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

Abstract

This invention discloses a fragmented track association method based on track release and GM-PHD, aiming to solve the problem of inaccurate track prediction in traditional TSA algorithms in multi-target scenarios due to the dynamic generation and disappearance of targets, and also addressing the challenge of ineffective information utilization during track fragmentation. By releasing old and new tracks as point data and integrating the data from the fragmentation period to form a new dataset, the track re-association effect is significantly improved. Using a GM-PHD filter for dynamic estimation of multi-target states improves the accuracy of track prediction. Through global optimal allocation and polynomial fitting, the fragmented tracks are re-associated and stitched together to construct a complete target track after fragmented track association.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and more specifically relates to a method for re-associating broken tracks based on track release and the Gaussian Mixture Probability Hypothesis Density (GM-PHD) algorithm in the field of target tracking technology. This invention can be used for real-time monitoring of target ships by shore-based maritime radar, addressing track erroneous associations and re-associating broken tracks. Background Technology

[0002] Discontinuous track association (TSA) is a technique used in multi-target tracking systems to effectively reconnect fragmented trajectory segments after they have been interrupted for various reasons. Track association involves not only associating different state points of the same target at the same time, but also effectively associating the preceding and following trajectory segments after a track break. During target tracking, trajectories may break due to factors such as highly maneuvering targets, false alarms, large measurement errors, close-range target formations, low detection probability, or long sampling intervals. When a trajectory is interrupted, traditional association techniques cannot accurately identify and connect these broken trajectory segments, thus affecting the performance of the entire tracking system. To ensure the continuity and accuracy of the target trajectory, these broken trajectories must be re-associated. Currently, the TSA algorithm (Track Segment Association) is widely used in various tracking systems. When handling track breaks, it typically involves predicting the old trajectory segments and then assigning the new trajectory segments back to a common time point in a two-dimensional manner to achieve the association of interrupted trajectories.

[0003] Hangzhou Dianzi University disclosed a method for associating interrupted track segments of maritime vessels based on Gaussian processes in its patent application, "A Method for Associating Interrupted Tracks Based on Gaussian Processes" (Application No. CN 202011410712.2, Publication No. CN 117233745A). The method's implementation steps are: 1) classifying interrupted tracks to obtain an initial track set; 2) using Gaussian processes to learn the unknown function of the target motion, predicting and reverse-predicting the new and old tracks in the initial track pairs; 3) performing velocity filtering, binary hypothesis testing, and two-dimensional allocation on the obtained track segments to resolve ambiguity issues, obtaining an optimal allocation track set; 4) fusing the predicted interrupted track values ​​of the optimal allocation track set using Gaussian processes to obtain a complete track. This method, using Gaussian processes for interrupted track association, improves the accuracy of track association, obtains the track at the interruption point, and increases the average track lifespan. However, this method still has three shortcomings: First, it uses a Gaussian process to recursively calculate the target's trajectory, resulting in high computational complexity that cannot meet real-time requirements in practical scenarios. Second, useful real trajectory information exists during trajectory breaks, but this algorithm does not utilize this information, causing the trajectory reassociation to fail to update in a timely manner based on the information during the break, leading to erroneous reassociation.

