A Maneuvering Target Tracking Method Based on Trajectory Poisson and Dobermann Filtering

Abstract

This invention discloses a maneuvering target tracking method based on trajectory Poisson-Dobernal filtering. By fusing interactive multi-model and trajectory Poisson-Dobernal filtering methods, it achieves accurate tracking of maneuvering target trajectories. This invention fills a technological gap in the current field of maneuvering target tracking, providing an effective solution for achieving more accurate and real-time target tracking. This invention employs the Poisson-Dobernal approximation (PMB) concept, using KL divergence to obtain the Poisson-Dobernal components from the Poisson-Dobernal mixture components after filtering updates. This overcomes the computational complexity problem caused by the large number of Poisson-Dobernal mixture components in existing technologies, thus reducing algorithm complexity, improving filtering efficiency, and enhancing real-time filtering performance.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, and further relates to a maneuvering target tracking method based on trajectory Poisson-Dobernoli filtering in the field of maneuvering target tracking technology. This invention solves the model mismatch problem caused by the use of a single motion model in traditional multi-model filtering algorithms for tracking highly maneuvering targets, while also enabling real-time acquisition of the target trajectory. Background Technology

[0002] Methods for tracking maneuvering targets mainly include the IMM-JPDA method, which combines the Interactive Multiple Model (IMM) with the traditional Joint Probabilistic Data Association (JPDA) method; the IMM-PHD method, which combines IMM with the Probability Hypothesis Density (PHD) method; and the IMM-PMBM method, which combines IMM with the Poisson Multi-Bernoulli Mixture (PMBM) method. However, the IMM-JPDA method is limited to fixed target tracking scenarios, and the IMM-PHD method, as a first-moment approximation solution of Bayesian multi-target filtering, has certain accuracy limitations. Furthermore, the IMM-PMBM method cannot obtain the target's trajectory, which is a crucial indicator for target tracking.

[0003] Henan University disclosed a maneuvering target tracking method based on variational Bayesian multi-model particle filtering in its patent application "A Maneuvering Target Tracking Method Based on Variational Bayesian Multi-Model Particle Filtering" (Patent Application No.: 202211190099.7, Publication No.: CN 115688534 A). This method addresses the problem that multi-model particle filtering algorithms rely on the transition probability matrix and the model state of randomly distinguishing particles. It introduces multinomial and Dirichlet distributions to perform prior modeling of the model state and transition probability matrix, respectively. Within the variational Bayesian framework, the target state, model state, and transition probability matrix are jointly optimized using the coordinate ascent method to improve target tracking accuracy. However, this method has drawbacks. The fact that the solved variational distribution is used as an approximation of the target state's posterior probability distribution inevitably affects the accuracy of the target state. Furthermore, each state estimation in this method only yields all target states at the current moment in the scene, failing to establish a one-to-one correspondence between targets and their states. It also lacks the target's trajectory for target differentiation.

[0004] Chen Zhuangzhuang et al., in their paper "Interactive Multi-Model Poisson-Do-Bernoulli Hybrid Filtering for Maneuvering Target Tracking" (Systems Engineering and Electronics Technology (2023-04-03), ISSN: 1001-506X), disclosed a maneuvering target tracking method based on Poisson-Do-Bernoulli hybrid filtering. The implementation steps of this method are: first, setting the state equation and measurement equation of the tracking system; initializing the system parameters; and sampling in the initial state to obtain the weighted particle set. ,in The number of particles is [value], and the initial weight of each particle is [value]. The particle states are then input into the Poisson-Bernoulli mixture filter method for prediction and update operations. Because the number of particles and components in the multi-Bernoulli mixture is too large, affecting the filtering efficiency, a pruning operation is performed to obtain the desired result. Weighted set of particles at time t Finally, state estimation is performed and

[0005] The outputs of each motion model are weighted and fused to obtain the target state. However, this method still has shortcomings. It combines IMM and PMBM for tracking maneuvering targets. The large number of multi-Bernoulli mixture components increases computational complexity, impacting efficiency. Furthermore, each state estimation only yields the current target state within the scenario, failing to obtain the target's trajectory for differentiation. Trajectory data not only supports pattern recognition of target behavior but also provides a strong data foundation for system optimization, planning, and future prediction applications. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the existing technology by providing a maneuvering target tracking method based on trajectory Poisson and Bernoulli filtering, which aims to solve the problems of high computational complexity and inability to obtain target trajectory data in real time.

