Multi-model PBP-TPMB maneuvering extended target tracking method

Abstract

The application discloses a multi-model PBP-TPMB maneuvering extended target tracking method based on an association matrix and belongs to the field of target tracking. The method comprises the following steps: firstly, on the basis of a particle belief propagation (PBP) data association mode, an association matrix is fused to avoid traversing the likelihood of all measurements and targets and to reduce the calculation amount of data association; secondly, in the scene where a maneuvering point target and an extended target are close to each other, the multi-target tracking during the point target shielding is realized through a fuzzy processing method; finally, the complete track information during the target movement is reserved through a TPMB filtering based on a track set, and a reverse smoothing is fused, so that the target track estimation set output by the algorithm is closer to the real target. Through the multi-model PBP-TPMB filtering, the application solves the problem of tracking a maneuvering extended target in a close scene, and the effective tracking of a maneuvering point target and an extended target is achieved.

Description

Technical Field

[0001] This invention relates to a multi-model PBP-TPMB maneuvering extended target tracking method, belonging to the field of target detection and tracking. Background Technology

[0002] With the continuous development of modern software and hardware technologies, target tracking technology has been widely applied. For example, in service technologies such as food delivery, bike sharing, and navigation, the most critical task is to obtain real-time vehicle location information through sensors to plan the optimal route. However, obtaining the optimal delivery route requires not only receiving signals returned from mobile devices using facilities such as satellites and base stations, but also high-performance target tracking algorithms. Target tracking technology plays an irreplaceable role in both civilian and military fields, and has broad research potential and development prospects in areas such as missile defense, underwater detection and tracking, autonomous driving, and industrial robots.

[0003] Multiple target tracking (MTT) refers to the process by which a sensor acquires a noisy and disordered measurement sequence within a monitoring area, iteratively estimates the states of multiple targets, and thus forms multiple time-step target trajectories. Unlike single target tracking, MTT, in addition to addressing filtering issues such as noise and clutter interference, as well as target misdetection and new target emergence, also needs to consider the problem of decreased tracking accuracy due to unclear target measurement distinctions caused by target maneuvering or multiple targets approaching or intersecting, and issues related to target track maintenance.

[0004] Radar, sonar, infrared, and other sensors are used to collect target measurement data with clutter from a monitored area. Based on the target size and the number of measurements returned by the sensors, targets can be divided into point targets and extended targets. Unlike image targets, which have feature information, radar targets are described by measurement points. If the target size is small compared to the sensor resolution, it is usually considered a point target. In the point target model, the target state typically includes motion information, such as position and velocity. At any given moment, a point target generates at most one measurement. Point targets only generate a single measurement and cannot describe the target's shape or other feature information. Extended targets, on the other hand, are defined as targets that generate multiple measurements within their shape range at each moment. The target state typically includes motion information and target shape range information. Extended target tracking technology effectively solves the problem that point target tracking algorithms cannot accurately describe the target shape.

[0005] When a target's motion changes, it is called a maneuvering target. For example, vehicles at an intersection may change from uniform motion to acceleration / deceleration or turning, or a drone may change from climbing or diving to stable uniform motion during flight. In maneuvering target tracking, establishing a suitable motion model for the target is crucial for timely and accurate tracking, and the degree to which the motion model matches the target's actual motion directly affects the algorithm's tracking performance.

[0006] The PMBM filtering algorithm is based on the multi-hypothesis tracking concept, combining the advantages of Poisson random sets and multi-Bernoulli random sets. It detects unknown targets through the Poisson Point Process (PPP) and detects surviving targets through the Multi-Bernoulli Mixture (MBM) process. Compared to CPHD and GLMB filtering, PMBM filtering provides more accurate estimations of the target's centroid motion state and the number of targets. The data association method in this filtering update step is a two-step processing approach: Clustering and Assignment (C&A). This method first clusters measurements based on factors such as density or distance. Second, for each measurement partition, i.e., the correspondence between measurement clusters and targets, an effective assignment method is needed. These C&A-based data association methods often have good tracking performance when targets are relatively dispersed, but target tracking performance degrades when targets are adjacent or overlap.

[0007] PMBM filtering is effective in estimating the number and state of moving targets, but it cannot preserve complete target trajectory information. For the problem of target trajectory maintenance, Xia et al. proposed the Trajectory-PMBM filtering method for extended targets in 2019, achieving simultaneous estimation of target state and trajectory information for multiple extended targets. Their team proposed the Trajectory-PMB filtering method in 2020, which uses KL divergence minimization for PMB approximation, achieving multi-target trajectory estimation and maintenance with lower computational complexity.

[0008] Within the Trajectory Poisson Multi-Bernoulli (TPMB) filtering framework, data association is achieved using the particle confidence propagation method. This yields the marginal association probabilities and Bernoulli densities in the filtering update step, enabling the PMB approximation. This truncates underweight global hypotheses, reducing the computational burden of data association. The prediction step of the PMMB filter retains only a mixed component of a single global hypothesis, thus approximating the target state and further reducing computation. The TPMB filtering update step is implemented through Bayesian updates, which generate a PMMB distribution. The marginal density of the target state set is then calculated using the PMB approximation, marginalizing the uncertainty of the global hypotheses. Regarding the implementation of the PMB approximation, firstly, globally hypotheses with low weights that are negligible are pruned using clustering and assignment methods or sampling-based methods. Then, the marginal association probabilities are approximated by enumerating the pruned global hypotheses.

[0009] Both C&A methods based on multiple hypotheses and sampling-based methods can avoid enumerating all data association hypotheses by pruning hypotheses with low weights. However, this limits target tracking performance when data association uncertainty is high. A more efficient data association method in extended target tracking that avoids enumerating all local association hypotheses is to directly calculate the posterior density probability of marginal multi-targets, where the uncertainty of data association is marginalized. However, in the above methods, for the case of close-proximity targets, measurement clustering generates many partitions, leading to a decrease in target tracking performance, and even missed tracking when targets are close or overlap. Summary of the Invention

[0010] To address the problem of insufficient tracking accuracy for multiple maneuvering extended targets in close proximity scenarios, this invention provides a multi-model PBP-TPMB maneuvering extended target tracking method, the technical solution of which is as follows:

[0011] Within the framework of trajectory Poisson-Do-Bernoulli filtering (TPMB), firstly, the interactive multi-model method (IMM) is used for target prediction, and the tracking of maneuvering targets is achieved through predictions from multiple motion models; secondly, measurement data is correlated and filtered and updated through particle confidence propagation (PBP) based on the correlation matrix; finally, the target state is estimated and inverse smoothing is performed to output the complete target trajectory estimation result.

[0012] The method for tracking maneuvering extended targets includes:

[0013] Step 1: Assuming the current time step is k, obtain the posterior probability density and measurement set of the target at time k-1, perform multi-model prediction, and output the target PPP component and MBM component predicted under multiple motion models;

[0014] Step 2: The predicted target components and measurement set obtained in Step 1 are processed using the Particle Confidence Propagation (PBP) method based on the correlation matrix to obtain the updated target posterior probability density.

[0015] Step 3: Process the updated target posterior probability density obtained in Step 2 using the target state estimation to obtain the estimated trajectory set;

[0016] Step 4: Use the reverse smoothing method to process the target state estimation set obtained in Step 3, and finally obtain a smooth trajectory set.