[0004] The patent document "Method for Correlation of Disrupted Tracks of Maritime Targets by High-Orbit Optical Satellites" (application number: CN201911036959.X, publication number CN 110686679A) discloses a method for re-correlation of interrupted tracks of maritime targets based on optical satellites. The steps of this method are as follows: 1) Extrapolate outward from the first track and outward from the second track to obtain the state estimates of the first and second tracks at the same time; 2) Perform preliminary association between the first and second tracks whose state estimates at the same time satisfy the constraints to obtain a preliminary association set; 3) Use the χ2 distribution hypothesis testing method to further associate the tracks in the preliminary association set to obtain a further association set; use the two-dimensional optimal allocation principle to solve the further association set to obtain the association set with the minimum global cost, which is the first-stage association set; 4) Use the distance two-dimensional optimal allocation to solve the possible association segment pairs in the complement of the first-stage association set in the preliminary association set to obtain an intermediate association set; 5) Use amplitude relationship detection to filter the intermediate association set to obtain a second-stage association set; 6) Fit the association track pairs in the first-stage association set and the second-stage association set with an Nth-order polynomial to obtain a continuous track. The drawback of this method is that it uses the Kalman recursion algorithm, which is only applicable to linear cases. However, many nonlinear situations exist in the sea environment, and in nonlinear cases, the Kalman recursion algorithm cannot correctly reconnect broken tracks. This is because track breakage is mainly caused by two factors: first, signal loss due to obstacle obstruction, resulting in the tracking system lacking correct input data and causing track breakage; second, in multi-target environments, when multiple targets are close together, their signals may overlap or become confused, making it difficult for sensors to distinguish between different targets. This leads to the tracking system failing to accurately reconnect to the correct target trajectory, resulting in track interruption or incorrect reconnection. Traditional reconnection methods after track interruption only address track breakage caused by obstacle obstruction; they cannot accurately reconnect to the correct target trajectory when multiple targets are close together.

[0005] In summary, the TSA interrupted trajectory association algorithm has the following two main problems:

[0006] First, traditional TSA algorithms cannot dynamically handle track breakage caused by target generation and disappearance. Traditional TSA algorithms typically assume a fixed number of targets and focus only on associating and repairing existing tracks. These algorithms rely on a fixed number of targets and perform data association using parameters such as position and velocity. However, when targets suddenly generate or disappear, the algorithms cannot flexibly adjust the number of targets. This results in the system being unable to update tracks in a timely manner when targets appear or disappear, leading to the inability to correctly re-associate tracks after they are interrupted.

[0007] Second, traditional algorithms cannot utilize the data during track breaks, even though some useful information exists during track breaks. If the ship makes a turn during the break, discarding this broken information directly would lead to a serious mismatch before and after the break, ultimately causing the track association to fail. Summary of the Invention

[0008] The purpose of this invention is to address the shortcomings of the existing technology by proposing a broken track association method based on track release and GM-PHD. This method aims to solve the problem of inaccurate track prediction by traditional TSA algorithms in multi-target scenarios due to the dynamic generation and disappearance of targets. At the same time, it effectively utilizes the data during track breaks to improve the track reassociation effect.

[0009] The technical approach to achieving the objective of this invention is as follows: This invention releases the received new and old tracks as point data and integrates the data from the break period to form a new dataset containing break information. This process solves the problem of existing technologies being unable to effectively utilize data during track breaks, enabling the invention to successfully integrate information from the break period even when tracks undergo significant changes, significantly improving the track re-association effect. Furthermore, this invention employs a Gaussian Probability Mixture Density (GM-PHD) algorithm to filter the new dataset, using Probability Hypothesis Density (PHD) to estimate the states of multiple targets. This not only avoids the complex data association problems of traditional filters but also dynamically handles target generation and disappearance. This improvement overcomes the limitations of traditional TSA algorithms in multi-target scenarios, especially in cases of dynamic target generation and disappearance. The GM-PHD algorithm maintains the accuracy of track prediction, effectively solving the limitation of the TSA algorithm on a fixed number of targets. This invention categorizes GM-PHD processed data into new and old tracks based on time classification, performs speed matching between the new and old tracks, and calculates time and distance differences to infer the speed of the track during the break, thus initially screening potentially associated track pairs. For the selected track pairs, further recursive and predictive processing is performed: new tracks are recursively extrapolated forward, and old tracks are predicted backward, to improve association accuracy. Then, hypothesis testing is conducted on the predicted data to further screen track pairs with high matching probability. For track pairs that pass the test, a global optimal allocation method is used to solve the many-to-many matching problem, finding the optimal pairing combination by minimizing the matching cost. Finally, the associated track segments are re-associated, and the tracks in the broken intervals are processed using polynomial fitting, splicing them with the new and old tracks to form a complete target track after the broken track association.

[0010] The steps of this 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 to form a point set of the track segment, release the data in the point set, and merge the released point data with the clutter and target point data acquired by the radar during the break to form a point dataset.

