A method for tracking multiple targets of a marine radar based on an evaluation function

Abstract

This invention proposes a multi-target tracking method for marine radar based on an evaluation function. The method includes: after mapping radar echo data to obtain radar images, using a density clustering algorithm for target identification, dividing the target and background on the point cloud image; for the identified targets, proposing an evaluation function for target morphological feature information, further classifying and filtering the targets; further using a Kalman filter algorithm for target tracking after classification, and using the JPDA algorithm for data association, outputting the multi-target tracking results. This invention addresses the problems of numerous noisy targets in marine radar image target identification results and the high computational complexity and low efficiency of the JPDA algorithm in scenarios with multiple targets. By filtering out noisy targets, the number of feasible events input to the JPDA algorithm is reduced, improving the computational efficiency of the JPDA algorithm in multi-target tracking scenarios and enhancing the algorithm's applicability.

Description

Technical Field

[0001] This invention relates to the field of multi-target tracking algorithm technology, and specifically to a multi-target tracking method for marine radar based on an evaluation function. Background Technology

[0002] The signals received by a marine radar receiver not only contain the target echoes needed, but also a large amount of noise and clutter. Therefore, marine radar needs to detect targets in a very complex signal background through signal processing, and to discover the true target signals to the greatest extent possible. Through data processing, the radar can further process the radar target's point and track information, thereby achieving the goal of high-precision real-time tracking of the target.

[0003] In complex environments, target tracking algorithms based on data association algorithms have been widely applied. These mainly include Nearest Neighbor Data Association (NNDA), Probability Data Association (PDA), Joint Probability Data Association (JPDA), and Multiple Hypothesis Tracking (MHT). NNDA is commonly used for single-target tracking due to its high efficiency, but it is prone to errors in multi-target tracking scenarios. JPDA can be used for multi-target tracking, but it has high computational complexity and low efficiency.

[0004] This invention proposes an evaluation function based on target morphological feature information. This function is used to classify the target extraction results output by the DBSCAN algorithm, further filtering out uninteresting noisy targets. This evaluation function has low computational complexity, excellent filtering effect on noisy targets, and can reduce the number of feasible events input into the JPDA algorithm, improving the computational efficiency of the JPDA algorithm in multi-target tracking scenarios and enhancing the algorithm's applicability. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-target tracking method for marine radar based on an evaluation function. Addressing the issues of numerous noisy targets in marine radar image target recognition results and the high computational complexity and low efficiency of the Joint Probability Data Association (JPDA) algorithm in multi-target tracking scenarios, this invention proposes an evaluation function based on target morphological features. This evaluation function is used to classify the target recognition results output by the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm, further filtering out uninteresting noisy targets. This reduces the number of feasible events input into the JPDA algorithm, improves the computational efficiency of the JPDA algorithm in multi-target tracking scenarios, and enhances the algorithm's applicability.

[0006] To achieve the above functions, this invention designs a multi-target tracking method for marine radar based on an evaluation function. For radar echo data, the following steps S1-S4 are executed to complete multi-target tracking:

[0007] Step S1: Analyze the radar echo data according to the radar communication protocol, and convert the polar coordinate system to the Cartesian coordinate system through coordinate transformation to obtain the radar image in the Cartesian coordinate system.

[0008] Step S2: For the radar image, a density clustering algorithm is used to perform multi-target recognition, segmenting the identified targets and background on the radar image;

[0009] Step S3: For each target identified by the density clustering algorithm, use the evaluation function based on the target morphological feature information to calculate the evaluation score of each target, obtain the evaluation score of each target, and filter out the targets with evaluation scores less than the preset evaluation score threshold as noise targets.

[0010] Step S4: For each target obtained in step S3, use the joint probabilistic association algorithm to perform data association, obtain the trajectory of each target, and complete multi-target tracking on the radar image.

[0011] As a preferred embodiment of the present invention: during the coordinate transformation process in step S1, the correspondence between the polar coordinate system and the Cartesian coordinate system is as follows:

[0012] ;

[0013] ;

[0014] In the formula, x and y are the abscissa and ordinate in the Cartesian coordinate system, respectively. The distance from the point to the origin. The angle between the radar ray and the x-axis is given.

