Feature-assisted time-matched PHD-based nonlinear multi-target tracking method for radar

Abstract

This invention discloses a feature-assisted time-matching (PHD) radar nonlinear multi-target tracking method. Addressing the issues of measurement-prediction time mismatch caused by the diversity of target sampling times in radar applications, poor real-time performance in dense clutter environments, and nonlinear dynamics, this invention divides the measurement area into several independent sectors based on the radar antenna's beamwidth. It then utilizes parallel filtering to achieve time matching on the PHD filter, thereby eliminating estimation errors caused by the diversity of target sampling times. Furthermore, it leverages feature information from the radar echo to assist in multi-target tracking, thus resolving the time cost issues caused by time matching and clutter. This method simultaneously solves the problems of estimation errors caused by the diversity of sampling times, time cost consumption caused by dense clutter, and nonlinear motion of multiple targets. It is adaptable to practical radar multi-target application scenarios and can be widely applied in the field of radar multi-target tracking.

Description

Technical Field

[0001] This invention relates to the field of radar target tracking technology, and in particular to a feature-assisted time matching (PHD) radar nonlinear multi-target tracking method. Background Technology

[0002] Multi-target tracking is one of the important functions of radar systems. It involves estimating the state of multiple targets in real time from radar measurement data. Traditional radar multi-target tracking algorithms based on data association, such as Joint Probabilistic Data Association (JPDA), Multiple Hypothesis Tracking (MHT), and Probabilistic Multiple Hypothesis Tracking (PMHT), transform the multi-target tracking problem into a single-target tracking problem.

[0003] When clutter density is high and the number of measurements is large, the computational load increases exponentially. Probabilistic hypothesis density (PHD) filters do not require explicit data correlation and are therefore widely used in multi-target tracking (MTT). However, existing PHD filters still face some challenges in radar applications, such as mismatch between prediction and measurement data, clutter, low detection probability, and nonlinear dynamics.

[0004] In radar applications, due to the limited antenna beamwidth, targets located at different spatial positions are usually detected at different times during the scanning process. In existing PHD filters, all targets use the same sampling time, which leads to a mismatch between predicted and measured data, thus affecting the accuracy of multi-target tracking. Furthermore, the diversity of sampling times can also cause estimation errors. Time matching incurs time costs, and dense clutter and low detection probability can also lead to false alarms, thus affecting real-time performance. Summary of the Invention

[0005] To address the above technical problems, this invention provides a radar nonlinear multi-target tracking method based on feature-assisted time matching (PHD), comprising the following steps:

[0006] S1. Based on the beamwidth of the radar antenna, the monitoring area is divided into N. S Multiple independent sectors, with target states within the same sector having the same sampling time, are represented as follows:

[0007]

[0008]

[0009] Among them, X k Z represents the multi-target state at time k. k This indicates multi-target measurement at time k. Let k be the projection of the target onto sector i in the measurement space at time k. Representing the state space of a single objective The projection falls on the state subspace of sector i. This indicates the sampling time of sector i. This represents the sampling time value space of the target in sector i. It is the set of measurements from sector i at time k. Represents single-target measurement space The projection falls on the measurement subspace of sector i. Represents the single-target state space in sector i. The set of all finite subsets contained therein Represents the single-target measurement space in sector i The set of all finite subsets contained therein;

[0010] Based on the state model of multiple targets and multiple targets and measurements, in scenarios with diverse sampling times, the probability hypothesis density is expressed as:

[0011]

[0012] in, Indicates sector i in The probability hypothesis density at time step;

[0013] S2. Assume the posterior probability hypothesis density of the (k-1)th scan period is D. k-1|k-1 (x), then the prediction probability hypothesis density for the k-th scan period is:

[0014]

[0015] in, Let represent the probability hypothesis density of newly generated targets within sector i. This represents the target probability hypothesis density extrapolated from sector j. This represents the corresponding pseudo-Markov density;

[0016] S3, the posterior probability hypothesis density of the k-th scan period is expressed as:

[0017]

[0018] in, Let represent the pseudo-likelihood function corresponding to the i-th sector.