[0012] Step 2: Use GM-PHD to perform tracking filtering on the point dataset to obtain the track set containing tag information after tracking;

[0013] Step 3: Perform velocity matching on the track set to obtain a candidate track set;

[0014] Step 4: Back-engineer or predict the new and old track segments in the candidate track set to obtain the recursive candidate track set.

[0015] Step 5: Perform a chi-square test on the candidate track set, and further filter the candidate tracks that do not meet the correlation conditions to obtain the filtered candidate track set.

[0016] Step 6: Optimize the allocation of the filtered candidate track set to obtain the track set to be associated;

[0017] Step 7: Fuse the flight track segments.

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

[0019] First, this invention overcomes the deficiency of existing technologies in effectively utilizing data during track breaks by introducing a track release step, integrating the released data with the data from the track break period, and then re-tracking and filtering it. This allows the invention to successfully re-associate tracks even when there are significant changes in the track during the break, significantly improving the effectiveness of track break processing.

[0020] Secondly, this invention introduces a Gaussian mixture probability density algorithm (GM-PHD), which estimates the states of multiple targets using probability hypothesis density (PHD). This enables dynamic handling of target generation and disappearance, adapting to the complex changes in multi-target scenarios. It overcomes the problem of inaccurate trajectory prediction in traditional TSA algorithms due to the dynamic generation and disappearance of targets in multi-target scenarios. This invention effectively solves the limitation of traditional TSA algorithms requiring a fixed number of targets, improving the ability to correlate broken trajectories in multi-target environments.

[0021] Third, by combining track release with data during the break and GM-PHD filtering, this invention not only improves the accuracy of correlation of broken tracks, but also enhances the adaptability and robustness of the algorithm in dynamic multi-target environments, fully demonstrating its superiority in handling multi-target scenarios. Attached Figure Description

[0022] Figure 1 This is a flowchart of the present invention;

[0023] Figure 2 This is a simulation diagram of the present invention, wherein, Figure 2 (a) is a diagram of the actual motion trajectory of the target in the simulation experiment of this invention. Figure 2 (b) is a graph of the original data from the simulation experiment of this invention. Figure 2 (c) is a flight path image after tracking using the GM-PHD algorithm in the simulation experiment of this invention. Figure 2 (d) is the trajectory diagram after the simulation experiment of this invention. Detailed Implementation

[0024] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0025] Reference Figure 1 The implementation steps of the embodiments of the present invention will be further described below.

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

[0027] Track breakage can be caused by several factors: First, signal loss due to obstacle obstruction, resulting in incorrect input data for the tracking system and track breakage. Second, in multi-target environments, when multiple targets are close together, their signals may overlap or become confused, making it difficult for sensors to distinguish between different targets. This prevents the tracking system from accurately associating with the correct target trajectory, leading to track interruption or incorrect association. Traditional reassociation methods after track interruption only address track breakage caused by obstacle obstruction, neglecting track breakage due to incorrect association. To address this, this invention releases the broken data and avoids directly using incorrectly associated tracks, thus preventing track breakage caused by incorrect association.

[0028] Traditional algorithms cannot utilize data during track breaks, even though some useful information exists during these breaks. For example, if a ship performs a turn during the break, discarding this information directly would lead to a severe mismatch before and after the break, ultimately causing the track association to fail. Therefore, this invention incorporates data from the break period into the initial data, fully utilizing this portion of the data.

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

[0030] The first step is to define the tracks in the set whose start time is before the break as old tracks and those whose start time is after the break as new tracks, based on the start time of each track.

[0031] The second step is to restore the estimated or measured positions of all tracks in the point set to independent points, thus obtaining the restored point set dataset.

[0032] The third step is to clean and filter the recovered point data, remove outliers that deviate significantly from other points, and use the processed point set as the input point dataset.

[0033] Step 2: Use GM-PHD to perform tracking filtering on the point dataset to obtain the track set containing tag information after tracking.

