probability of the point trace, φ k|k-1 (x|ξ) represents the probability density of the state of the point trace at the k-1th time to the state of the point trace at the kth time, v k-1 (x) represents the intensity of the k-1 time points, v γ,k(x) represents the new target intensity of the point at the kth moment.

[0039] The second step is to update the probability density of each point trace at each time according to the following formula:

[0040]

[0041] Among them, v k (x) represents the difference between the observed data at the kth moment and the predicted v k|k-1 (x) The updated probability density of the k-th time point obtained after the combination, p D,k (x) represents the detection probability of the point trace at the kth time, g k (z|x) represents the likelihood function value of the point observation value z obtained according to the state of the point at the kth moment, κ k (z) represents the intensity of the Poisson clutter RFS of the observation value z of the k-th time point.

[0042] Step 3: Perform speed matching on the track set to obtain a candidate track set.

[0043] Step 3.1, classify the tracks in the track set according to the start time to form an old track set and a new track set; wherein, the tracks whose start time is before the break belong to the old tracks, and the tracks whose start time is after the break belong to the new tracks.

[0044] Step 3.2, the end time of the old track and the start time of the new track are roughly screened. If the time difference between the two exceeds the broken time window, the matching of this pair of tracks is directly excluded.

[0045] Step 3.3, divide the track into time windows according to the break time, and calculate the starting coordinates of each new track in the adjacent window End coordinates of the old track The distance between them is divided by the time difference between the two to get the speed V nm ; Set the speed V nm The maximum speed V specified by the sea track max For comparison, if V nm <V max , then it is believed that and There is a possibility of matching, and the matching pairs are are stored in the candidate track set in the form of.

[0046] Step 3.4, all matching pairs that meet the speed matching conditions are stored in the candidate track set to form a candidate track set.

[0047] Step 4: Use the Kalman tracking algorithm to reverse or predict the new and old track segments in the candidate track set to obtain a recursive candidate track set.

[0048] Step 4.1, filter parameters P0, Q0, R0 are initialized, where represents the target state estimate at the initial moment, P0 represents the initial covariance matrix, Q0 represents the initial target process noise matrix, and R0 represents the initial observation noise matrix.

[0049] Step 4.2, predict the state and estimation error covariance respectively according to the following formula:

[0050]

[0051]

[0052] in, Represents the estimated value The predicted value, F k-1 represents the radar tracking target state transfer matrix at the k-1th radar sampling moment, represents the estimated value of the radar tracking target state at the k-1th radar sampling moment, P kk-1 Indicates P k-1 The predicted value, P k-1 represents the covariance matrix of the k-1th radar sampling moment, the superscript T represents the transpose operation, Q k-1 represents the process noise variance matrix at the k-1th radar sampling moment.

[0053] Step 4.3, calculate the measurement prediction, innovation covariance matrix and Kalman gain according to the following formula:

[0054]

[0055] in, Indicates estimated value The measured predicted value of represents the estimated value of the observed state of the target, H k represents the observation matrix at the kth radar sampling moment, S k represents the new information covariance matrix at the kth radar sampling moment, H k-1 represents the observation matrix at the k-1th radar sampling moment, R k represents the observation noise matrix at the kth radar sampling moment, K k represents the Kalman gain at the kth radar sampling moment, and the superscript -1 indicates the inversion operation.

[0056] Step 4.4, calculate the state estimate and the estimation error covariance according to the following formula:

[0057]

[0058] P k =P kk-1 -K k H k P kk-1

[0059] in, represents the estimated value of the radar tracking target state at the kth radar sampling moment, z k represents the observed state value of the target, P k represents the estimated error covariance at the kth radar sampling moment.

[0060] Step 4.5, the inverse / predicted new track and the predicted old track obtained in the first four steps are stored in the recursive candidate track data set according to the corresponding order in the candidate track set.

[0061] Step 5: Perform a chi-square test on the candidate track set, and screen the candidate tracks that do not meet the association conditions again to obtain a screened candidate track set.

[0062] The chi-square test on the candidate track set refers to screening possible associated paired track pairs from the recursive candidate track data set. The steps are as follows:

[0063] The first step is to use the following formula to obtain the candidate track data set T after recursion: OY , filter the possible associated track pairs:

[0064]

[0065] P O,Y (k b )=P O (k b )+P Y (k b )

[0066] Among them, Δ O,Y (k b ) represents the kth b The estimated error of the new / old track segment at time, Indicates the kth b The state of the new track at this moment, Indicates the kth b The state of the old track at a certain moment, P O,Y (k b ) represents the kth b The estimation error of the new / old track segment at the moment, P O (k b) represents the kth b The covariance of the new track at time, P Y (k b ) represents the kth b The covariance of the old track at that moment.