[0015] As a preferred technical solution of the present invention: In step S2, core point determination is performed on each point in the radar image based on the density clustering algorithm. For any point p, if point p is a core point, the cluster formed by the points that are directly density reachable from the core point p is determined to be the target in the radar image; if point p is not a core point, point p is marked as a noise point.

[0016] As a preferred embodiment of the present invention, the evaluation function for the target morphological feature information in step S3 is as follows:

[0017] ;

[0018] In the formula, Let i be the evaluation score for objective i. For area evaluation function, For the mass density evaluation function, For distance evaluation function, , , These are the weighting coefficients for the area evaluation function, mass density evaluation function, and distance evaluation function, respectively, and k is the smoothing coefficient;

[0019] The area evaluation function is specifically as follows:

[0020] ;

[0021] In the formula, Let i be the area of ​​the current target. The area of ​​the standard target under the current radar range is T, where T is the area difference threshold.

[0022] The mass density evaluation function is as follows:

[0023] ;

[0024] In the formula, The centroid coordinates of the target The centroid coordinates of the target;

[0025] The distance evaluation function is as follows:

[0026] ;

[0027] In the formula, Let be the coordinates of the target in the Cartesian coordinate system.

[0028] As a preferred embodiment of the present invention, the specific steps of using the joint probabilistic association algorithm for data association in step S4 are as follows:

[0029] Step S41: Calculate the information covariance of the moving target: According to the key formula of Kalman filtering, This represents the covariance of the moving target t. Let represent the prior state estimate of the moving target t at time k+1, and j represent the measurement at time k+1. Let represent the posterior state estimate of the moving target t at time k+1, then the information covariance of the moving target t at time k+1. As shown in the following formula:

[0030] ;

[0031] In the formula, H represents the measurement matrix. The covariance matrix representing the measurement noise;

[0032] Step S42: Calculate the probability that the measurement originates from a real target: In a multi-moving target scenario, Indicates the total number of moving targets. This represents the total number of measurements; measurement j originates from the event of the moving target t. ,in , The measurement j comes from a spurious event. The probability that measurement j comes from moving target t is: , As shown in the following formula:

[0033] ;

[0034] In the formula, The total number of feasible events. For the i-th feasible event, For the i-th feasible event, whether measurement j originates from the moving target t. For the measurement j to be derived from the moving target t, The measurement j is not derived from the moving target t;

[0035] State estimate of moving target t at time k+1 As shown in the following formula:

[0036] ;

[0037] Step S43: Generate a size of Confirmation matrix as follows:

[0038] ;

[0039] in This indicates whether the measurement j falls within the confirmation gate of the moving target t. This indicates that measurement j did not fall within the confirmation gate of the moving target t. This indicates that measurement j falls into the confirmation gate of the moving target t;

[0040] The generated confirmation matrix is ​​then clustered according to the following criteria:

[0041] In the process of clustering tracks, the criteria for determining whether tracks share one or more measurements are used. If they share measurements, they belong to the same category; otherwise, they do not belong to the same category.

[0042] if track and The tracks are respectively with The tracks share one or more measurements, but , If the tracks do not share measurements, then these three tracks are grouped into one cluster;

[0043] track and flight path Tracks were shared through indirect transmission. The measurement, but , If the tracks do not share measurements, then these three tracks will still be classified into one cluster;

[0044] Among them, the definition of shared measurement is that the measurement is located in the intersection region of the confirmation gates of two tracks;

[0045] Step S44: Divide the confirmation matrix of each cluster into several feasible matrices, each of which has a size of [missing value]. This represents a definite feasible event;

[0046] The feasible events identified by the confirmation matrix satisfy the following conditions: the source of each measurement is unique and can only come from either a moving target or clutter; for any given moving target, there is one or zero measurements corresponding to it; if multiple measurements correspond to a moving target, only one measurement is taken.