[0007] The approach to achieving the objective of this invention is as follows: By fusing the Trajectory Poisson Multi-Bernoulli (TPMB) filtering method and the IMM method, this invention constructs a state model and a measurement model for the trajectory set. This ensures that during the tracking process, each estimation yields the state of all targets from the start to the current tracking moment, thereby enabling real-time acquisition of target trajectory data in maneuvering target tracking. This solves the problem of inability to distinguish targets during tracking in existing technologies. This invention employs the Poisson Multi-Bernoulli approximation idea (PMB). After filtering and updating the Poisson Multi-Bernoulli mixed components, the KL (Kullback–Leibler) divergence is used to obtain the Poisson Multi-Bernoulli components. This ensures that there is only one global hypothesis after each tracking, solving the computational complexity problem caused by the large number of Poisson Multi-Bernoulli mixed components in existing technologies.

[0008] The technical solution of the present invention is as follows:

[0009] Step 1: Predict the target probability density function at the current tracking moment. ;

[0010] Step 2: Update the tracking data by correlating the target probability density at the current tracking time with the measurement at the current time. The updated probability density function that satisfies the PMBM distribution is obtained. ;

[0011] Step 3: Use the KLD technique to transform the PMBM distribution into a PMB distribution;

[0012] Step 4: Obtain the target probability density through model interaction and fusion. ;

[0013] Step 5, for Resampling operation is performed on the weighted particle set in the data;

[0014] Step 6: Discard the weights of the Poisson component and the weighted particle weights of the Bernoulli component that are less than their respective thresholds.

[0015] Step 7: Determine if the current time is the last time of tracking. If yes, proceed to step 8; otherwise, proceed to step 1.

[0016] Step 8: Estimate and track the state of the maneuvering target on the target trajectory set.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] First, this invention tracks a trajectory set by fusing the Trajectory Poisson Multi-Bernoulli (TPMB) filtering method and the IMM method, thereby acquiring the target's trajectory data in real time. This overcomes the problem in existing technologies that cannot distinguish targets during tracking, filling a technological gap in the field of maneuvering target tracking and providing an effective solution for achieving more accurate and real-time target tracking.

[0019] Secondly, this invention employs the Poisson Multi-Bernoulli (PMB) approximation concept. After filtering and updating the Poisson Multi-Bernoulli mixed components, the Poisson Multi-Bernoulli components are obtained using KL divergence. This overcomes the computational complexity problem caused by the large number of Poisson Multi-Bernoulli mixed components during the tracking process in existing technologies. This invention provides an effective approach to reducing algorithm complexity, improving filtering efficiency, and enhancing filtering real-time performance. Attached Figure Description

[0020] Figure 1 This is a flowchart of the present invention;

[0021] Figure 2 This is the algorithm diagram of the interactive multi-model of this invention;

[0022] Figure 3 This is a simulation experiment diagram of the present invention. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0024] Reference Figure 1 The implementation steps of the embodiments of the present invention will be further described below.

[0025] Step 1: Predict the target probability density function at the current tracking moment. as follows:

[0026] ;

[0027] in, This represents the summation operation. This represents the union operation. Indicates the target's sequence number. This represents the total number of targets. Indicates the first A Bernoulli random finite set of n objectives Describes a Poisson random finite set. Let represent a random finite set of all targets. and Representing the Poisson part and the first part respectively The probability density of the Bernoulli part of each target. This indicates a multiplication operation.

[0028] In the embodiments of the present invention, it is set that The intensity of the Poisson component at time t is expressed as The multiple Bernoulli parameters after model interaction and resampling are expressed as follows: , This represents the total number of Bernoulli components. This represents the Bernoulli component index. The existence probability of each Bernoulli component and the single-object density are expressed as follows: and Its single-target density is represented by a weighted particle ensemble. , express Time of the first The model number Bernoulli's first component The state information of each particle express Time of the first The model number Bernoulli's first component The weight of each particle.

[0029] The predicted Poisson intensity at time 1 is composed of the surviving target RFS and the newly formed target RFS. The predicted Poisson intensity is:

[0030] ;

[0031] in, Indicates the probability of survival. The Poisson strength of the new target is represented by the parameter of the predicted Bernoulli part, which is denoted as... The probability density function uses a set of particles This indicates that three of the parameters are calculated using the following formula:

[0032] ;

[0033] ;

[0034] ;

[0035] in, Indicates the first Time of the first The target transition matrix of each model Indicates the first Momentary noise,

[0036] Step 2: Update the tracking data by correlating the target probability density at the current tracking time with the measurement at the current time. The updated probability density function that satisfies the PMBM distribution is obtained. .