[0019] The technical solution further defined in this invention is:

[0020] Furthermore, in step S1, based on the state model of the multi-target state and multi-target measurement, the probability hypothesis density is expressed in the following form:

[0021]

[0022] Leveraging the independence of targets within sectors, the above formula can be further rewritten as the sum of probability hypothesis densities across different sectors, yielding the probability hypothesis density representation based on sector partitioning:

[0023]

[0024] in, This represents the probability hypothesis density corresponding to the target contained in sector i;

[0025] For any sets X and Y, 1 Y (X) has the following definition:

[0026]

[0027] In scenarios with diverse sampling times, the probability hypothesis density is expressed as:

[0028]

[0029] in, Indicates sector i in The probability hypothesis density at time step.

[0030] In the aforementioned feature-assisted time-matching PHD radar nonlinear multi-target tracking method, step S1 involves the state of each target including its kinematic state x. k and characteristic states Represented as

[0031] in, [x k ,y k ] T Indicates the target location. Indicates the target speed. Indicates the target acceleration; Indicates the target Doppler frequency, x snr,k Indicates the target signal-to-noise ratio;

[0032] Measurements for each target include kinematic measurements z. k =[r,θ] T +w k and feature measurement Represented as

[0033] in, To represent the distance being measured, θ = arctan2(y k ,x k () indicates the measurement orientation. This indicates the measured Doppler frequency, z. snr,kThis indicates the measured signal-to-noise ratio.

[0034] In the aforementioned feature-assisted time-matching (PHD) radar nonlinear multi-target tracking method, step S2 involves the following calculation of the corresponding pseudo-Markov density:

[0035]

[0036] in, Indicates in The probability hypothesis density of the derived target from the previous time step x′. Indicates that the target state x′ is in The probability of survival at any given moment. Indicates from Time's up The single-objective state transition function at time t.

[0037] In the aforementioned feature-assisted time-matching (PHD) radar nonlinear multi-target tracking method, step S3, the pseudo-likelihood function corresponding to the i-th sector is calculated as follows:

[0038]

[0039] in, for The detection probability of state x at time time. The clutter density at that moment,

[0040] In the aforementioned feature-assisted time-matching PHD radar nonlinear multi-target tracking method, step S3 utilizes feature information from the radar echo to correct g. z (x), rewritten as

[0041] g z (x)=g z (z k |x k )·p f (z fk )

[0042] Among them, g z (z k |x k ) indicates in Target state x in sector i at time i k The likelihood function, p f (z fk ) indicates in The feature likelihood of the target within sector i at time step i.

[0043] The beneficial effects of this invention are:

[0044] (1) In this invention, the measurement area is divided into several independent sectors according to the beamwidth of the radar antenna, and time matching on the PHD filter is achieved by parallel filtering, thereby eliminating the estimation error caused by the diversity of target sampling time and improving the multi-target tracking performance.

[0045] (2) In this invention, the feature information in the radar echo is used to assist in multi-target tracking. This feature information can filter out a large amount of clutter and distinguish different targets, thereby solving the time cost consumption caused by time matching and clutter and improving the real-time performance of multi-target tracking.

[0046] (3) In this invention, the estimation error caused by the diversity of sampling time, poor real-time performance under dense clutter and low detection probability environment and nonlinear target motion are solved at the same time. At the same time, the method can track nonlinear multiple targets of radar and realize accurate real-time tracking of nonlinear multiple targets of radar under dense clutter and low detection probability environment. Attached Figure Description

[0047] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram of the target's actual trajectory in an embodiment of the present invention;

[0049] Figure 3 This is a diagram showing the initial state and lifecycle data of the target in an embodiment of the present invention;

[0050] Figure 4 In this embodiment of the invention, different filters are used at detection probabilities P. D,k Comparison of average OSPA distances when λ = 0.98 and clutter rate λ = 50;

[0051] Figure 5 In this embodiment of the invention, different filters are used at detection probabilities P. D,k Comparison of time costs when clutter ratio λ = 0.98 and clutter rate λ = 50;