[0047] Step S45: Calculate the probability of feasible events, as shown in the following formula:

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] In the above formula, Let M represent the i-th feasible event, and M be the total number of feasible events. Indicates a feasible event In the context of measurement j, the correlation between the actual moving target and the measurement j is considered. Indicates whether the moving target t is in a feasible event. In the set, Indicates a feasible event The number of erroneous measurements. Indicates the detection probability, and V represents the volume of the confirmation gate. As an intermediate variable, Let t be the measured value of the moving target at time k+1. For measurement The measured value, For u-interconnected information covariance, This is the normalization constant;

[0054] Step S46: Calculate the joint event probability and output the posterior state estimate of the moving target t at time k+1, where the joint event probability is the association probability between measurement j and the moving target t. Then the state estimate of the moving target at time k+1 is... :

[0055] ;

[0056] Step S47: According to Calculate the position of the moving target t, where Let H be the system's measurement value at time k+1, and let H be the measurement matrix. Let k be the state variable value of the system at time k+1. To measure the noise, the posterior covariance of the moving target t is updated using the following formula:

[0057] ;

[0058] ;

[0059] In the formula, For the goal The posterior covariance, As an intermediate variable, Indicates that the measurement comes from the target. The probability, It is the identity matrix. This is the filter gain matrix.

[0060] Beneficial effects: Compared with the prior art, the advantages of the present invention include:

[0061] This invention addresses the problem of numerous noisy targets in the target recognition results of marine radar images and the high computational complexity and low efficiency of the JPDA algorithm in scenarios with multiple targets. It proposes an evaluation function based on target morphological feature information. The evaluation function is used to classify the target recognition results output by the DBSCAN algorithm, further filtering out noisy targets of no interest. This reduces the number of feasible events input into the JPDA algorithm, improves the computational efficiency of the JPDA algorithm in multi-target tracking scenarios, and enhances the applicability of the algorithm. Attached Figure Description

[0062] Figure 1 This is a flowchart of a multi-target tracking method for marine radar based on an evaluation function, provided according to an embodiment of the present invention;

[0063] Figure 2 is a comparison of experimental results before and after target classification using the evaluation function, according to an embodiment of the present invention.

[0064] Figure 2(a) shows the target recognition result output by the DBSCAN algorithm; Figure 2(b) shows the target recognition result after target classification.

[0065] Figure 3 is a diagram showing the multi-target tracking results of a marine radar according to an embodiment of the present invention;

[0066] Figure 3(a) shows the tracking result for frame 5, Figure 3(b) shows the tracking result for frame 10, and Figure 3(c) shows the tracking result for frame 15. Detailed Implementation

[0067] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0068] Reference Figure 1 The present invention provides a method for multi-target tracking of marine radar based on an evaluation function, which performs the following steps S1-S4 on radar echo data to complete multi-target tracking:

[0069] Step S1: Analyze the radar echo data according to the radar communication protocol, and convert the polar coordinate system to the Cartesian coordinate system through coordinate transformation to obtain the radar image in the Cartesian coordinate system.

[0070] According to the principle of marine radar, the radar emits electromagnetic waves in one direction, determines whether a target exists on the ray based on the radar echo data, and then forms binary data packets to be broadcast via UDP multicast. In the coordinate transformation process of step S1, the correspondence between the polar coordinate system and the Cartesian coordinate system is as follows:

[0071] ;

[0072] ;

[0073] In the formula, x and y are the abscissa and ordinate in the Cartesian coordinate system, respectively. The distance from the point to the origin. The angle between the radar ray and the x-axis is given.

[0074] Step S2: For the radar image in the Cartesian coordinate system obtained in step S1, a density clustering algorithm is used to perform multi-target recognition. The recognized targets and background are segmented on the radar image. The density clustering algorithm is a spatial data clustering algorithm based on density space. It performs density clustering on the point cloud image obtained from radar echo data to achieve the function of target recognition.

[0075] The basic concepts defined in density clustering algorithms are as follows:

[0076] EPS: Neighborhood radius. The area within the EPS of a given object is called the neighborhood radius of that object.

[0077] MinPts: Minimum number of contained points; if the number of objects contained within the radius of a given object exceeds MinPts, then the object is called a core object.

[0078] Core objects: Points whose number of neighbors exceeds MinPts;

[0079] Direct density reachability: There exist points p and q. If point q is within the EPS neighborhood of p, and p is a core object, then p and q are said to be directly density reachable.