[0034] Traditional tracking algorithms typically assume a fixed number of targets and focus solely on associating and repairing existing tracks. These algorithms rely on a fixed number of targets and associate data using parameters such as position and velocity. However, when targets suddenly appear or disappear, the algorithms cannot flexibly adjust the number of targets. This results in the system failing to update tracks in a timely manner when targets appear or disappear, leading to incorrect track associations. This invention, however, uses GM-PHD to perform tracking filtering on the point dataset, obtaining a track information dataset containing tag information after tracking.

[0035] The GM-PHD filter dynamically models the state changes of multiple targets by recursively calculating the probability hypothesis density function of the targets. This includes the appearance of new targets and the disappearance of existing targets, allowing the filter to flexibly adapt to 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 trace at each time step using 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 state of the point at time k, predicted based on the state of the point at time k-1. S φ represents the survival probability of the dot. k|k-1 (x|ξ) represents the probability density of the state transition of the trace at time k-1 to the state at time k. k-1 (x) represents the intensity of the trace at time k-1, v γ,k(x) represents the intensity of the newly generated target at the k-th time point.

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

[0040]

[0041] Among them, v k (x) represents the combination of the observation data of the point at time k and the predicted v. k|k-1 (x) is the update probability density of the k-th time point obtained after combination, p D,k (x) represents the detection probability of the trace at time k, g k (z|x) represents the likelihood function value of the observed value z of the point trace obtained based on the state of the point trace at time k. k (z) represents the intensity of the Poisson clutter RFS of the observation value z at time k.

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

[0043] Step 3.1: Classify the tracks in the track set according to their start time to form an old track set and a new track set; tracks whose start time is before the break are old tracks, while tracks whose start time is after the break are new tracks.

[0044] Step 3.2: Perform a rough screening of the end time of the old track and the start time of the new track. If the time difference between the two exceeds the time window of the break, the pair of tracks is directly excluded from the match.

[0045] Step 3.3: Divide the track into time windows based on the break time, and calculate the starting coordinates of each new track within an adjacent window. End coordinates of the old flight path The distance between them, divided by the time difference between them, gives the velocity V. nm ; speed V nm The maximum speed V specified by the sea surface track max Compare, if V nm <V max Then it is believed and There is a possibility of a match; the matching pair will be... The candidate tracks are stored in the form of a set of tracks.

[0046] Step 3.4: Store all matching pairs that meet the speed matching conditions into the candidate track set to form the candidate track set.

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

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

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

[0050]

[0051]

[0052] in, Indicates the estimated value The predicted value, F k-1 This represents the radar target tracking state transition matrix at the (k-1)th radar sampling time. P represents the radar target state estimate at the (k-1)th radar sampling time. kk-1 P represents k-1 The predicted value, P k-1 Let Q represent the covariance matrix at the (k-1)th radar sampling time, with the superscript T indicating the transpose operation. k-1 Let represent the process noise variance matrix at the (k-1)th radar sampling time.

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

[0054]

[0055] in, Indicates the estimated value The predicted measurement value, H represents the estimated observed state of the target. k S represents the observation matrix at the k-th radar sampling time. k H represents the information covariance matrix at the k-th radar sampling time. k-1 R represents the observation matrix at the (k-1)th radar sampling time. k Let K represent the observation noise matrix at the k-th radar sampling time. k This represents the Kalman gain at the k-th radar sampling time, with the superscript -1 indicating the inversion operation.

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

[0057]

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

[0059] in, Let z represent the radar target state estimate at the k-th radar sampling time. k P represents the observed state value of the target. k Let represent the estimation error covariance at the k-th radar sampling time.

[0060] Step 4.5: Store the new track and the predicted old track obtained from the previous four steps in the recursive candidate track dataset in the corresponding order in the candidate track set.

[0061] Step 5: Perform a chi-square test on the candidate track set, and further filter the candidate tracks that do not meet the correlation conditions to obtain the filtered candidate track set.