[0017] Optionally, the PPP prediction intensity of undetected targets within the monitoring area at time k in step one is:

[0018]

[0019] in, and The particle weights represent the number of sampled particles corresponding to the potential target component and the newly generated target component, respectively. and The calculation is as follows:

[0020]

[0021]

[0022] The state transition method of the target is as follows:

[0023]

[0024] Where F(·) is the state transition equation expression for uniform linear motion;

[0025] The MBM component prediction process includes:

[0026] For the detected surviving targets, the target state of the i-th MBM component at time k is represented as:

[0027]

[0028] The multi-model target state prediction calculation method is as follows:

[0029]

[0030] Where M is the number of motion models, Let n be the target state transition matrix under the nth motion model of the i-th target component at time k. It represents the conversion probability between different motion models;

[0031] The probability r of the existence of the target component and the particle weighted sum w of the surviving target are expressed as:

[0032]

[0033]

[0034] The posterior density of the target at time k-1 is used as the potential target for calculation, thus ensuring the integrity of the trajectory; the number of particles satisfies... And the survival target Since the target at different times belongs to the same trajectory, it satisfies...

[0035] like That is, considering the survival of the target, the target state at time k is predicted. Add to trajectory set middle:

[0036]

[0037]

[0038]

[0039] Among them, the predicted trajectory set During the prediction process, birth intensity is used as a means of prediction. The motion model F(·) performs particle sampling on the new target, and the motion model is used to perform particle sampling on the new target. Perform particle sampling on maneuvering targets. Let be the transition probabilities of different motion models transforming into the nth model at time k. Given the nth target motion state transition matrix, then under a total of M motion model state predictions, the following is generated: One predicted particle;

[0040] At time k, considering the possibility of the target being eliminated, the particle weights will change. In the next time step, all particles will be copied and their weights will be updated according to the survival probability. If the target is determined to be eliminated, the MBM components with a probability of existence lower than the target survival threshold will be retained, and their multi-model predictions will be pruned, retaining only the particles generated by the single motion model prediction.

[0041] If the target disappears at time k, retain the target's posterior information at time k-1 in the trajectory set:

[0042]

[0043]

[0044] in, For trajectory set The posterior density of the single-target state at time k-1.

[0045] Optionally, step two includes:

[0046] (1) Particle trajectory initialization;

[0047] In the particle confidence propagation method, the propagation information is optimized through P iterations, thereby converging the confidence of all nodes. At this point, the label of each node is the optimal label.

[0048] Poisson strength is expressed as The form of a particle set;

[0049] In the p=1th iteration, the trajectory variable nodes To factor nodes s k The information being disseminated A set of weighted particles express;

[0050] The updates for new and potential targets, as well as surviving targets, each consider whether the target is alive at the current moment.

[0051] (2) Evaluation of measurement information;

[0052] Calculate each factor node s k Vector measurement variable nodes The message conveyed Factor Node s k This represents the information transmission process between the survival trajectory and all measurements.

[0053]

[0054]

[0055] In the p∈{1,…,P} iterations, information propagation between each target variable node and the measurement variable node is realized according to the factor graph formula;

[0056] By introducing an correlation matrix and setting a gating threshold between particle states and measurement information, the information within the gating threshold is calculated when calculating the correlation likelihood matrix. The particle likelihood calculation method for target generation is as follows:

[0057]

[0058] Where d(z,x) is the Euclidean distance between the particles generated by the surviving target and the existing measurement positions, and δ is the gating threshold of the correlation between the particles and the measurement.

[0059] Both data association and measurement update methods achieve information transmission through computation. The target state update is represented as

[0060] After one iteration, the particle weights converge to a value that closely approximates the true state of the target. In subsequent iterations, each variable node... To factor nodes s k The information being disseminated All represent the unnormalized Bernoulli component density, other propagation information, and particle weights, etc., when i∈{1,…,n} k|k-1}, j∈{1,…,m k At that time, for each predicted surviving target, particles are generated and updated with existing measurements:

[0061]

[0062]

[0063] When i∈{n k|k-1 +1,…,n k|k}, j∈{1,…,in k|k-1 In the context of updating potential targets and measurements, since the assumptions of the multi-motion model are deleted when the target is determined to be destroyed, here the information is only updated by updating the particles generated by the single-motion model prediction process and the existing measurements. The particle weights are:

[0064]

[0065]

[0066] (3) Confidence calculation

[0067] The information and particle weights calculated through multiple iterations of the above steps converge to values ​​that approximate the true target state. Therefore, the confidence level of the target state in each MBM component is... It can be represented by the following Bernoulli random set:

[0068]

[0069] To ensure the validity of the trajectory confidence, the particle weights and Bernoulli components are calculated in subsequent iterations. Finally, the particle weights are normalized.

[0070] Optionally, step three includes:

[0071] The updated target posterior probability density is stored in the form of MBM components. MBM components with a probability higher than a threshold are selected. The target state at time k is estimated from a set of weighted particles and output as the target trajectory, represented as:

[0072]

[0073] The estimation of the newly generated target is achieved through a Poisson point process, and the output of the newly generated target generates a trajectory set, denoted as trajectory X. b =(t b ,x 1:v ), where the birth time is t b =k, trajectory length v=1, for unknown target trajectories, there is no need to perform particle sampling in the prediction step for undetected targets;

[0074] After outputting the estimated target trajectory set at each time step, redundant MBM components are pruned and resampled to avoid particle sample degradation.

[0075] Optionally, step four includes:

[0076] After outputting the filtered and estimated target trajectory set, inverse smoothing can be performed using the estimated particle states. For each trajectory, inverse particle smoothing of length v is performed from the annihilation time e to the target appearance time t. The target state at time k can be approximately calculated based on the weighted particle set obtained from the filtered estimation. The marginal smoothing distribution of the target is as follows:

[0077]

[0078] in and These represent the filtered density and the predicted density of the target at time k in the trajectory set, respectively. All targets are monitored for a total of K time steps, and the measurement information y generated within each time step is used to determine the density. 1:k Perform inverse smoothing estimation.

[0079] Optionally, for point targets that are adjacent to or overlap with the extended target, only multi-model prediction is performed without updating. After target separation, the location of overlapping point targets is determined by matching the MBM component predicted by the multi-model prediction with the newly generated PPP component within the extended area, thereby enabling subsequent target tracking. Specifically, this includes:

[0080] Step 1: Assuming the current time step is k, obtain the posterior probability density and measurement set of the target at time k-1, determine whether the point target has entered the overlapping region with the extended target, and output the MBM component of the overlapping point target.

[0081] Step 2: Using a multi-model fuzzy prediction method, process the MBM components of the overlapping point targets obtained in Step 1, and output the predicted point targets. Quantity;

[0082] Step 3: Based on the predictions obtained in Step 2 The component is matched and updated with the newly generated PPP component, and the updated component is output. Quantity;

[0083] Step 4: For the updated data obtained in Step 3 The target component outputs the estimated target trajectory set.