[0067] The second step is to determine whether the test estimates of the new / old tracks obey the independent Gaussian distribution condition. If so, the new track segment T O With the old track fragment T Y Determine that they belong to the same target, record it as H0, otherwise, determine the new track segment T O With the old track fragment T Y do not belong to the same target, denoted as H1, and from the track pair set T OY Remove the track pair from the .

[0068] The independent Gaussian distribution conditions are as follows:

[0069]

[0070] in, It means that the degree of freedom is n z The critical value of the chi-square distribution, which is a fixed value for querying the chi-square distribution table, n z Represents the dimension of the target state of the new track and the old track at the current moment, P Q Indicates the tail probability corresponding to the new track and the old track at this moment.

[0071] Step 6: optimally allocate the screened candidate track set to obtain a track set to be associated.

[0072] The optimal allocation of the screened candidate track set refers to obtaining the optimal solution of global allocation according to the auction algorithm, and combining the optimal solutions of each new and old track to obtain a set of optimally allocated track pairs.

[0073] Furthermore, the track Perform global optimal allocation, where the variables of global optimal allocation are:

[0074]

[0075] The associated cost function is:

[0076]

[0077] For the global optimal allocation problem, the following cost function is minimized:

[0078]

[0079] Step 7: fuse the track segments.

[0080] The target track of the interruption interval is fitted using the polynomial fitting method, and the fitting order is usually determined based on empirical values. The data used consists of two parts:

[0081]

[0082] in, represents the estimated state vector of the nth segment of the track, k represents the time, represents the estimated state vector of the mth track. The purpose of this formula is to splice multiple tracks of the target to obtain the final merged track. The formula shows that the merged track consists of two parts: the first half is the state estimate of track n, and the time range is from k b arrive The second half is the state estimate of track m, with a time range from k b arrive Through this splicing method, the new and old track segments can be integrated to obtain the complete target track after the broken tracks are associated.

[0083] The technical effects of the present invention are further described below in conjunction with simulation experiments.

[0084] 1. Simulation experiment conditions:

[0085] The hardware platform of the simulation experiment of the present invention is: the processor is Inter(R)Core(TM)i7-12800HX CPU, the main frequency is 2.00GHz, the memory is 32GB, and the graphics card is RTX3070Ti.

[0086] The software platform for the simulation experiment of the present invention is: Windows 11 operating system, MATLAB 2022b and

[0087] 2. Simulation content and result analysis:

[0088] The simulation experiment of the present invention adopts the fracture track association algorithm based on track release and GM-PHD to perform fracture track association on the fracture track of uniform moving targets within the monitoring area [-1000, 1000]m×[-1000, 1000]m. The input data used in the simulation experiment of the present invention is Figure 2 (a) The actual target track is shown in Figure 2 The circle in (a) indicates the starting point of the track, and the square indicates the end point of the track.

[0089] exist Figure 2 In the scenario shown in (a), the target state is modeled as where (x,y) and They represent the target position and velocity components in the Cartesian coordinate system respectively. During the tracking filtering process, the state transition of the target is described by the following constant velocity (CV) model:

[0090] x k =F CV x k-1 +w k-1

[0091] The state transfer matrix F in the formula CV Written as:

[0092]

[0093] in, is the Kronecker product, I2 is the two-dimensional identity matrix, T s =1 is the sampling period. Process noise w k-1 It obeys a zero-mean Gaussian distribution, in which the process noise covariance matrix is ​​written as

[0094]

[0095] Among them, σ w =5m / s 2 is the standard deviation of process noise. The survival probability of the target is set to p S =0.95.

[0096] The target measurement is modeled by the following linear measurement model:

[0097] z k =[x,y] T +v k

[0098] Among them, the measurement noise v k Subject to covariance The zero-mean Gaussian distribution has a noise standard deviation of σ v =10m. In addition, the clutter in the scene is modeled as Poisson RFS, and the number of clutter in each scanning cycle follows the mean value λ c = 10, the spatial density is uniformly distributed in the monitoring area. The adaptive regeneration intensity is set to 10 -8 .