[0080] Density achievable: If a series of points exist within a certain region. If for any point ,point If all values ​​are directly achievable by density, then they are called points. Time Density can be achieved.

[0081] Density clustering algorithms are based on the fact that a cluster can be uniquely determined by its core objects. The algorithm can be expressed as:

[0082] (1) For any given core object All have regions All from Density achievable objects The set that constitutes the complete cluster. And there must be .

[0083] (2) For a given cluster and any core point , It is equivalent to a set.

[0084] In step S2, to determine the clusters, the density clustering algorithm selects regions... Choose any point and from Start searching China satisfies and And from All points where density is reachable. If If it is the core point, then there is of The number of points contained in the neighborhood is greater than , and the core point Clusters formed by directly density-reachable and density-reachable points constitute the targets in radar images. If... If it is a boundary point, then of The number of objects contained in the neighborhood is less than That is, there is no object that can be obtained from the object. Density can reach, These are temporarily marked as noise points. During algorithm execution, core points need to be determined for each object, and then a depth-first search is started from any point to complete clustering. The clustering results output by the algorithm are the targets in the radar image. It should be noted that not all targets clustered by the density clustering algorithm are of interest to this method and need to be tracked. Therefore, for the targets output by the density clustering algorithm, an evaluation function based on target morphological feature information is used to further filter out uninteresting targets before the filtered targets are sent to the tracking algorithm module for tracking.

[0085] Step S3: For each target identified by the density clustering algorithm, use the evaluation function based on the target morphological feature information to calculate the evaluation score of each target, obtain the evaluation score of each target, and filter out the targets with evaluation scores less than the preset evaluation score threshold as noise targets.

[0086] The evaluation function for the target morphological feature information in step S3 is as follows:

[0087] ;

[0088] In the formula, Let i be the evaluation score for objective i. For area evaluation function, For the mass density evaluation function, For distance evaluation function, , , These are the weighting coefficients for the area evaluation function, mass density evaluation function, and distance evaluation function, respectively, and k is the smoothing coefficient;

[0089] The area evaluation function represents the absolute value of the difference between the target area and the standard target area under the current radar range. Its physical meaning is that the area of ​​the target of interest fluctuates around the standard target area. The area evaluation function can reduce the evaluation function score of noisy targets with excessively large areas. The specific formula for the area evaluation function is as follows:

[0090] ;

[0091] In the formula, Let i be the area of ​​the current target. The area of ​​the standard target under the current radar range is T, where T is the area difference threshold.

[0092] The mass density evaluation function represents the uniformity of a target's mass density by the degree of overlap between the target's centroid and centroid. Physically, the point cloud image of a target of interest typically has a relatively regular shape, meaning its mass density is relatively uniform. Conversely, noisy targets often have irregular shapes, indicating that their mass density is also non-uniform. The specific formula for the mass density evaluation function is as follows:

[0093] ;

[0094] In the formula, The centroid coordinates of the target The centroid coordinates of the target;

[0095] The range evaluation function represents the relative distance between the target and the ship. Its physical meaning is that the relative distance between the target of interest and the ship is usually not too far. The range evaluation function can reduce the evaluation score of noisy targets at the edges of radar images. The specific formula for the range evaluation function is as follows:

[0096] ;

[0097] In the formula, Let be the coordinates of the target in the Cartesian coordinate system.

[0098] Figure 2 shows a comparison of the experimental results before and after target classification. Figure 2(a) shows the target recognition result output by the density clustering algorithm after the original scheme; Figure 2(b) shows the target recognition result after target classification. The experimental data comes from a field marine survey of a reservoir. The bounding boxes in the images represent the output targets. The experimental results show that the density clustering algorithm outputs 11 targets. After classification by the target classification method based on the evaluation function of target morphological features, 7 targets are classified as noise targets and filtered out, while 4 targets are identified as targets of interest. This demonstrates that the target classification method based on the evaluation function of target morphological features can effectively filter out noise targets in marine radar images, reduce the feasible target events input to the JPDA algorithm, reduce the computational load of the JPDA algorithm, and improve the algorithm's computational speed.

[0099] Step S4: For each target obtained in Step S3, use the joint probabilistic association algorithm to perform data association, obtain the trajectory of each target, and complete multi-target tracking on the radar image. The specific operation is as follows:

[0100] (1) Perform Kalman filter tracking on each moving target.