[0084] Optionally, step 1 includes:

[0085] Assuming the current time is k, the i-th surviving target x i The information propagated by the factor nodes is u i,j Then the particle weight is w i,j And satisfying i∈{1,…,n k|k-1};

[0086] If the information propagated by target i is u i,1 ,u i,2 ,…,u i,M There are multiple pieces of information u in the middle. i,e With the information with the highest weight If they are similar, then target i can correspond to multiple measurement points, which conforms to the property of an extended target, namely:

[0087]

[0088] Where δ f To determine the likelihood similarity threshold, in a spatial model where point targets and extended targets coexist, each MBM component is determined according to... Distinguish between target types; if in the i-th MBM component, parameter c p =1, meaning that at time k-1, the target is determined to be a point target, and the point target x i The information being disseminated i,j The similar likelihoods with multiple measurement points indicate that the target at that point has entered the overlapping region occluded by the extended target.

[0089] Optionally, step 2 includes:

[0090] After the MBM component of a point target enters the overlapping region, the measurement update is stopped, and only multi-model fuzzy prediction is performed.

[0091] Assume that time k is the start time t of the fuzzy processing of the overlapping point target. s End time t e =k+a, then in the next a consecutive time steps, the MBM component corresponding to the target point is predicted by M motion models, denoted as k+a.

[0092] Keeping the existence probability of the multiple Bernoulli components constant, and assuming the overlapping point target is alive, the Gaussian distribution describing the motion information of the point target is as follows: Then the multi-model fuzzy prediction of the MBM component over a consecutive time steps within the overlapping region is:

[0093]

[0094]

[0095] in, Let be the normalization factor for the probability of the MBM component existing in the overlapping region at a time steps. t is the start time of fuzzy processing s Until the end time t e During this period, the state transition probabilities of the motion model at each time step are:

[0096]

[0097] in, Let be the motion model probability matrix of the i-th MBM component at time k. In the fuzzy prediction of a point target, assuming the target motion model remains unchanged, the motion model probability of the point target is... Obeying the probability matrix of the motion model when it enters the overlapping region And will no longer be updated;

[0098] Fuzzy prediction of the motion state of a point target only retains the final time t e The multi-model prediction results show that the Bernoulli component exists at each time step with a probability. The predicted weights for the MBM components are as follows:

[0099]

[0100]

[0101] After completing the fuzzy prediction of the MBM components, the filtered prediction state output for the surviving target is given. The component output consists of M Bernoulli components predicted by different motion models.

[0102] Optionally, step 3 includes:

[0103] By detecting and matching newly emerging PPP components appearing in the extended area of ​​the overlapping region, the updating and subsequent tracking of overlapping point targets can be achieved.

[0104] The extended region is t e The expansion of the overlapping region at time points is represented as Matching newly emerging targets within this area determines the location of overlapping targets at point t. e The state at any given moment;

[0105] For t eAll newly generated target PPP components appearing at each time point are updated using PBP-TPMB, and the predicted Poisson distribution intensity is:

[0106]

[0107] in L represents the expected number of potential targets. b To represent the number of particles in the newly generated target;

[0108] Among all newly generated target PPP components, those located within the extended region and c p For point targets with a probability density of 1, take their posterior probability density and the fuzzy prediction. Perform matching and update. The motion model probability is used as a priori condition for the trajectory of the target point in the overlapping region.

[0109] The posterior probability density of the PPP component of the new target is obtained through the multi-model PBP-TPMB method, denoted as... Take its updated target state If the target state of this component is x p Located in the extended area Inside, it is believed That is, the target x at the overlapping point i In t e The target state at any given moment;

[0110] Optionally, step 4 includes:

[0111] Predict MBM components With the corresponding new PPP component After matching, the m-th predicted component is used. As the overlapping target x i If the state estimation output at time steps within the overlapping region does not match the PPP component, then the point target x is determined to be... i They perished within the overlapping area;

[0112] x i In t e The target state estimation result at time t is Component parameters For time steps k∈{t} that coincide with the extended target s ,…,t e -1}, the estimated result of the target state is The set of parameters of the target state in the component.

[0113] In summary, if target x i In t eIf the target state is alive at all times, then the estimated result is: satisfy

[0114] The beneficial effects of this invention are:

[0115] (1) Based on TPMB filtering, this invention incorporates interactive multi-model algorithm to realize maneuvering target tracking, and provides factor graph representation of extended target posterior variables and associated variables to realize data association of particle confidence propagation;

[0116] (2) The present invention proposes a multi-model TPMB filtering framework for maneuvering targets. By running confidence propagation based on the correlation matrix on the constructed factor graph, a message passing equation based on a random finite set is derived. The particle filtering experiment of IMM-PBP-TPMB is realized, proving the effectiveness of the proposed method for tracking adjacent multi-maneuvering extended targets.

[0117] (3) This invention proposes a method for blurring the overlapping area when the point target and the extended target overlap, which solves the problem that the point target cannot be effectively tracked when it is occluded by the extended target.

[0118] By using a data association method based on particle confidence propagation of the correlation matrix, the problem that clustering and allocation-based data association methods are difficult to effectively track adjacent maneuvering extended targets is solved. This achieves the effect of effectively tracking multiple adjacent maneuvering extended targets. Furthermore, in scenarios where point targets and extended targets coexist, the detection and tracking of adjacent point targets and extended targets are realized. Attached Figure Description

[0119] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0120] Figure 1 This is the flowchart of the PMBM filtering algorithm.

[0121] Figure 2 It is a factor graph representation of the confidence propagation process.

[0122] Figure 3 This is a schematic diagram of the method flow of the present invention.

[0123] Figure 4 This is a schematic diagram of overlapping and blurred areas.

[0124] Figure 5It is a real trajectory map of targets in a multi-expanded target experimental scenario.

[0125] Figure 6 This is a comparison chart of tracking results for multiple extended target experimental scenarios.

[0126] Figure 7 It is a comparison of the root mean square error (GOSA) of multi-extended target experiments.

[0127] Figure 8 It is the real trajectory of multi-point target and extended target scenarios.

[0128] Figure 9 This is a comparison chart of tracking results for multi-point targets and extended targets.

[0129] Figure 10 It compares the root mean square error (GMSA) of multi-point target and extended target scenarios. Detailed Implementation

[0130] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0131] The basic knowledge involved in this application will be introduced as follows:

[0132] 1. PMBM Filtering Principle

[0133] In target tracking problems, at each moment, the state of a target—its creation, disappearance, emergence, or continued existence—will cause changes in the target's position and number, and the measurements obtained by the sensor at each moment will also change simultaneously, resulting in uncertainty. Similar to the Poisson-Bernoulli mixture filter (PMBM) for point targets, the extended target PMBM model is also based on the multi-hypothesis tracking idea, consisting of a Poisson point process (PPP) random finite set and a multi-Bernoulli mixture (MBM) random finite set. The overall process of implementing extended target tracking using the PMBM filtering algorithm is as follows: Figure 1 As shown.

[0134] Compared to the extended target represented by GGIW density in the filtering recursion process, the point target is filtered using Gaussian density, which does not require consideration of information such as the target's extended state. However, the point target differs from the extended target in the measurement generation model and filtering recursion process. Measurement values ​​for the point target and the extended target are generated by selecting different measurement likelihood functions f(Z|x).