[0052] Figure 6 This is a comparison chart of the average OSPA distance of different filters in this embodiment of the invention when the clutter rate λ = 100;

[0053] Figure 7 This is a comparison chart of the average OSPA distance of different filters in this embodiment of the invention when the clutter rate λ = 200;

[0054] Figure 8 This is a comparison chart of the average OSPA distance of different filters in this embodiment of the invention when the clutter rate λ = 250;

[0055] Figure 9This is a comparison chart of the average OSPA distance of different filters in this embodiment of the invention when the clutter rate λ = 300;

[0056] Figure 10 This is a schematic diagram illustrating the relationship between the tracking performance of different filters and clutter rate in an embodiment of the present invention;

[0057] Figure 11 This is a schematic diagram illustrating the relationship between the real-time performance of different filters and clutter rate in an embodiment of the present invention;

[0058] Figure 12 In this embodiment of the invention, different filters are used at detection probabilities P. D,k Comparison of average OSPA distances when = 0.95;

[0059] Figure 13 In this embodiment of the invention, different filters are used at detection probabilities P. D,k Comparison of average OSPA distance when = 0.9;

[0060] Figure 14 In this embodiment of the invention, different filters are used at detection probabilities P. D,k Comparison of average OSPA distances when = 0.85;

[0061] Figure 15 In this embodiment of the invention, different filters are used at detection probabilities P. D,k Comparison of average OSPA distance when = 0.8;

[0062] Figure 16 This is a schematic diagram illustrating the relationship between the tracking performance of different filters and the detection probability in an embodiment of the present invention;

[0063] Figure 17 This is a schematic diagram illustrating the relationship between the real-time performance of different filters and the detection probability in an embodiment of the present invention. Detailed Implementation

[0064] This embodiment provides a feature-assisted time-matching (PHD) radar nonlinear multi-target tracking method, such as... Figure 1 As shown, it includes the following steps

[0065] S1. Sector Division: Based on the beamwidth of the radar antenna, the monitored area is divided into N sectors. S Multiple independent sectors, with target states within the same sector having the same sampling time, are represented as follows:

[0066]

[0067]

[0068] Among them, X kZ represents the multi-target state at time k. k This indicates multi-target measurement at time k. Let k be the projection of the target onto sector i in the measurement space at time k. Representing the state space of a single objective The projection falls on the state subspace of sector i. This indicates the sampling time of sector i. This represents the sampling time value space of the target in sector i. It is the set of measurements from sector i at time k. Represents single-target measurement space The projection falls on the measurement subspace of sector i. Represents the single-target state space in sector i. The set of all finite subsets contained therein Represents the single-target measurement space in sector i The set of all finite subsets contained therein;

[0069] Based on this state model, the probability hypothesis density is expressed in the following form:

[0070]

[0071] Leveraging the independence of targets within sectors, the above formula can be further rewritten as the sum of probability hypothesis densities across different sectors, yielding the probability hypothesis density representation based on sector partitioning:

[0072]

[0073] in, This represents the probability hypothesis density corresponding to the target contained in sector i;

[0074] For any sets X and Y, 1 Y (X) has the following definition:

[0075]

[0076] In scenarios with diverse sampling times, the probability hypothesis density is further expressed as:

[0077]

[0078] in, Indicates sector i in The probability hypothesis density at time step.

[0079] In step S1, the state of each target includes the kinematic state x. k and characteristic state xf k , represented as

[0080] in, [x k ,y k ] T Indicates the target location. Indicates the target speed. Indicates the target acceleration; Indicates the target Doppler frequency, x snr,k Indicates the target signal-to-noise ratio;

[0081] Measurements for each target include kinematic measurements z. k =[r,θ] T +w k and feature measurement Represented as

[0082] in, To represent the distance being measured, θ = arctan2(y k ,x k () indicates the measurement orientation. This indicates the measured Doppler frequency, z. snr,k Indicates the measurement signal-to-noise ratio;

[0083] In step S1, the selection of feature information is not limited to Doppler frequency and signal-to-noise ratio.