[0037] Given the above-mentioned predicted PMB form and measurement set , This indicates the number of measurements. The updated distribution has the form PMBM. .for Strength of the Poisson part at time The Dobernoli section is updated based on the association.

[0038] The association refers to associating the target with the measurement similarity index based on the following three scenarios:

[0039] Scenario 1: The target is not detected at the current moment;

[0040] The fact that the current survival trajectory is associated with an empty measurement set indicates a missed detection, thus a missed detection hypothesis is established. Its parameters are expressed as follows: The probability density function uses a set of particles The parameters are calculated as follows:

[0041] ;

[0042] ;

[0043] ;

[0044] in, Indicates the detection probability. This represents the likelihood value of the current particle.

[0045] Scenario 2: The current measurement is generated by a newly emerging target.

[0046] For each new trajectory, there are two assumptions, for a given measurement If it is detected that the trajectory falls within a given likelihood threshold, it is considered to originate from a true trajectory, and its parameters are established as follows: The probability density function uses a set of particles The single trajectory assumption is represented, and the parameters are calculated as follows:

[0047] ;

[0048] ;

[0049] ;

[0050] ;

[0051] in, This represents the weight of the corresponding predicted Poisson particle. This indicates the intensity of clutter.

[0052] Otherwise, it is assumed that potential new trajectories originate from clutter, and the target is... The assumed weights are set as follows The probability of its existence is set to 0.

[0053] Scenario 3: The measurement at the current moment is generated by the target from the previous moment surviving at the current moment.

[0054] For the survival trajectory, it will be associated with each measurement at the current moment, and a parameter will be established for it. The probability density function uses a set of particles The single trajectory assumption is represented, and the parameters are calculated as follows:

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] in, It represents the index of the measurement.

[0060] Step 3: Use the KLD technique to transform the PMBM distribution into a PMB distribution.

[0061] The TPMB filter is first updated via a Bayesian update, which produces a PMBM distribution. Then, the PMBM distribution is transformed into a PMB distribution in a space with auxiliary variables using the KLD technique.

[0062] The KLD technique is a method for measuring the difference between two probability distributions. KLD measures the uncertainty of one probability distribution relative to another, according to the following formula:

[0063] ;

[0064] in, This represents the KLD values ​​of the distribution functions P and Q. Indicates the index of the event. and They represent the first The probabilities of events in P and Q KLD represents the logarithmic operation with base e. The smaller the value of KLD, the more similar the two distributions are; conversely, the larger the value, the greater the difference between the distributions.

[0065] Step 4: Obtain the target probability density through model interaction and fusion. .

[0066] The aforementioned model refers to a filter that includes at least a uniform velocity model, a uniform acceleration model, and a uniform velocity turning model. In this embodiment of the invention, the uniform velocity model and the uniform velocity turning model are fused. The interactive fusion of these two models refers to using a cyclic filtering method to model each target state using each model, then tracking the modeled target and fusing its tracked state information, and finally weighting and fusing the state information output by each model. The specific steps of the fusion are as follows:

[0067] Assumption The intensity of the Poisson part at time can be represented by the particle set. It means that in the formula Represents particle weights. Indicates the particle state. Indicates particle index, The total number of particles corresponds to the Poisson part. The model probability density at time t is calculated as follows:

[0068] ;

[0069] in, The model represents the first... The model is transferred to the first... The transition probability of each model. The Dirichlet function can be used to obtain the Poisson probability density through the fusion of probabilities from different models. The approximate result of the Poisson intensity at time t is as follows:

[0070] ;

[0071] Similarly, for using particle sets The Bernoulli component, represented by the model probability density function, is:

[0072] ;

[0073] The Bernoulli probability density obtained by interactive fusion is:

[0074] ;

[0075] in, Indicates the state of a particle. This represents the weight of a particle.

[0076] Step 5, for The weighted set of particles in the data is resampled.

[0077] To prevent reduced sample diversity due to particle degradation, a resampling step is performed after the interaction. The resampling approach involves replicating particles with larger weights and discarding particles with smaller weights to refit the density. The resampling process is applied to both the Poisson and Bernoulli parts.

[0078] Step 6: Discard the weights of the Poisson components and the weighted particle weights of the Bernoulli components that are less than their respective thresholds.