[0062] The chi-square test on the candidate track set refers to filtering potentially associated track pairs from the recursive candidate track dataset. The steps are as follows:

[0063] The first step is to use the following formula to calculate the candidate track dataset T after recursion. OY In the process, filter for potentially associated track pairs:

[0064]

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

[0066] Where, Δ O,Y (k b ) represents the k-th b The estimation error of the new / old track segment at each moment, Indicates the kth b The status of a new flight path at any given moment. Indicates the kth b The state of the old flight path at that moment, P O,Y (k b ) represents the k-th b The estimation error of the new / old track segment at each moment, P O (k b) represents the k-th b The covariance of the new trajectory at each moment, P Y (k b ) represents the k-th b The covariance of the old flight path at a given moment.

[0067] The second step is to determine whether the test estimators of the new / old tracks follow mutually independent Gaussian distributions. If so, then the new track segment T is... O With old flight path fragments T Y If they belong to the same target, record it as H0; otherwise, determine that it is a new track segment T. O With old flight path fragments T Y If they do not belong to the same target, denoted as H1, and are included in the set T of track pairs. OY Remove the track pair from the list.

[0068] The conditions for the mutually independent Gaussian distributions are as follows:

[0069]

[0070] in, This indicates that it has n degrees of freedom. z The critical value of the chi-square distribution is a constant value obtained by querying the chi-square distribution table, n. z P represents the dimension of the target state of the new and old track points at the current moment. Q This represents the tail probability corresponding to the new track and the old track at that moment.

[0071] Step 6: Optimize the allocation of the selected candidate track set to obtain the track set to be associated.

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

[0073] Furthermore, regarding the track pair Perform a globally optimal allocation, where the variables for the globally optimal allocation are:

[0074]

[0075] The association cost function is:

[0076]

[0077] For the globally optimal allocation problem, we can minimize the following cost function:

[0078]

[0079] Step 7: Fuse the flight track segments.

[0080] Polynomial fitting is used to fit the target trajectory within the interrupted interval; the order of the fit is usually determined empirically. The data used consists of two parts:

[0081]

[0082] in, Let k represent the estimated state vector of the nth segment of the trajectory, and k represent time. This represents the estimated state vector of the m-th segment of the trajectory. The purpose of this formula is to concatenate multiple trajectories of the target to obtain the final merged trajectory. The formula indicates that the merged trajectory consists of two parts: the first part is the state estimate of trajectory n, with a time range from k... b arrive The latter half consists of the state estimates for track m, with a time range from k. b arrive This splicing method can integrate the old and new track segments to obtain a complete target track after the broken track segments are associated.

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

[0084] 1. Simulation experimental conditions:

[0085] The hardware platform for the simulation experiment of this invention is as follows: the processor is an Intel(R) Core(TM) i7-12800HX CPU with a main frequency of 2.00GHz, the memory is 32GB, and the graphics card is an RTX3070Ti.

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

[0087] 2. Simulation content and result analysis:

[0088] The simulation experiment of this invention employs a fractured trajectory association algorithm based on trajectory release and GM-PHD to associate fractured trajectories of uniformly moving targets within a monitored area of ​​[-1000, 1000]m × [-1000, 1000]m. The input data used in the simulation experiment of this invention is... Figure 2 (a) shows the actual trajectory of the target. Figure 2 In (a), the circle represents the starting point of the track and the square represents the ending point of the track.

[0089] exist Figure 2 In the scenario shown in (a), the target state is modeled as follows: Where (x,y) and Let represent the target's position and velocity components in Cartesian coordinates, respectively. During the tracking filtering process, the target's state transition is described by the following constant velocity (CV) model:

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

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

[0092]

[0093] in, The product is the Kronecker product, I2 is the two-dimensional identity matrix, and T s =1 represents the sampling period. Process noise w k-1 The process noise covariance matrix follows a zero-mean Gaussian distribution, and in this distribution, it can be written as:

[0094]

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

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

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

[0098] Among them, the measurement noise v k Obeying covariance It has a zero-mean Gaussian distribution with a noise standard deviation of σ. v =10m. Furthermore, clutter in the scene is modeled as a Poisson RFS, and the amount of clutter in each scan period follows a mean of λ. c The Poisson distribution with a density of 10 results in a uniform spatial density within the monitored area. The adaptive neonatal intensity is set to 10. -8 .