[0084] S2. Prediction: Assume the posterior probability hypothesis density of the (k-1)th scan cycle is D. k-1|k-1 (x), then the prediction probability hypothesis density for the k-th scan period is:

[0085]

[0086] in, Let represent the probability hypothesis density of newly generated targets within sector i. This represents the target probability hypothesis density extrapolated from sector j; The corresponding pseudo-Markov density is calculated as follows:

[0087]

[0088] in, Indicates in The probability hypothesis density of the derived target from the previous time step x′. Indicates that the target state x′ is in The probability of survival at any given moment. Indicates from Time's up The single-objective state transition function at time t.

[0089] S3, the posterior probability hypothesis density of the k-th scan period is expressed as:

[0090]

[0091] in, The pseudo-likelihood function corresponding to the i-th sector is calculated as follows:

[0092]

[0093] in, for The detection probability of state x at time time. The clutter density at that moment, Finally, state extraction is performed;

[0094] Correcting g using characteristic information in radar echoes z (x), rewritten as

[0095]

[0096] Among them, g z (z k |x k ) indicates in Target state x in sector i at time i k The likelihood function, Indicates in The feature likelihood of the target within sector i at time step i.

[0097] Experimental conditions:

[0098] Taking target tracking in a two-dimensional plane as an example, the filtering performance of the method of the present invention is studied in different scenarios.

[0099] Scenario 1: The radar scan range is 2000m, covering a semi-circular area with an azimuth of 180°. There are 12 targets within the monitored area; Figure 2 The image shows real target trajectories in common scenarios such as target spawning, target death, target turning, and trajectory intersection; as shown. Figure 3 The diagram shows the initial state and lifecycle of the target; the monitoring area is divided into 20 sectors; the radar range resolution is 10m, and the radar azimuth resolution is 1°; the survival probability of each target is P. s,k =0.99; the clutter is uniformly distributed in the monitored area, the clutter quantity follows a Poisson distribution, the average clutter rate is λ = 50, and the detection probability is P. D,k =0.98.

[0100] Scenario 2: This scenario is the same as Scenario 1, except that the clutter rate is different. As the clutter rate increases, the tracking accuracy and real-time performance of the method in this embodiment are evaluated.

[0101] Scenario 3: This scenario is the same as Scenario 1, except that the detection probability is different. When the detection probability decreases, the tracking accuracy and real-time performance of the method in this embodiment under dense clutter (λ=300) conditions are evaluated.

[0102] The single-objective motion equation used in the simulation is as follows:

[0103]

[0104] Among them, the target kinematic state Each target in the method of this embodiment also includes a characteristic state. Let d = 2 be the Kronecker product of matrices A and B, where d = 2 is the dimension of the measurement space, and w k This indicates that the mean is 0 and the covariance is... Gaussian process noise, where the state transition matrix F k|k-1 The covariance matrix Q k|k-1 They are respectively:

[0105]

[0106]

[0107] Among them, T s The sampling period is Σ = 0.1, and the standard deviation of the acceleration is Σ = 0.1. This refers to the maneuver-related time, i.e., the time required for the target to maneuver.

[0108] The observation equation for a single target is:

[0109]

[0110] Among them, the measurement matrix H k =[1 0 0], and State x k Location information and orientation information; e k To measure noise, the radar range resolution and azimuth resolution in the simulation are 10m and 1°, respectively, corresponding to e k It follows a Gaussian distribution with a mean of 0 and a covariance of R = diag([100,1]).

[0111] The Doppler frequency of the target in this embodiment is calculated as follows:

[0112]

[0113] Among them, f d f represents the Doppler frequency. rThe value represents the radar frequency, c represents the speed of light, and vr represents the radial velocity of the target.

[0114] The signal-to-noise ratio of the target at adjacent time points follows a normal distribution with a mean of 0 and a variance of 2. The simulation is implemented using a Gaussian mixture (GM) model. To evaluate the performance of the method in this embodiment, 100 Monte Carlo experiments are performed for each tracking scenario. The results of the radar nonlinear multi-target tracking method with feature-assisted time matching (PHD) in this embodiment are compared with the performance of the standard PHD filter, the time-matched PHD (TM-PHD) filter, and the time-matched Joint-GLMB (TM-Joint-GLMB) filter. OSPA error and time consumption are used as the performance evaluation indicators of the filter.