[0079] With each update and iteration, the number of assumptions regarding the multiple Bernoulli part of the Poisson particle count increases significantly. To avoid the resulting computational complexity, two thresholds are set corresponding to the Poisson and multiple Bernoulli parts, discarding Poisson and multiple Bernoulli components that are below the thresholds. These thresholds are small values ​​set based on the expected GOSPA value of the target tracking result. In this embodiment, the set value is... .

[0080] Step 7: Determine if the current time is the last time of tracking. If yes, proceed to step 8. Otherwise, increment the tracking time by 1 to obtain the current tracking time and then proceed to step 1.

[0081] Step 8: Estimate and track the state of the maneuvering target on the target trajectory set.

[0082] This invention is based on the TPMB method. Because TPMB tracks a trajectory set, it can acquire the target's trajectory data during the tracking process. Therefore, this invention first constructs a state model and a measurement model for the trajectory set. For the state model, the target trajectory set is... ,in, Indicates the initial moment of tracking a maneuvering target. This indicates the length of the trajectory used for tracking a maneuvering target. The length of the target state is A finite sequence. The set of all surviving trajectories is represented by... It indicates that there are . The time-track length satisfies the following relationship: The target trajectory may be determined by the probability of survival. Survival, or by probability Disappearance. For the measurement model, suppose the trajectory has the following definition for the measurement model of the trajectory set. Let the trajectory... If its trajectory set represents all or surviving trajectories, then the trajectory may be detected with a probability.

[0083] ;

[0084] Detected, or with probability Missed detection.

[0085] The technical effects of this invention will be further explained below with reference to simulation experiments:

[0086] 1. Simulation experiment conditions:

[0087] The hardware platform for the simulation experiment of this invention is: Intel(R) Core(TM) i7-10700KF processor with a main frequency of 3.8GHz and 16GB of memory.

[0088] The software platform for the simulation experiment of this invention is: Windows 10 operating system and MATLAB R2020b.

[0089] The simulation experiment of this invention tracks four maneuvering targets within a uniform noise region of [-1000m, 1000m] × [-1000m, 1000m]. The initial states and actual motion information of the four maneuvering targets are shown in Table 1. The experiment assumes four newly generated targets with a probability of 0.2, and the newly generated targets follow a Gaussian distribution. Its covariance matrix is ​​set as The sampling rate set in the experiment was... The noise during the target's motion follows a zero-mean Gaussian distribution, denoted as . , in Measurement noise is set to... Its covariance is The state transition matrix of the target is denoted as... In this scenario, one CV model and two CT models were set up. The state transition equation and measurement equation of the target in this experiment are as follows:

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] in, This indicates that the target rotates clockwise per second. State transition model and It has the same form, but it causes the target to rotate counterclockwise every second. ,have .

[0096] The system's Markov state transition matrix is ​​set as follows:

[0097] ;

[0098] Set the initial probability of each model to 1 / 3.

[0099] The number of sampled particles for each target is set to 1500, and the number of newly generated particles is 600. The clutter follows a uniform Poisson distribution and obeys the mean. The algorithm's global hypothesis count is limited to 100, the existence probability threshold is set to 0.5, and the detection probability and survival probability are set to... and The GOSPA parameter is set to... and .

[0100] Table 1. Overview of the Actual Motion State of the Target

[0101]

[0102] 2. Simulation content and result analysis.

[0103] The simulation experiment of this invention uses the method of this invention to track four maneuvering targets in the above-mentioned simulation scenario, and the tracking results are shown in the figure below. Figure 3 As shown in (a), the track accuracy graph is as follows: Figure 3 (b) shows the timeline for tracking consumption, as shown in Table 2.

[0104] Table 2. Time consumed by target tracking

[0105]

[0106] The following is combined Figure 3 The simulation diagrams further illustrate the effects of the present invention.

[0107] Figure 3 (a) This evaluates the tracking accuracy of the IMM-SMC-TPMB method in a linear environment. Using the method of this invention, tracking results for four maneuvering targets are obtained, and then the obtained results are compared with the actual results, plotted as follows: Figure 3 The figure shown in (a) is shown in the middle. Figure 3 (a) The x-axis represents the range of the tracking scene in meters, and the y-axis represents the range of the tracking scene in meters. Figure 3(a) The filtered tracking results of the IMM-SMC-TPMB method under a Monte Carlo experiment are presented, with different colored circles distinguishing different trajectories. Black circles represent the true results, and the four different colored circles represent the results after tracking four targets.