[0135] The PMBM model consists of two independent RFS models: PPP RFS, which describes the distribution of undetected potential targets (i.e., the set of newly emerging targets that may appear within the monitoring area), and MBM RFS, which describes the distribution of surviving targets (targets detected at least once during the monitoring period). Assumptions... This represents the set of targets that have never been detected. If the target set is detected at least once, then the complete target set at time k is... The PMBM filtering process for the target set is expressed as follows:

[0136]

[0137]

[0138]

[0139] in, Let λ represent the prior probability density of undetected targets. k|k-1 (x) is the Poisson intensity of the currently undetected potential target x. The multi-Bernoulli mixture representation represents the surviving target at time k.

[0140] PMBM filtering uses a multiple hypothesis approach to correlate data, based on the PMBM probability density f. k|k-1 (X k In ), there exists n k|k-1 Each Bernoulli component can produce at most 100 Bernoulli components, and each Bernoulli component can produce at most 1000 Bernoulli components. A local hypothesis corresponding to the measurement set. A corresponding local hypothesis is selected for each Bernoulli component. A global hypothesis is obtained. Where A k|k-1 Let be the set of all global hypotheses at time k.

[0141] Each global hypothesis represents a multi-Bernoulli distribution, then the corresponding local hypothesis a i The density of the i-th Bernoulli component is:

[0142]

[0143] in, It is the probability of the existence of the Bernoulli component. It is a Bernoulli component probability distribution, and the weight of the global hypothesis 'a' is... This weight is proportional to n k|k-1 Local hypothesis a i The product of weights, and Multiple global assumptions may arise during the data association process because, when there are multiple extended targets, distance-based clustering algorithms may produce various measurement clustering results when the targets are close to each other.

[0144] The PMBM filtering algorithm achieves target tracking through two steps: prediction and update.

[0145] (1) PMBM Prediction

[0146] Assume the probability density of the multi-objective state at time k-1 is f k|k-1 (X k If the probability density is calculated using a Poisson random finite set (RFS) and a MBM random finite set, then the predicted probability density is still composed of the RFS and the MBM. The prediction strength of the Poisson RFS is...

[0147] λ k|k-1 (x)=λ b (x)+∫p s (y)f k|k-1 (x|y)λ k-1 (y)dy

[0148] Where, p s (·) represents the target survival probability, λ k-1 (·) represents the posterior strength of the Poisson RFS target at time k-1.

[0149] For the predicted intensity of MBM RFS, assuming the posterior parameters of the target at time k-1 are expressed as follows: and The corresponding prediction intensity is expressed as

[0150]

[0151]

[0152]

[0153] (2) PMBM Update

[0154] The PMBM filtering form is the same as the multi-objective Bayesian filtering, so the joint probability density of the PMBM filtering at time k is expressed as:

[0155]

[0156] Among them, g p (·|·) and g mbm (·|·) are the likelihood functions of Poisson RFS and MBM RFS, respectively, which can be simplified to

[0157]

[0158] 2. TPMB Filtering Principle

[0159] Unlike PMBM filtering methods based on target sets, TPMB filtering represents target components including birth and death times, as well as the target's state during this period, effectively recording complete target trajectory information. and Let x represent the random finite set of the target state and the random finite set of measurement at time k, respectively.k It includes single-target state information, such as motion information (position and velocity); if the target is an extended target, it also includes extended state information (shape and size). 1:k Let k be the measurement sequence at time k and all times prior. The target's trajectory information is a finite sequence of its state over consecutive time steps, represented as...

[0160] X=(t,x 1:v )

[0161] Where t is the initial time of the trajectory, v is the time elapsed since the trajectory began moving, and x... 1:v =(x 1 (x, ..., x) is a finite sequence of target states. The variable (t, v) belongs to set I. (k) ={(t,v):0≤t≤k,1≤v≤k-t+1}. Therefore, the single trajectory space containing complete time information and target state information at time k is represented as:

[0162]

[0163] in To perform intersection and union operations, this formula describes the target x at time k. k The birth time, survival time, and target status at each moment.

[0164] At time k, newly emerging targets within the monitoring area are categorized according to birth intensity. The detection is performed using the Poisson point process, while for the already detected target x k-1 Its survival probability P S (x k-1 and Markov transfer density g k (x k |x k-1 The trajectory of a target evolves independently of other targets within the monitoring area; otherwise, the target's trajectory follows a 1-P pattern. S (x k-1 The probability of a trajectory disappearing is determined by its survival probability at the current time step k. Considering target occlusion, eliminated trajectories may still be retained as potential target components. To ensure track maintenance effectiveness, all target trajectories are retained in the trajectory set regardless of whether they have ended. Therefore, the Bernoulli RFS transition density of a single target trajectory is:

[0165] f k|k-1 =π x (x t:e |t,e,x t′:e′ )×π e (e|t,x t′:e′ )Δ t′ (t)

[0166]

[0167]

[0168] Where Δ(·) is the Kronecker delta function.

[0169] The component density of the multi-target trajectory set TPMB, which includes both undetected and detected targets, is:

[0170]

[0171] Where A k|k-1 This is the global hypothesis generated based on the measurement set and all MBM components.

[0172] 3. Confidence propagation principle

[0173] For methods dealing with complex global functions that involve many variables, a given function can be decomposed into a product of multiple local functions, each depending on a subset of the variables. Such a decomposition can be represented by a bipartite graph, called a factor graph. The particle confidence propagation method is a message-passing method described on a factor graph, which follows a simple computational rule and can accurately or approximately compute various marginal functions derived from the global function.

[0174] The factor nodes of the surface vector measurement are represented as where j∈{1,…,m} k}, If and only if the j-th measurement When it can be associated with the i-th Bernoulli component, This holds true. The corresponding surviving target i∈{1,…,n k|k-1 Bernoulli components and all m in the current time step k The correlation between measurements can be represented by the message passing process between factor nodes and variable nodes. Based on the local assumption of the Dobernouri components, the j-th measurement... Not compatible with i∈{n k|k-1 +1,…,n k|k-1 If the Bernoulli components of {+j-1} are related, then the variable node... satisfy {0,1,…,n k|k-1 ,n k|k-1 +j,…,n k|k Then the joint posterior of the target state set and the surface vector correlation vector is:

[0175]

[0176]

[0177] in, To detect undetected targets The target posterior probability density obtained by performing a Poisson point process. and These correspond to the confidence levels of surviving and potential targets, respectively, and are based on prior information predicted from the targets. The calculations show that N and M represent the number of targets and measurements, respectively.

[0178] Figure 2 This demonstrates the confidence propagation relationship of information between the various factor nodes of the target state set and the measurement set, and the propagation of information. and It is obtained from the following formula.

[0179]

[0180]

[0181]

[0182]

[0183] Where r is the probability of the Bernoulli component existing. Generate the likelihood of the measurement for the target.

[0184] Example 1:

[0185] This embodiment provides a multi-model PBP-TPMB maneuvering extended target tracking method based on the correlation matrix. The method includes: first, within the framework of trajectory Poisson-Dobernoli filtering (TPMB), an interactive multi-model method (IMM) is used for target prediction. Tracking of the maneuvering target is achieved through predictions from multiple motion models. Second, measurement data is correlated using particle confidence propagation (PBP) based on the correlation matrix, followed by filtering and updating to reduce the computational complexity of the data correlation step and improve the overall performance of the target tracking method. Tracking of adjacent targets is achieved. Finally, the target state is estimated, and inverse smoothing is performed to output a complete target trajectory estimation result.