[0101] (2) Use the nearest neighbor joint probability density association algorithm to associate moving targets.

[0102] This includes the following steps S41-S47:

[0103] Step S41: Calculate the information covariance of the moving target: According to the key formula of Kalman filtering, Kalman filter tracking is an application of the Kalman filter algorithm. It uses a recursive filtering algorithm to derive new state estimates based on the obtained measurements through recursive equations. The system model of Kalman filtering consists of state equations and observation equations. Among them, the state equations are the prediction equations, and the observation equations are the correction equations.

[0104] The state equation for the Kalman filter is shown below:

[0105] ;

[0106] ;

[0107] In the state equations, the system is Use the system's measured variable values ​​at all times To predict the next moment of the system state variable values , where the coefficient Let be the system state transition matrix, with coefficients... The input control matrix is ​​given. The system noise at the current time is... ,exist The control input variable at time is The system is used in Measurement of time Correct the system's state variables at the current moment. ,in Indicates measurement noise. This represents the measurement matrix.

[0108] The observation equations for Kalman filtering are shown below:

[0109] ;

[0110] ;

[0111] ;

[0112] in, Indicates the gain factor. This represents the covariance of the posterior estimation error. This represents the covariance of the prior estimation error; This represents the posterior corrected state estimate of the system's state at the current moment; Indicates that the system is in Prior state prediction estimation at time step. This represents the covariance matrix of the measurement noise.

[0113] This represents the covariance of the moving target t. Let represent the prior state estimate of the moving target t at time k+1, and j represent the measurement at time k+1. Let represent the posterior state estimate of the moving target t at time k+1, then the information covariance of the moving target t at time k+1. As shown in the following formula:

[0114] ;

[0115] Step S42: Calculate the probability that the measurement originates from a real target: In a multi-moving target scenario, Indicates the total number of moving targets. This represents the total number of measurements; measurement j originates from the event of the moving target t. ,in , The measurement j comes from a spurious event. The probability that measurement j comes from moving target t is: , As shown in the following formula:

[0116] ;

[0117] In the formula, The total number of feasible events. For the i-th feasible event, For the i-th feasible event, whether measurement j originates from the moving target t. For the measurement j to be derived from the moving target t, The measurement j is not derived from the moving target t;

[0118] State estimate of moving target t at time k+1 As shown in the following formula:

[0119] ;

[0120] Step S43: In the original joint probabilistic data association algorithm, the concept of an acknowledgment matrix is ​​defined to determine the source of each moving target measurement and represent the complex relationship between the echo and each target acknowledgment gate. The acknowledgment matrix is ​​decomposed into various feasible events, and the probabilities of joint events and associated events are calculated accordingly. Based on this, the target track state update is completed by weighting the associated probabilities.

[0121] Generate size is Confirmation matrix as follows:

[0122] ;

[0123] in This indicates whether the measurement j falls within the confirmation gate of the moving target t. This indicates that measurement j did not fall within the confirmation gate of the moving target t. This indicates that measurement j falls into the confirmation gate of the moving target t;

[0124] The generated confirmation matrix is ​​then clustered. Clustering is an unsupervised classification process where entities within a single cluster are similar, while entities in different clusters are distinct. A cluster represents a connected region in a multidimensional space containing a set with high density. The purpose of clustering is to reduce computation and facilitate data processing.

[0125] The clustering criteria are as follows:

[0126] In the process of clustering tracks, the criteria for determining whether tracks share one or more measurements are used. If they share measurements, they belong to the same category; otherwise, they do not belong to the same category.