[0108] from Figure 3 (a) It can be seen that the method of the present invention can complete the tracking of multiple maneuvering targets relatively accurately, and can distinguish the trajectories of four different targets and track the multi-target tracks.

[0109] Figure 3 (b) evaluates the track matching degree of the IMM-SMC-TPMB method in a linear environment. Using the method of this invention, the tracks of four maneuvering targets are compared with the tracks of the real target to observe the degree of matching, and the results are plotted as follows: Figure 3 The curve shown in (b) is shown in the middle. Figure 3 (b) The horizontal axis represents time, in seconds, and the vertical axis represents the accuracy of the target trajectory. This accuracy refers to the degree of matching between the actual trajectories of the four maneuvering targets and the trajectories of the four maneuvering targets obtained by the method of this invention.

[0110] from Figure 3 (b) It can be seen that the method of the present invention can track the tracks of multiple maneuvering targets more accurately, thereby distinguishing different targets.

[0111] In summary, it can be seen that the method of the present invention can accurately track multiple maneuvering targets while obtaining the target's trajectory, and the method of the present invention consumes less time, thus improving the real-time performance of the present invention.

Claims

1. A method for maneuvering target tracking based on trajectory Poisson-Multinomial filtering, characterized in that, The fusion TPMB method tracks the whole tracking process on the track set, and changes the PMBM distribution into the PMB distribution by using the KLD technology when updating the probability density of the target each time. The steps of the tracking method include the following: Step 1, predict the target probability density function at the current tracking time ; Step 2, update with the target probability density at the current tracking time and the measurement at the current time , to get the updated probability density function satisfying the PMBM distribution ; The association refers to associating the target and the measurement similarity index according to the following three cases: Case one: the target is not detected at the current time; The current living track is associated with an empty measurement set, which indicates that track missing detection occurs, and a missing detection hypothesis is established for the track; Case two: the current measurement is generated by a new target; There are two hypotheses for each new-born track, for a given measurement When it is detected that it is in a given likelihood threshold, it is considered to come from a real track, and a single-track hypothesis is established for it; Otherwise, the potential new-born track is considered to come from clutter, and the target is assumed to have a weight of , and a probability of existence of 0. Case three: the measurement at the current time is generated by the target at the previous time that survives at the current time; For the living track, the track is associated with each measurement at the current time, thereby generating a new single-track hypothesis; Step 3: change the PMBM distribution into the PMB distribution by using the KLD technology; Step 4, obtaining target probability density by model interaction fusion ; Step 5, a resampling operation is performed on the weighted particle set in ; Step 6: discard the components with the weight of the Poisson component and the weighted particle weight of the Bernoulli component being less than the respective thresholds; Step 7: determine whether the current time is the last time of tracking, if yes, execute step 8, otherwise execute step 1; Step 8: estimate and track the state of the maneuvering target on the target track set.

2. The method of claim 1, wherein, The target probability density function described in step 1 As follows: ； wherein, denotes a summation operation, denotes a union operation, denotes the order number of the target, denotes the total number of targets, denotes the Bernoulli random finite set of the th target, denotes the Poisson random finite set, denotes the random finite set of all targets, and denote the probability density of the Poisson part and the Bernoulli part of the th target, respectively, denotes a product operation.

3. The method of claim 1, wherein, The KLD technology in step 3 is a method for measuring the difference between two probability distributions. According to the following formula, the KLD measures the uncertainty of one probability distribution relative to another probability distribution: ； wherein, represents the KLD value of the distribution function P and the distribution function Q, represents an index of an event, and respectively represent the probability of the event in P and Q, represents the e-based logarithm operation, the smaller the value of KLD, the more similar the two distributions represent; on the contrary, the larger the value, the greater the difference between the distributions.

4. The method of claim 1, wherein, The model in step 4 refers to that the filter at least includes a uniform speed model, a uniform acceleration model, and a uniform turning model.

5. The method of claim 1, wherein, The model interactive fusion in step 4 is to use the cyclic filtering method, model each target state by each model, track the modeled target, fuse the state information after tracking, and weight and fuse the output state information of each model.

6. The method of claim 1, wherein, The threshold in step 6 is a decimal value set according to the expected GOSPA value of the target tracking result.

7. The method of claim 1, wherein, The target trajectory set described in step 8 is where, denotes the initial time of the maneuvering target tracking, denotes the length of the trajectory of the maneuvering target tracking, denotes the length of the target state, which is a finite sequence of .

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