[0186] Step 1: Assuming the current time step is k, obtain the posterior probability density and measurement set of the target at time k-1, perform multi-model prediction, and output the target components predicted under multiple motion models (including PPP components and MBM components).

[0187] The specific processing steps include:

[0188] (1) PPP component prediction

[0189] Trajectory information needs to be considered during the filtering process. Therefore, at each time step, it is necessary to determine whether the target has disappeared, that is, to compare the relationship between the current time and the time when the target disappeared. The trajectory density of a single target is expressed as:

[0190]

[0191] Where t is the target's birth time, L is the number of particles generated by the target, and v is the trajectory length of target x (i.e., the size of the target's survival time step). Let v be the Dirac function, if v (l) =v, then otherwise pass This is used to indicate whether the particle trajectory length matches the target, thus determining whether the target has been destroyed at the current moment. The target trajectory x is calculated. 1:v The trajectory density requires determining whether the birth time and target duration *v* of all particles generated for the target are consistent with the target's timeframe. Particles meeting these conditions are then weighted and summed as the single-target trajectory density. The complete target trajectory represented by the particles is: w (l) The weight of particle l is represented by w. (l) >0, the above formula represents the trajectory of a single target described by L particles. This indicates that the l-th particle is generated at the moment of the target's birth. This indicates that the l-th particle can match the complete target trajectory x. 1:v , t (l) Let x represent the birth time corresponding to the l-th particle. (l) This represents the l-th particle sampled from the target x.

[0192] In the TPMB filtering framework, the PPP process is used for the detection of potential targets. Considering the prediction of a single motion model, the PPP prediction intensity of undetected targets in the monitoring area at time k is:

[0193]

[0194] in and These represent the number of sampled particles corresponding to the potential target component and the newly generated target component, respectively. The potential target component corresponds to the situation where the target has not been generated and measured normally; in this case, the possibility of the target continuing to survive should also be considered. This indicates the expected number of potential targets. This indicates that the l-th particle was born at the same time as the potential target x. This indicates that the trajectory length of the l-th particle is the same as the trajectory length of the potential target x. Represents the current trajectory x 1:vCorresponding to potential targets. The newly generated target component corresponds to the trajectory of randomly generated targets within the monitoring area, δ k [t] indicates that the current time k is the birth time t of the new target, and δ1[v] indicates that the length of the new target is 1. For the trajectory of new life The first target component is target x. k .

[0195] Particle weights in the formula and The calculation is as follows:

[0196]

[0197]

[0198] in, Indicate target The probability of survival, L represents the Poisson intensity of the newly formed target at time k. b This represents the number of sampled particles corresponding to the newly generated target component.

[0199] The state transition method of the target is as follows:

[0200]

[0201] Where F(·) is the state transition equation expression for uniform linear motion.

[0202] (2) MBM component prediction

[0203] For the detected surviving targets, the target state of the i-th MBM component at time k is represented as:

[0204]

[0205] The multi-model target state prediction calculation method is as follows:

[0206]

[0207] Where M is the number of motion models, Let be the target state transition matrix of the i-th target component at time k under the n-th motion model. This represents the transition probability between different motion models. The probability of the target component existing, r, and the particle-weighted sum w of the surviving targets are expressed as:

[0208]

[0209]

[0210] The posterior density of the target at time k-1 is used as the potential target in the calculation, thus ensuring the integrity of the trajectory. The number of particles satisfies... And the survival target Since the target at different times belongs to the same trajectory, the birth time of particle l satisfies

[0211] like That is, considering the survival of the target, the target state at time k is predicted. Add to trajectory set middle

[0212]

[0213]

[0214]

[0215] Among them, the predicted trajectory set In the above prediction steps, birth intensity is used as a basis for prediction. The motion model F(·) performs particle sampling on the new target, and the motion model is used to perform particle sampling on the new target. Particle sampling is performed on the maneuvering target. Then, under a total of M motion model state predictions, the following is generated: There are 10 predicted particles. At time k, considering the possibility of the target's demise, the particle weights will change. In the next time step, all particles are replicated, and their weights are updated according to the survival probability. If the target is determined to be dead, the MBM components with a probability of existence lower than the target's survival threshold are retained, and their multi-model predictions are pruned, retaining only the particles generated by the single motion model prediction.

[0216] If the target disappears at time k, retain the target's posterior information at time k-1 in the trajectory set.

[0217]

[0218]

[0219] in, Representation of trajectory set The posterior density of the single-target state at time k-1, This represents the particle weight.

[0220] Step 2: The predicted target components and measurement set obtained in Step 1 are processed using the Particle Confidence Propagation (PBP) method based on the correlation matrix to obtain the updated target posterior probability density.

[0221] The specific processing steps include:

[0222] (1) Particle trajectory initialization

[0223] In the particle confidence propagation method, the propagation information is optimized through P iterations, thereby converging the confidence of all nodes. At this point, the label of each node is the optimal label.

[0224] The target trajectory is represented as The form of a particle set. Among them, This represents the state of a single target extracted from the trajectory set at time k. For the potential target, a Poisson distribution, Representing the complete set of potential target trajectories, through Each particle is used to initialize the trajectory.

[0225] trajectory variable nodes To factor nodes s k The information being disseminated A set of weighted particles It indicates. Among them. It is the information transmitted from the target node i to the target node j during the p-th iteration. Represents the weight of the l-th particle in p iterations. and These represent the birth time information and trajectory information of particle l generated by target i at time k.

[0226] The updates of new and potential targets, as well as surviving targets, must take into account whether the target is alive at the current moment.

[0227] (2) Measurement Information Evaluation

[0228] Measurement and evaluation require calculation of each factor node. s k Vector measurement variable nodes The message conveyed Factor Node s k This represents the information transmission process between the survival trajectory and all measurements.

[0229]

[0230]

[0231] in This represents the Poisson intensity of the clutter at time k. For the j-th measurement at time k, L i This represents the number of particles generated for target i. This represents the survival time of the l-th particle generated from target i at the current moment. With particle trajectory length Whether a match occurs, i.e., whether target i is still alive at time k. This represents the Poisson intensity of target i, used to calculate the likelihood of the target generation measurement.

[0232] In the p∈{1,…,P} iterations, information propagation between each target variable node and the measurement variable node is achieved according to the factor graph formula. During this process, the computational complexity of particle weights is relatively high. Therefore, this invention introduces an association matrix. By setting a gating threshold between particle states and measurement information, when calculating the association likelihood matrix, it is unnecessary to consider the information propagated between all variable nodes; only the information within the gating threshold needs to be calculated, thereby reducing the computational complexity of particle weights. The particle likelihood calculation method for target generation is as follows:

[0233]

[0234] Where d(z,x) is the Euclidean distance between the particle generated by the surviving target and the existing measurement position, and δ is the gating threshold of the correlation between the particle and the measurement.

[0235] Both data association and measurement update methods achieve information transmission through calculation, based on the information calculated above. The target state update can be represented as The target state update, based on the association method, reduces the computational complexity of particle weights by setting a gating mechanism between the particle state and measurement information, and only requiring the calculation of information within the gating range. After completing the information transfer iteration, the particle weights converge to a value that closely approximates the true target state.