[0099] ADP-GM-PHD filtering was performed under different detection probabilities and clutter rates. The scenario parameters were set as follows: a) Detection probability is 0.98 and clutter rate is 10; b) Detection probability is 0.98 and clutter rate is 5; c) Detection probability is 0.8 and clutter rate is 10; d) Detection probability is 0.8 and clutter rate is 5.

[0100] Simulation raw data such as Figure 2 As shown in (b), after passing through GM-PHD, 16 broken tracks were formed, as follows: Figure 2 As shown in (c) Figure 2 (c) Different colors represent different track numbers. After reassociation using this method, the tracks are re-identified as 10 tracks, consistent with the actual track results generated in the previous simulation experiments of this invention, such as... Figure 2 As shown in (d).

[0101] The simulation results of this invention demonstrate that it can still correctly re-associate broken tracks in scenarios where multiple targets appear or disappear dynamically and the track motion changes significantly during track breakage.

Claims

1. A method for correlating broken tracks based on track release and GM-PHD, characterized in that, The released spot data is merged with the clutter and target spot data acquired by radar during the breakup period to form a spot dataset, and GM-PHD is used to perform tracking filtering on the spot dataset; the steps of this 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 to form a point set of the track segment, release the data in the point set, and merge the released point data with the clutter and target point data acquired by the radar during the break to form a point dataset. Step 2: Use GM-PHD to perform tracking filtering on the point dataset to obtain the track set containing tag information after tracking; Step 3: Perform velocity matching on the track set to obtain a candidate track set; Step 4: Backtrack the new track segments in the candidate track set and predict the old track segments to obtain the recursive candidate track set. Step 5: Perform a chi-square test on the candidate track set, and further filter the candidate tracks that do not meet the correlation conditions to obtain the filtered candidate track set. Step 6: Perform optimal allocation on the filtered candidate track set to obtain the track set to be associated; the optimal allocation means that the optimal solution of global allocation is obtained according to the auction algorithm, and the optimal solution of each new and old track is combined to obtain the set of optimally allocated track pairs. Step 7: Fuse the flight track segments.

2. The method for correlating 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 set described in step 1 are as follows: The first step is to define the tracks in the track set whose start time is before the break as old tracks and those whose start time is after the break as new tracks, based on the start time of each track. The second step is to restore the estimated or measured positions of all tracks in the point set to independent points, thus obtaining the restored point set dataset. The third step is to clean and filter the recovered point data, remove outliers that deviate significantly from other points, and use the processed point set as the input point dataset.

3. The method for correlating broken tracks based on track release and GM-PHD according to claim 1, characterized in that, Step 2, which describes using GM-PHD to track and filter the point dataset, refers to achieving target tracking by continuously predicting and updating the probability density of points at each time step in the dataset. The probability density of the points reflects the probability of the target's existence in the state space. By integrating the intensity function, the number of targets in the points at the current time step can be updated in real time. The specific steps are as follows: The first step is to predict the probability density of the trace at each time step using the following formula: ； in, Let represent the probability density of the state of the point at time k, predicted based on the state of the point at time k-1. This represents the survival probability of the dot. Let represent the probability density of the state transition of the trace at time k-1 to the state at time k. This represents the intensity of the trace at time k-1. This represents the intensity of the newly generated target at the k-th time point; The second step is to update the probability density of the trace at each time step according to the following formula: ； in, This indicates that the observed data of the point at time k is compared with the predicted data. The updated probability density of the k-th time point obtained after combination Let represent the detection probability of the trace at time k. This represents the likelihood function value of the observed value z of the point trace obtained based on the state of the point trace at time k. This represents the intensity of the Poisson clutter RFS of the observation value z at time k.