[0099] ADP-GM-PHD filtering is performed under different detection probability and clutter rate scenarios, and the scenario parameters are set as follows: a) detection probability is 0.98, and the clutter rate is 10; b) detection probability is 0.98, and the clutter rate is 5; c) detection probability is 0.8, and the clutter rate is 10; d) detection probability is 0.8, and the clutter rate is 5.

[0100] The original simulation data is as follows Figure 2 (b) As shown. After GM-PHD, 16 broken tracks are formed, as shown in Figure 2 (c) Figure 2 Different colors in (c) represent different track numbers. After re-association by this method, the tracks are re-identified as 10 tracks, which is consistent with the real track results generated by the simulation experiment before this invention, as shown in Figure 2 (d) as shown.

[0101] The simulation experiment results of the present invention prove that the present invention can still correctly reassociate the broken track in the scenario where multiple targets appear or disappear dynamically and the track motion changes greatly during the track break.

Claims

1. A method for associating broken tracks based on track release and GM-PHD, characterized in that: The point trace data after release and the point trace data of clutter and target acquired by radar during the break period are merged into a point trace data set, and GM-PHD is used to track and filter the point trace data set; the steps of the association method include the following: Step 1: input the track segment to be associated, extract the target position at each time point in the track segment, form a point track set of the track segment, release the data in the point track set, and merge the released point track data with the clutter and target point track data obtained by the radar during the break period into a point track data set; Step 2: Use GM-PHD to track and filter the point track data set to obtain the track set containing label information after tracking; Step 3, perform speed matching on the track set to obtain a candidate track set; Step 4, reverse or predict the new and old track segments in the candidate track set to obtain a recursive candidate track set; Step 5, performing a chi-square test on the candidate track set, and re-screening the candidate tracks that do not meet the association conditions to obtain a screened candidate track set; Step 6, optimally allocating the screened candidate track set to obtain a track set to be associated; Step 7: fuse the track segments.

2. The method for associating broken tracks based on track release and GM-PHD according to claim 1, characterized in that: The steps for releasing the data in the point trace set described in step 1 are as follows: The first step is to set the track start time before the break as the old track and the track start time after the break as the new track according to the start time of each track. The second step is to restore the estimated positions or measured positions of all tracks in the point track set into independent point tracks to obtain a restored point track data set; The third step is to clean and filter the restored point trace data, remove abnormal points that are obviously deviated from other points, and use the processed point trace set as the input point trace data set.

3. The method for associating broken tracks based on track release and GM-PHD according to claim 1, characterized in that: The use of GM-PHD to track and filter the point data set in step 2 means that the target is tracked by continuously predicting and updating the probability density of the point at each moment in the point data set. The probability density of the point reflects the probability of the target in the state space. By integrating the intensity function, the number of targets in the point at the current moment can be updated in real time. The specific steps are as follows: The first step is to predict the probability density of the point trace at each time according to the following formula: v k|k-1 (x)=∫p S ·φ k|k-1 (x|ξ)v k-1 (ξ)dξ+v γ,k (x) Among them, v k|k-1 (x) represents the probability density of the point state at the kth moment predicted based on the point state at the k-1th moment, p S represents the survival probability of the point, φ k|k-1 (x|ξ) represents the probability density of the state of the point trace at the k-1th time to the state of the point trace at the kth time, v k-1 (x) represents the intensity of the k-1 time points, v γ,k (x) represents the new target intensity of the point trace at the kth moment; The second step is to update the probability density of each point trace at each time according to the following formula: Among them, v k (x) represents the difference between the observed data at the kth moment and the predicted v k|k-1 (x) The updated probability density of the k-th time point obtained after the combination, p D,k (x) represents the detection probability of the point trace at the kth time, g k (z|x) represents the likelihood function value of the point observation value z obtained according to the state of the point at the kth moment, κ k (z) represents the intensity of the Poisson clutter RFS of the observation value z of the k-th time point.

4. The method for associating broken tracks based on track release and GM-PHD according to claim 1, characterized in that: The steps for speed matching of the track set described in step 3 are as follows: The first step is to classify the tracks in the track set according to the starting time to form an old track set and a new track set; among them, the tracks with the starting time before the break belong to the old tracks, and the tracks with the starting time after the break belong to the new tracks; The second step is to roughly screen the end time of the old track and the start time of the new track. If the time difference between the two exceeds the broken time window, the matching of this pair of tracks is directly excluded; The third step is to divide the track into time windows according to the break time and calculate the starting coordinates of each new track in the adjacent window. End coordinates of the old track The distance between them is divided by the time difference between the two to get the speed V nm ; Set the speed V nm The maximum speed V specified by the sea track max For comparison, if V nm <V max , then we think that T n O and There is a possibility of matching, and the matching pairs are The form of is stored in the candidate track set; The fourth step is to store all matching pairs that meet the speed matching conditions into the candidate track set to form a candidate track set.