[0127] if track and The tracks are respectively with The tracks share one or more measurements, but , If the tracks do not share measurements, then these three tracks are grouped into one cluster;

[0128] track and flight path Tracks were shared through indirect transmission. The measurement, but , If the tracks do not share measurements, then these three tracks will still be classified into one cluster;

[0129] Among them, the definition of shared measurement is that the measurement is located in the intersection region of the confirmation gates of two tracks;

[0130] Step S44: Divide the confirmation matrix of each cluster into several feasible matrices, each of size j*t. This represents a definite feasible event;

[0131] The confirmation matrix contains all possible feasible events; that is, the confirmation matrix itself contains multiple possible feasible events, which are parallel feasible events, but some of these events are mutually exclusive. The feasibility matrix, after considering this mutual exclusion information, splits the confirmation matrix into a single, definitive feasible event. In other words, the confirmation matrix is ​​divided into several feasibility matrices based on the actual logical event relationships, and each feasibility matrix is ​​also... The size represents a definite feasible event. Each feasible event, based on the confirmation matrix, satisfies the following conditions: the source of each measurement is unique, and there are only two possibilities: it comes from a moving target or from clutter; for any given moving target, there is one or zero measurements corresponding to it; if there are multiple measurements corresponding to a moving target, only one measurement is taken.

[0132] Step S45: Calculate the probability of feasible events, as shown in the following formula:

[0133] ;

[0134] ;

[0135] ;

[0136] ;

[0137] ;

[0138] In the above formula, Let M represent the i-th feasible event, and M be the total number of feasible events. Indicates a feasible event In the context of measurement j, the correlation between the actual moving target and the measurement j is considered. Indicates whether the moving target t is in a feasible event. In the set, Indicates a feasible event The number of erroneous measurements. Indicates the detection probability, and V represents the volume of the confirmation gate. As an intermediate variable, Let t be the measured value of the moving target at time k+1. For measurement The measured value, For u-interconnected information covariance, This is the normalization constant;

[0139] Step S46: Calculate the joint event probability and output the posterior state estimate of the moving target t at time k+1, where the joint event probability is the association probability between measurement j and the moving target t. Then the state estimate of the moving target at time k+1 is... :

[0140] ;

[0141] Step S47: According to Calculate the position of the moving target t, and update the posterior covariance of the moving target t according to the following formula:

[0142] ;

[0143] ;

[0144] In the formula, For the goal The posterior covariance, As an intermediate variable, Indicates that the measurement comes from the target. The probability, It is the identity matrix. This is the filter gain matrix.

[0145] Figure 3 shows the experimental results of multi-target tracking using the nearest neighbor joint probability density algorithm. The experimental data comes from a field marine survey of a reservoir. The white circles with different numbers in the figure represent the motion tracking results of different targets. The simulation shows that the present invention can achieve multi-target tracking of marine radar images under complex sea conditions.

[0146] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for multi-target tracking of a marine radar based on a merit function, characterized in that, For radar echo data, the following steps S1-S4 are performed to complete multi-target tracking: Step S1: According to the radar communication protocol, the radar echo data is parsed, and through coordinate conversion, the polar coordinate system is converted into the Cartesian coordinate system to obtain the radar image in the Cartesian coordinate system; Step S2: For the radar image in the Cartesian coordinate system, a density clustering algorithm is used for multi-target identification, and each target and background identified on the radar image is segmented, the density clustering algorithm is based on density space, and the point cloud image obtained by mapping the radar echo data is density clustered; Based on the density clustering algorithm, each point on the radar image is determined as a core point, for any point p, if the point p is a core point, then the cluster composed of the directly density reachable point and the density reachable point of the core point p is determined as a target in the radar image; if the point p is not a core point, then the point p is marked as a noise point; Step S3: For each target identified by the density clustering algorithm, an evaluation function based on target morphological feature information is used to calculate the evaluation score of each target, and the evaluation score of each target is obtained, and the target with an evaluation score less than a preset evaluation score threshold is filtered out as a noise target; The evaluation function of the target morphological feature information in step S3 is as follows: ； In the formula, evaluation score of target i, area evaluation function, mass density evaluation function, distance evaluation function, , , are the weighting coefficients of the area evaluation function, the mass density evaluation function, and the distance evaluation function, respectively, and k is a smoothing coefficient. The area evaluation function is specifically as follows: ； wherein is the area of the current target i, is the standard target area at the current radar range, T is the area difference threshold; The mass density evaluation function is specifically as follows: ； In the formula, centroid coordinates of the target, centroid coordinates of the target The distance evaluation function is specifically as follows: ； In the formula, are coordinates in a Cartesian coordinate system. Step S4: For each target obtained in step S3, a joint probability association algorithm is used for data association to obtain the track of each target, and the multi-target tracking on the radar image is completed, and the specific operation is as follows: Kalman filter tracking is performed on each moving target; The nearest neighbor joint probability density association algorithm is used for moving target association.