4. The method for correlating broken tracks based on track release and GM-PHD according to claim 1, characterized in that, The steps for velocity 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 their start time, forming an old track set and a new track set; tracks whose start time is before the break are old tracks, while tracks whose start time is after the break are new tracks. The second step is to perform a rough screening of the end time of the old track and the start time of the new track. If the time difference between the two exceeds the time window of the break, the pair of tracks is directly excluded from the match. The third step is to divide the track into time windows based on the break time, and calculate the starting coordinates of each new track within an adjacent window. End coordinates of the old flight path The distance between them, divided by the time difference between them, gives the speed. ; speed The maximum speed specified by the sea surface track Compare, if < Then it is believed and There is a possibility of a match; the matching pair will be set to { , Store the candidate tracks in the form of}; The fourth step is to store all matching pairs that meet the speed matching conditions into the candidate track set, thus forming the candidate track set.

5. The method for correlating broken tracks based on track release and GM-PHD according to claim 1, characterized in that, Step 4, which involves reverse-engineering new track segments from the candidate track set and predicting old track segments, uses the Kalman tracking algorithm. The steps are as follows: The first step is to configure the filter parameters. Initialization is performed, where, This represents the estimated target state at the initial moment. Denotes the initial covariance matrix. Represents the initial target process noise matrix. Represents the initial observation noise matrix; The second step is to predict the state and estimate the error covariance according to the following formulas: ； ； in, Indicates the estimated value The predicted value, Indicates the first The radar tracking target state transition matrix at each radar sampling time. Indicates the first The radar tracking target state estimate at each radar sampling time. express The predicted value, Indicates the first The covariance matrix at each radar sampling time, where the superscript T denotes the transpose operation. Indicates the first The process noise variance matrix at each radar sampling time; The third step is to calculate the measurement prediction, the information covariance matrix, and the Kalman gain according to the following formula: ； ； ； in, Indicates the estimated value The predicted measurement value, This represents the estimated observed state of the target. Indicates the first The observation matrix at each radar sampling time, Indicates the first The new information covariance matrix at each radar sampling time Indicates the first The observation matrix at each radar sampling time, Indicates the first The observation noise matrix at each radar sampling time. Indicates the first The Kalman gain at each radar sampling time, with the superscript -1 indicating the inversion operation; Fourth step, calculate the state estimate and the covariance of the estimation error according to the following formula: ； ； in, Indicates the first The radar tracking target state estimate at each radar sampling time. This represents the observed state value of the target. Indicates the first The estimation error covariance at each radar sampling time; The fifth step is to store the new trajectory obtained from the reverse derivation in the first four steps and the old trajectory obtained from the prediction in the corresponding order in the candidate trajectory set into the recursive candidate trajectory dataset.

6. The method for correlating broken tracks based on track release and GM-PHD according to claim 1, characterized in that, Step 5, which involves performing a chi-square test on the candidate track set, refers to filtering potentially associated track pairs from the recursive candidate track dataset. The steps are as follows: The first step is to use the following formula to calculate the candidate track dataset after recursion. In the process, filter for potentially associated track pairs: ； ； in, Indicates the first The estimation error of the new / old track segment at each moment, Indicates the first The status of a new flight path at any given moment. Indicates the first The state of the old flight path at that moment. Indicates the first The estimation error of the new / old track segment at each moment Indicates the first Covariance of the new trajectory at each moment Indicates the first Covariance of the old flight path at a given moment; The second step is to determine whether the test estimators of the new / old tracks follow mutually independent Gaussian distributions. If so, then the new track segment is... Fragments of old flight paths If they belong to the same target, denoted as H0; otherwise, determine... New flight path fragments Fragments of old flight paths If they do not belong to the same target, denote them as H1, and start from the set of track pairs. Remove the track pair from the list.

7. The method for correlating broken tracks based on track release and GM-PHD according to claim 6, characterized in that, The conditions for the mutually independent Gaussian distributions are as follows: ； in, This indicates that it has 10 degrees of freedom. The critical value of the chi-square distribution is a constant value obtained by querying the chi-square distribution table. P represents the dimension of the target state of the new and old track points at the current moment. Q This represents the tail probability corresponding to the new track and the old track at that moment.

8. The method for correlating broken tracks based on track release and GM-PHD according to claim 1, characterized in that, The fusion of track segments mentioned in step 7 refers to fitting the target track in the interrupted interval using a polynomial fitting method. The order of fitting is usually determined based on empirical values.

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