[0236] After one iteration, the particle weights converge to values ​​that closely approximate the true state of the target. In subsequent iterations, each variable node... To factor nodes s k The information being disseminated Both represent the unnormalized Bernoulli component density.

[0237] When i∈{1,…,n k|k-1}, j∈{1,…,m k At that time, for each predicted surviving target, particles are generated and updated with existing measurements.

[0238]

[0239]

[0240] in This represents the information propagated from the target variable node i′ to the measure variable node j′, n k|k This represents the number of targets at time k.

[0241] When i∈{n k|k-1 +1,…,nk|k}, j∈{1,…,in k|k-1 In the context of updating potential targets and measurements, since the assumptions of the multi-motion model are deleted when the target is determined to be destroyed, here the information is only updated by updating the particles generated by the single-motion model prediction process and the existing measurements. With particle weights

[0242]

[0243]

[0244] (3) Confidence calculation

[0245] The information and particle weights calculated through multiple iterations of the above steps converge to values ​​that approximate the true target state. Therefore, the confidence level of the target state in each MBM component is... It can be represented by the following Bernoulli random set

[0246]

[0247] Its calculation method and information Similarly, in addition, it is still necessary to consider the calculation of the probability of particle weights and Bernoulli components in subsequent iterations to ensure the validity of the trajectory confidence, and finally perform particle weight normalization.

[0248] Step 3: Process the updated target posterior probability density obtained in Step 2 using the target state estimation to obtain the estimated trajectory set;

[0249] The specific processing steps include:

[0250] The updated target posterior probability density is stored in the form of MBM components. MBM components with a probability higher than a threshold are selected. The target state at time k is estimated from a set of weighted particles and output as the target trajectory, represented as:

[0251]

[0252] The estimation of the newly generated target is achieved through a Poisson point process, and the output of the newly generated target generates a trajectory set, denoted as trajectory X. b =(t b ,x 1:v ), where the birth time is t b =k, trajectory length v=1. For unknown target trajectories, particle sampling is not required in the prediction step where no target is detected. After outputting the estimated target trajectory set at each time step, redundant MBM components are pruned and resampled to avoid particle sample degradation.

[0253] Step 4: Process the target state estimation set obtained in Step 3 using the reverse smoothing method to finally obtain a smoothed trajectory set;

[0254] The specific process includes:

[0255] After outputting the filtered and estimated target trajectory set, inverse smoothing can be performed using the estimated particle states. For each trajectory, inverse particle smoothing of length v is performed from the annihilation time e to the target appearance time t. The target state at time k can be approximately calculated based on the weighted particle set obtained from the filtered estimation. The target marginal smoothing distribution is as follows:

[0256]

[0257] in and These represent the filtered density and the predicted density of the target at time k in the trajectory set, respectively. All targets are monitored for a total of K time steps, and the measurement information y generated within each time step is used to determine the density. 1:K Perform inverse smoothing estimation.

[0258] Example 2:

[0259] This embodiment provides a supplement and extension to the multi-model PBP-TPMB method provided in Embodiment 1 in scenarios where the point target and the extended target overlap.

[0260] The multi-model PBP-TPMB method in Example 1 addresses the target tracking problem when multiple maneuvering extended targets are adjacent. However, when a maneuvering point target is adjacent to or even overlaps with an extended target, the point target may be occluded by the extended target. The measurements generated by the two targets are grouped into a single cluster. Neither clustering-based allocation nor confidence-based data association can match point targets generating a single measurement or perform tracking across multiple time steps. Especially when the point target is maneuvering, it may be occluded by the extended target for multiple consecutive time steps, making it impossible to correctly update the measurements generated by the point target, thus easily leading to missed tracking.

[0261] To address this issue, this embodiment proposes a method for blurring overlapping target regions. Based on multi-model PBP-TPMB filtering, this method performs multi-model prediction without updating point targets that are adjacent to or overlap with the extended target. After target separation, the position of the overlapping point targets is determined by matching the multi-model predicted MBM components with the newly generated PPP components within the extended region, thus enabling subsequent target tracking.

[0262] Step 1: Assuming the current time step is k, obtain the posterior probability density and measurement set of the target at time k-1, determine whether the point target has entered the overlapping region with the extended target, and output the MBM component of the overlapping point target.

[0263] The specific processing steps include:

[0264] In the method proposed in this invention, when the target distribution is relatively dispersed or multiple extended targets are adjacent, the multi-model PBP-TPMB maneuvering extended target tracking method described in Example 1 can effectively detect and track multiple maneuvering extended targets. This extended example mainly solves the problem of inaccurate detection and tracking of point targets when they overlap with extended targets. The specific process is as follows: Figure 3 As shown, determining whether the moving point target has entered the overlapping area with the extended target is the first step in executing this method.

[0265] The TPMB filtering method based on particle confidence propagation data association finds that when a point target and an extended target are adjacent, the information propagated by the point target will generate high and similar likelihoods with multiple measured variable nodes. When many similar values ​​appear in the likelihood matrix of the point target, it is considered that the point target has entered the overlapping region with the extended target. Therefore, multiple time steps of blurring processing are required within the overlapping region to enable subsequent tracking of the occluded point target.

[0266] Assuming the current time is k, the i-th surviving target x i The information propagated by the factor nodes is u i,j Then the particle weight is w i,j And satisfying i∈{1,…,n k|k-1 If target i propagates information u i,1 ,u i,2 ,…,u i,M There are multiple pieces of information u in the middle. i,e With the information with the highest weight If they are similar, then target i can correspond to multiple measurement points, which conforms to the property of an extended target, i.e.

[0267]

[0268] Where δ f To determine the threshold for likelihood similarity, in a spatial model where point targets and extended targets coexist, each MBM component is determined according to... Distinguish between target types; if in the i-th MBM component, parameter c p =1, meaning that at time k-1, the target is determined to be a point target, and the point target x i The information being disseminated i,j The similar likelihoods with multiple measurement points indicate that the target at that point has entered the overlapping region occluded by the extended target.

[0269] Based on the target state information of the i-th MBM component, the extended target state information that overlaps with it is located by comparing the Euclidean distances between the target positions of other MBM components. Assume the c-th MBM component is the overlapping extended target, and its target state is... The overlapping region is represented as The overlapping area moves toward the direction of the expanding overlapping target over time.

[0270] Step 2: Using the multi-model fuzzy prediction method, process the MBM components of the overlapping point targets obtained in Step 1, and output the predicted point targets. Quantity;

[0271] The specific processing steps include:

[0272] If the MBM components of overlapping point targets are updated through measurement, multiple high-weight information likelihoods will emerge, leading to multiple local hypotheses and resulting in redundant and invalid target estimation assumptions. Furthermore, fusing multiple predicted MBM components from interactive multi-model systems can disrupt the measurement update process, making it impossible to accurately track the trajectory of maneuvering point targets.