2. The method of claim 1, wherein, In the coordinate conversion process in step S1, the corresponding relationship between the polar coordinate system and the Cartesian coordinate system is as follows: ； ； In the formula, x and y are the horizontal coordinate and the vertical coordinate in the Cartesian coordinate system, respectively, is the distance from the point to the origin, is the angle between the radar ray and the x-axis.

3. The method of claim 1, wherein, The specific steps of using the joint probability association algorithm for data association in step S4 are as follows: Step S41: Calculate the information covariance of the moving target: according to the key formula of Kalman filter, denotes the covariance of the moving target t, denotes the prior state estimation value of the moving target t at k+1 time, j denotes the measurement at k+1 time, denotes the posterior state estimation value of the moving target t at k+1 time, then the information covariance of the moving target t at k+1 time is as follows: ； where H represents a measurement matrix, denotes a covariance matrix of the measurement noise; Step S42: Calculate the probability that the measurement originates from a real target: In multi-moving target scenarios, denotes the total number of moving targets, denotes the total number of measurements; The probability that the measurement j comes from a moving target t is where , The probability that the measurement j comes from a false event is The probability that the measurement j comes from a moving target t is , The following equation: ； wherein is the total number of feasible events, is the ith feasible event, is the feasible event from a moving target , is the measurement j from a moving target t in the ith feasible event, is the measurement j is from a moving target t, is the measurement j is not from a moving target t; The state estimation value of the moving target t at the k+1 time The following equation: ； Step S43: Generate a confirmation matrix of size as follows: ​ ； wherein represents that the measurement j falls into the validation gate of the moving target t, if represents that the measurement j does not fall into the validation gate of the moving target t, if represents that the measurement j falls into the validation gate of the moving target t. The generated confirmation matrix is clustered and divided, and the clustering and division are based on the following: In the clustering process of the track, whether one or more measurements are shared between the tracks is used as the criterion, if they are shared, they belong to the same class, otherwise they do not belong to the same class; If trajectories share one or more measurements, but trajectories share one or more measurements, but trajectories share one or more measurements, but , trajectories do not share measurements, then the three trajectories are grouped into one cluster; trajectories and trajectories all share measurements by means of indirect passing but , not sharing measurements between trajectories, the three trajectories are still clustered together; Wherein, the definition of shared measurement is that the measurement is located in the intersection region of the confirmation gate of two tracks; Step S44: dividing the confirmation matrix of each cluster into several feasible matrices, each feasible matrix having a size of , representing a certain feasible event; Based on the confirmation matrix, each feasible event divided satisfies the following conditions: the source of each measurement is unique, and there are only two possibilities from moving targets or from clutter; for any given moving target, there is one or zero measurement corresponding to it, if there are multiple measurements corresponding to a moving target, only one measurement is taken; Step S45: Calculate the probability of the feasible event, specifically as follows: ； ； ； ； ； In the above formula, represents the ith feasible event, and M is the total number of feasible events, represents the feasible event , the relevance between the real moving target and the measurement j; represents whether the moving target t is in the feasible event set, represents the feasible event , the number of false measurements in the feasible event represents the detection probability, and V represents the volume of the confirmation gate, is an intermediate variable, is the measurement value of the moving target t at the k+1 moment, is the measurement value of the measurement, is the u-interconnection information covariance, is a normalization constant; Step S46: Calculate the joint event probability, which is the association probability of the measurement j and the moving target t, and output the posterior state estimation of the moving target t at time k+1 , and the state estimation value of the moving target t at time k+1 is : ； Step S47: According to the position of the moving target t is calculated, wherein is the measurement value of the system at time k+1, H is the measurement matrix, is the state variable value of the system at time k+1, is the measurement noise, and the posterior covariance of the moving target t is updated according to the following equation: ； ； In the formula, For the goal The posterior covariance, As an intermediate variable, Indicates that the measurement comes from the target. The probability, It is the identity matrix. This is the filter gain matrix.

Images