5. The method for associating broken tracks based on track release and GM-PHD according to claim 1, characterized in that: In step 4, the new and old track segments in the candidate track set are reversed or predicted using the Kalman tracking algorithm, and the steps are as follows: The first step is to adjust the filter parameters P0, Q0, R0 are initialized, where represents the target state estimate at the initial moment, P0 represents the initial covariance matrix, Q0 represents the initial target process noise matrix, and R0 represents the initial observation noise matrix; In the second step, the state and estimated error covariance are predicted respectively according to the following formula: in, Represents the estimated value The predicted value, F k-1 represents the radar tracking target state transfer matrix at the k-1th radar sampling moment, represents the estimated value of the radar tracking target state at the k-1th radar sampling moment, P kk-1 Indicates P k-1 The predicted value, P k-1 represents the covariance matrix of the k-1th radar sampling moment, the superscript T represents the transpose operation, Q k-1 represents the process noise variance matrix at the k-1th radar sampling moment; In the third step, the measurement prediction, innovation covariance matrix and Kalman gain are calculated according to the following formula: in, Indicates estimated value The measured predicted value of represents the estimated value of the observed state of the target, H k represents the observation matrix at the kth radar sampling moment, S k represents the new information covariance matrix at the kth radar sampling moment, H k-1 represents the observation matrix at the k-1th radar sampling moment, R k represents the observation noise matrix at the kth radar sampling moment, K k represents the Kalman gain at the kth radar sampling moment, and the superscript -1 indicates the inversion operation; The fourth step is to calculate the state estimate and the estimation error covariance according to the following formula: P k =P kk-1 -K k H k P kk-1 in, represents the estimated value of the radar tracking target state at the kth radar sampling moment, z k represents the observed state value of the target, P k represents the estimated error covariance at the kth radar sampling moment; In the fifth step, the inverse / predicted new track and the predicted old track obtained in the first four steps are stored in the recursive candidate track data set according to the corresponding order in the candidate track set.

6. The method for associating broken tracks based on track release and GM-PHD according to claim 1, characterized in that: The chi-square test on the candidate track set in step 5 refers to screening possible associated paired track pairs from the recursive candidate track data set, and the steps are as follows: The first step is to use the following formula to obtain the candidate track data set T after recursion: OY , filter the possible associated track pairs: Among them, Δ O,Y (k b ) represents the kth b The estimated error of the new / old track segment at time, Indicates the kth b The state of the new track at this moment, Indicates the kth b The state of the old track at a certain moment, P O,Y (k b ) represents the kth b The estimation error of the new / old track segment at the moment, P O (k b ) represents the kth b The covariance of the new track at time, P Y (k b ) represents the kth b The covariance of the old track at that moment; The second step is to determine whether the test estimates of the new / old tracks obey the independent Gaussian distribution condition. If so, the new track segment T O With the old track fragment T Y Determine that they belong to the same target, record it as H0, otherwise, determine the new track segment T O With the old track fragment T Y do not belong to the same target, denoted as H1, and from the track pair set T OY Remove the track pair from the .

7. The method for associating broken tracks based on track release and GM-PHD according to claim 6, characterized in that: The independent Gaussian distribution conditions are as follows: in, It means that the degree of freedom is n z The critical value of the chi-square distribution, which is a fixed value for querying the chi-square distribution table, n z Represents the dimension of the target state of the new track and the old track at the current moment, P Q Indicates the tail probability corresponding to the new track and the old track at this moment.

8. The method for associating broken tracks based on track release and GM-PHD according to claim 1, characterized in that: The optimal allocation of the screened candidate track set in step 6 refers to obtaining the optimal solution of global allocation according to the auction algorithm, and combining the optimal solutions of each new and old track to obtain a set of optimally allocated track pairs.

9. The method for associating broken tracks based on track release and GM-PHD according to claim 1, characterized in that: The fusion of the track segments in step 7 refers to: fitting the target track of the interruption interval using a polynomial fitting method, and the order of the fitting is usually determined based on an empirical value.

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