[0273] The proposed method stops measurement updates for point targets after their MBM components enter the overlapping region, and instead performs only multi-model fuzzy prediction. Assume that time k is the start time t of the fuzzy processing for the overlapping point targets. s End time t e =k+a, then in the next a consecutive time steps, the MBM component corresponding to the target point is predicted by M motion models, denoted as k+a. Keeping the existence probability of the multiple Bernoulli components constant, and assuming the overlapping point target is alive. The Gaussian distribution describing the motion information of the point target is as follows: Then the multi-model fuzzy prediction of the MBM component over a consecutive time steps within the overlapping region is:

[0274]

[0275]

[0276] in, Let be the normalization factor for the probability of the MBM component existing in the overlapping region at a time steps. t is the start time of fuzzy processing s Until the end time t e During this period, the state transition probabilities of the motion model at each time step are:

[0277]

[0278] in, Let be the motion model probability matrix of the i-th MBM component at time k. In the fuzzy prediction of a point target, it is assumed that the target motion model remains unchanged. The motion model probability of the point target... Obeying the probability matrix of the motion model when it enters the overlapping region And it will no longer be updated.

[0279] Fuzzy prediction of the motion state of a point target only retains the final time t e The multi-model prediction results show that the Bernoulli component exists at each time step with a probability. The predicted weights for the MBM components are as follows:

[0280]

[0281]

[0282] After completing the fuzzy prediction of the MBM components, the filtered prediction state output for the surviving target is given. The component output consists of M Bernoulli components predicted by different motion models.

[0283] Step 3: Based on the predictions obtained in Step 2 The component is matched and updated with the newly generated PPP component, and the updated component is output. Quantity;

[0284] The specific processing steps include:

[0285] After overlapping targets separate, based on the properties of TPMB filtering, the measurements generated by outlier targets will be detected as PPP components of newly generated targets. In this invention, the newly generated PPP components appearing in the extended region of the overlapping area are detected and matched to update and subsequently track overlapping targets.

[0286] The extended region is t e The expansion of the overlapping region of time, such as Figure 4 As shown, it is represented as Matching newly emerging targets within this area determines the location of overlapping targets at point t. e The state at any given moment.

[0287] For t e All newly generated target PPP components appearing at each time point are updated using PBP-TPMB, and the predicted Poisson distribution intensity is:

[0288]

[0289] Among all newly generated target PPP components, those located within the extended region and c p For point targets with a probability density of 1, take their posterior probability density and the fuzzy prediction. Perform matching and update. The motion model probability is used as a prior condition for the trajectory of the output point target within the overlapping region. The posterior probability density of the PPP component of the new target is obtained through the multi-model PBP-TPMB method, denoted as... Take its updated target state If the target state of this component is x p Located in the extended area Inside, it is believed That is, the target x at the overlapping point i In t e The target state at any given moment.

[0290] Step 4: Regarding the updated data obtained in Step 3 Target components, outputting the estimated target trajectory set;

[0291] The specific processing steps include:

[0292] After the above fuzzy prediction and update processing of the overlapping point targets, the predicted MBM components will be... With the corresponding new PPP component After matching, the m-th predicted component is used. As the overlapping target x i Output the state estimation results at time steps a within the overlapping region. If it does not match the PPP component, then the point target x is determined to be... i They disappeared within the overlapping area.

[0293] x i In t e The target state estimation result at time t is Component parameters For time steps k∈{t} that coincide with the extended target s ,…,t e -1}, the estimated result of the target state is The set of parameters of the target state in the component.

[0294] In summary, if target x i In t e If the target state is alive at all times, then the estimated result is: satisfy

[0295] To verify the effectiveness of the proposed multi-model PBP-TPMB maneuvering extended target tracking method based on the correlation matrix, the following experiment was conducted:

[0296] 1. Experimental Measurement Standards

[0297] To verify the effectiveness of the proposed multi-model PBP-TPMB method, the experimental section compares it with traditional CA-PMBM filtering and multi-model CA-PMBM filtering. Experiments were conducted on scenarios involving three maneuvering extended targets approaching each other, and maneuvering targets involving multiple point targets approaching extended targets. Experimental results were measured using the Generalized Optimal Submode Assignment (GOSPA). In the experimental scenarios, it was assumed that the targets had three motion modes: uniform linear motion (CV), turning motion (CT), left turn, and right turn. The corresponding motion model transition matrix and process noise are as follows:

[0298]

[0299]

[0300]

[0301] The sampling time interval T = 1 s, the standard deviation of motion noise σ = 0.01, the target detection probability Pd = 0.95, the survival probability Ps = 0.99, and the clutter follows a Poisson distribution with a mean of λ = 8. The model transition probability from motion model a to b is...

[0302]

[0303] Assume that the true target set and the estimated target set of the output are random finite sets:

[0304]

[0305] Then in each set, there is a single real target. With the estimated target The distance between them is

[0306]

[0307] Where w γ +w x +w X =1, constant c γ c x and c X These represent the maximum expected errors for measuring rate, motion state, and extended state, respectively.

[0308]

[0309] Among them, |·|, |·|2 and |·| F These are the absolute value, Euclidean norm, and Frobenius norm, respectively.

[0310] GOSPA error does not simply consider the Euclidean distance error between all targets in the real target set and the estimated target set, but rather emphasizes the accuracy of target number estimation through missed detection error and false detection error. Assume the real target set G... k The number of targets included is N s,k Estimate the target set E k Includes target number like GOSPA error is

[0311]

[0312] like The GOSPA method divides the error into three parts. For target distance error, To account for the error of missed target detection, The error is defined as the false detection target error. Here, c is the baseline distance cutoff, representing the maximum allowable positional error. Exceeding this maximum error indicates target mismatch, which is judged as either a missed detection or a false detection, and is represented by the missed or false detection target error. p is the penalty for outliers; the larger the p value, the greater the penalty for outliers. In the experimental part of this invention, p=2 and c=10 were set, and simulation experiments were conducted in scenarios with 3 maneuvering extended targets approaching each other and 5 coexisting point targets and extended targets. The experiments were performed 50 Monte Carlo (MC) simulations.

[0313] 2. Experiment and Results Analysis

[0314] The specific experiments in this application evaluated the performance of the inventive method in two experimental scenarios: a scenario in which three maneuvering extended targets approach each other and a scenario in which maneuvering point targets and extended targets coexist. The experimental results are as follows.

[0315] Experiment 1: Multiple Extended Target Scenarios

[0316] (1) Scene setting

[0317] The method of this invention focuses on solving the problem of multiple maneuvering extended targets being adjacent to each other. Therefore, there are a total of 3 maneuvering extended targets in this scenario. The monitoring area is [-100, 100] m × [-100, 100] m, and the total monitoring time is K = 100 s.

[0318] Target 1 appears at k=1s, (0m, -80m), and moves at a constant speed of 1.5m / s along the positive y-axis. At k=40s, it makes a clockwise turn with an angular velocity of θ=π / 30. At k=60s, the target returns to constant speed linear motion and disappears at k=100s. Targets 2 and 3 appear at (-40, 50)m and (50, 50)m respectively, and move at constant speeds of (1, -1)m / s and (-1, -1)m / s respectively. During their motion, the targets maneuver similarly to target 1: first, they move at a constant speed linear motion at k=1s; then, at k=40s, they make a clockwise turn with an angular velocity of θ=π / 30; finally, at k=60s, they return to constant speed linear motion until they disappear at k=100s.

[0319] In this experimental scenario, three targets simultaneously appear within the monitoring area, move together towards the center of the area, and begin maneuvering at k=40s. Then, around k=50s, they reach the center of the monitoring area, with the three targets in close proximity. The target trajectories are as follows: Figure 5 As shown.