[0115] Simulation content:

[0116] Scenario 1: With detection probability P D,k =0.98, clutter rate λ=50, compare the tracking performance and real-time performance of the proposed method (FATM-PHD) in this embodiment with the standard PHD filter, TM-PHD filter and TM-Joint-GLMB filter, as follows: Figure 4 The image shows a comparison of the average OSPA error of different filters; as shown... Figure 5 The image shows a comparison of the time costs of different filters.

[0117] Scenario 2: With detection probability P D,k When λ = 0.98, the tracking performance and real-time performance of different filters are compared under different clutter rates (λ = 100, λ = 200, λ = 250, λ = 300), as follows: Figures 6 to 9 The image shows a comparison of the average OSPA distance for different filters at different clutter rates; as shown... Figure 10 The figure shows the relationship between the tracking performance of different filters and the clutter rate; as shown... Figure 11 The figure shows the relationship between the real-time performance of different filters and the clutter rate.

[0118] Scenario 3: When the clutter rate λ = 300, compare the different filters at different detection probabilities (P... D,k =0.95, P D,k =0.9, P D,k =0.85, P D,k Tracking performance and real-time performance at 0.8, such as Figures 12 to 15 The image shows a comparison of the average OSPA distance for different filters under different detection probabilities; as shown... Figure 16 The figure shows the relationship between the tracking performance of different filters and the detection probability; as shown... Figure 17 The figure shows the relationship between the real-time performance of different filters and the detection probability.

[0119] Simulation Result Analysis:

[0120] from Figure 3 and Figure 4 It can be seen that when the detection probability P is high D,k =0.98, and with a low clutter number λ=50, the filtering algorithm proposed in this invention has slightly better tracking performance than the TM-Joint-GLMB filter, and is significantly better than the standard PHD filter and TM-PHD filter. The real-time performance of the filtering algorithm proposed in this embodiment is significantly better than the TM-Joint-GLMB filter and close to that of the standard PHD filter.

[0121] from Figures 5 to 10 It can be seen that, at the detection probability P D,k When the clutter ratio is 0.98, the average OSPA error of the method in this embodiment is almost unaffected by the increase in clutter ratio, while the average OSPA error of the other three filters increases with the increase in clutter ratio. As the clutter ratio increases, the tracking performance of the method in this embodiment is more and more significantly better than that of the other three filters. As the clutter ratio increases, the time cost of the method in this embodiment increases with the time cost of the other three filters, but the real-time performance of the method in this embodiment is significantly better than that of the TM-Joint-GLMB filter and the TM-PHD filter, and is close to that of the standard PHD filter.

[0122] from Figures 11 to 16 It can be seen that when the clutter rate λ = 300, as the detection probability decreases, the average OSPA error of the method in this embodiment increases compared to the average OSPA error of the other three filters. However, the tracking performance of the method in this embodiment is significantly better than that of the other three filters. The real-time performance of the method in this embodiment is significantly better than that of the TM-Joint-GLMB filter and the TM-PHD filter, and is close to that of the standard PHD filter.

[0123] Simulation results demonstrate that the feature-assisted time-matched PHD radar nonlinear multi-target tracking method proposed in this embodiment has better effectiveness.

[0124] To address the estimation errors caused by the diversity of sampling times, this embodiment proposes a time-matched PHD filter based on sector division. Since time matching incurs time costs, and dense clutter and low detection probability can lead to false alarms and affect real-time performance, this embodiment proposes a radar nonlinear multi-target tracking method based on a feature-assisted time-matched PHD filter. This method simultaneously solves the problems of estimation errors caused by the diversity of sampling times, time costs caused by dense clutter, and nonlinear motion of multiple targets.

[0125] Based on the beamwidth of the radar antenna, the measurement area is divided into several independent sectors, and time matching on the PHD filter is achieved by using parallel filtering, thereby eliminating the estimation error caused by the diversity of target sampling time; then, the characteristic information in the radar echo is used to assist in multi-target tracking, thereby solving the time cost problem caused by time matching and clutter.

[0126] In addition to the embodiments described above, the present invention may have other implementations. All technical solutions formed by equivalent substitution or equivalent transformation fall within the protection scope claimed by the present invention.

Claims

1. A radar nonlinear multi-target tracking method based on feature-assisted time matching (PHD), characterized in that: Includes the following steps S1. Based on the beamwidth of the radar antenna, the monitoring area is divided into N. S Multiple independent sectors, with target states within the same sector having the same sampling time, are represented as follows: Among them, X k Z represents the multi-target state at time k. k This indicates multi-target measurement at time k. Let k be the projection of the target onto sector i in the measurement space at time k. Representing the state space of a single objective The projection falls on the state subspace of sector i. This indicates the sampling time of sector i. This represents the sampling time value space of the target in sector i. It is the set of measurements from sector i at time k. This represents the measurement subspace in the single-target measurement space Z where the projection falls on sector i. Represents the single-target state space in sector i. The set of all finite subsets contained therein Represents the single-target measurement space in sector i The set of all finite subsets contained therein; Based on the state model of multiple targets and multiple targets and measurements, in scenarios with diverse sampling times, the probability hypothesis density is expressed as: in, Indicates sector i in The probability hypothesis density at time step; S2. Assume the posterior probability hypothesis density of the (k-1)th scan period is D. k-1|k-1 (x), then the prediction probability hypothesis density for the k-th scan period is: in, Let represent the probability hypothesis density of newly generated targets within sector i. This represents the target probability hypothesis density extrapolated from sector j. This represents the corresponding pseudo-Markov density; S3, the posterior probability hypothesis density of the k-th scan period is expressed as: in, Let represent the pseudo-likelihood function corresponding to the i-th sector.

2. The radar nonlinear multi-target tracking method with feature-assisted time matching PHD according to claim 1, characterized in that: In step S1, based on the state model of the multi-target state and multi-target measurement, the probability hypothesis density is expressed in the following form: Leveraging the independence of targets within sectors, the above formula can be further rewritten as the sum of probability hypothesis densities across different sectors, yielding the probability hypothesis density representation based on sector partitioning: in, This represents the probability hypothesis density corresponding to the target contained in sector i; For any sets X and Y, 1 Y (X) has the following definition: In scenarios with diverse sampling times, the probability hypothesis density is expressed as: in, Indicates sector i in The probability hypothesis density at time step.

3. The radar nonlinear multi-target tracking method with feature-assisted time matching PHD according to claim 1, characterized in that: In step S1, the state of each target includes kinematic state x. k and characteristic states Represented as in, [x k ,y k ] T Indicates the target location. Indicates the target speed. Indicates the target acceleration; Indicates the target Doppler frequency, x snr,k Indicates the target signal-to-noise ratio; Measurements for each target include kinematic measurements z. k =[r,θ] T +w k and feature measurement Represented as in, Indicates the distance being measured. Indicates the measurement orientation. Indicates the measured Doppler frequency, z snr,k This indicates the measured signal-to-noise ratio.

4. The radar nonlinear multi-target tracking method with feature-assisted time matching PHD according to claim 1, characterized in that: In step S2, the corresponding pseudo-Markov density is calculated as follows: in, Indicates in The probability hypothesis density of the derived target from the previous time step x′. Indicates that the target state x′ is in The probability of survival at any given moment. Indicates from Time's up The single-objective state transition function at time t.

5. The radar nonlinear multi-target tracking method with feature-assisted time matching PHD according to claim 1, characterized in that: In step S3, the pseudo-likelihood function corresponding to the i-th sector is calculated as follows: in, for The detection probability of state x at time time. The clutter density at that moment, 6. The radar nonlinear multi-target tracking method with feature-assisted time matching PHD according to claim 5, characterized in that: In step S3, the characteristic information in the radar echo is used to correct g. z (x), rewritten as Among them, g z (z k |x k ) indicates in Target state x in sector i at time i k The likelihood function, Indicates in The feature likelihood of the target within sector i at time step i.

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