[0320] (2) Analysis of experimental results

[0321] In this experimental scenario, the number of measurements from the three targets follows a gamma distribution, generating approximately 10 measurements from each target. The clutter rate λ at each time step... C =8, taking the actual target state and measurement every 10 time points, and the target state estimation results of three filtering methods. To demonstrate the effect of target tracking in the case of multiple extended targets in close proximity, Figure 6 Ellipses are used to represent extended targets, and the data presented include measurements generated by each target, clutter within the monitoring area, the true state of the target, and target state estimation results using different filtering methods. Figure 6 It is evident that, in the tracking scenarios of the three extended targets, the proposed multi-model PBP-PMBM filtering method has the highest estimation accuracy for the target state.

[0322] Figure 6In (a), the traditional CA-PMBM filtering method, based on clustering and data association, gradually causes tracking errors when the three targets turn (approximately k = 40 s). This method predicts the target state using a single motion model, making it prone to missing targets during maneuvers. In contrast, the IMM-CA-PMBM filtering method, which incorporates an interactive multi-model approach, can track maneuvering targets when they are widely distributed. However, in this experimental scenario, when the three extended targets move to the center of the monitoring area (approximately k = 50 s), they become adjacent or even overlap, hindering measurement segmentation and increasing the time complexity of data association, leading to inaccurate measurement clustering. Furthermore, the failure to match targets with measurements can result in false positives or false negatives. The proposed method demonstrates good tracking performance even when the three extended targets are maneuvering and adjacent to each other.

[0323] Figure 6 Figures (b) and (c) compare the tracking results of the IMM-CA-PMBM and IMM-PBP-TPMB filters when three extended targets are adjacent at k=51s. This demonstrates that the proposed method outperforms other methods in scenarios where targets are close together. Due to target maneuvering, the CA-PMBM filter misses some targets at this moment. As shown in the figures, at k=51s, the CA-PMBM method generates multiple global assumptions, resulting in an estimated number of four extended targets, exceeding the actual number of targets and causing a significant false detection error. In contrast, in the right figure, under the same target state and measurement distribution, the proposed IMM-PBP-TPMB filter accurately distinguishes the state information of the three extended targets, avoiding missed or false detections even when targets are close together, demonstrating excellent performance.

[0324] In the experimental scenario with three maneuvering extended targets, the GOSPA error of the target detection results is as follows: Figure 7 As shown. By Figure 6 A comparison of the target filtering results shows that in this experimental scenario, when the target is turning, the CA-PMBM filter misses targets, leading to increased missed detection errors and distance errors. Therefore... Figure 7 In the error results, after k=40s, the root mean square GOSPA value of the CA-PMBM filter suddenly increases. While the IMM-CA-PMBM method, due to the fusion of interactive multi-models, can accurately track the target trajectory during target maneuvering at k=40s, as the three extended targets gradually approach, the density-based measurement clustering (DBSCAN) method divides the data into numerous measurement clusters, leading to redundant global assumptions. The failure of measurement cluster matching results in significant false positive / false negative OSPA errors. Therefore, the IMM-CA-PMBM method produces a large root mean square GOSPA error after the target approaches.

[0325] The IMM-PBP-TPMB filtering method proposed in this invention can achieve tracking of adjacent maneuvering extended targets without causing target loss. When three targets are close together at k=50s, there is good data correlation effect, and the tracking effect is relatively stable and good throughout the target movement process.

[0326] Table 1 Comparison of running speeds of the methods

[0327]

[0328] Table 1 shows the running speed of each method during the scenario, comparing the running times of CA-PMBM filtering, IMM-CA-PMBM filtering, IMM-PBP-TPMB filtering without incorporating the correlation matrix, and the proposed IMM-PBP-TPMB filtering method. CA-PMBM and IMM-CA-PMBM filtering are Kalman filters based on clustering and data association methods, resulting in shorter overall running times and good tracking performance in scenarios with dispersed target distributions. However, IMM-PBP-TPMB filtering is a particle filter based on confidence propagation data association, which incurs significant computational cost due to multiple iterations of particle weight calculation. While maintaining similar tracking performance, compared to the IMM-PBP-TPMB method without incorporating the correlation matrix, the proposed method reduces the computational cost of particle likelihood calculations during target-measurement matching, thereby lowering the overall time complexity.

[0329] Experiment 2: Scenario of Coexistence of Multiple Targets and Extended Targets

[0330] (1) Scene setting

[0331] In the simulation experiment where multiple point targets and extended targets coexist, a scenario with two point targets (T1 and T2) and three extended targets (T3, T4, and T5) is considered. Table 2 shows the specific motion state information of the targets.

[0332] Table 2 Target motion information in multi-target simulation scenario

[0333]

[0334] Based on the target information described in the table, draw the complete multi-target motion trajectory as follows: Figure 8 As shown.

[0335] (2) Analysis of experimental results

[0336] The IMM-PBP-TPMB filtering method proposed in this invention is compared with the results of CA-PMBM filtering and IMM-CA-PMBM filtering. When multiple targets are relatively dispersed, the tracking effect of the three filtering results is good. When the target maneuvers, CA-PMBM filtering produces missed tracking. When multiple targets are close together, the proposed IMM-PBP-TPMB filtering method can estimate the state and motion trajectory of point targets and extended targets respectively, and has a good target tracking effect.

[0337] Figure 9 (a) Comparison of the results of IMM-CA-PMBM filtering and the proposed method in a scenario where multiple point targets and extended targets coexist. As can be seen from the figure, from 1 to 50 seconds, the extended targets T3, T4 and T5 are relatively dispersed from the point target T1, and the tracking effect is good. After that, the extended targets are close together, and the tracking effect of IMM-CA-PMBM filtering decreases. The proposed method outputs the complete trajectory of the extended targets and the point targets.

[0338] pass Figure 9 As can be clearly seen in (b) and (c), the traditional CA-PMBM filtering method based on clustering and data association uses a single motion model at k=38s, which causes missed tracking when targets T2, T3, and T4 maneuver, and only outputs the estimation results of two targets; the IMM-CA-PMBM method, which incorporates multiple models, has a good tracking effect when all targets are relatively dispersed at the current time; the IMM-PBP-TPMB filtering method proposed in this invention produces a good tracking effect when targets T1, T3, T4, and T5 are close to each other.

[0339] Figure 9 (d) and (e) show the comparison between the estimation results of the three filtering methods and the real scene when k=55s. As shown in Table 2, multiple targets gradually approach each other between 35 and 55 seconds. The CA-PMBM filter can only track the target T5 moving at a constant speed, and due to the proximity of multiple targets, it misses other point targets and extended targets. The IMM-CA-PMBM filter has too many target state estimates. In contrast, the proposed IMM-PBP-TPMB filter has a good estimation effect when multiple targets are close together, correctly estimates the number of targets, and the classification of targets is very close to the real target state, showing a very good target tracking effect.

[0340] Figure 9This paper compares the root mean square (RMS) GOSPA errors of three filtering methods in scenarios involving multiple targets and maneuvering extended targets. In multi-target scenarios, when targets are relatively dispersed, the CA-PMBM and IMM-CA-PMBM methods, based on clustering and data association, show good target state estimation performance. However, after 31 to 40 seconds when targets approach, the CA data association method suffers from increased GOSPA error due to difficulties in measurement clustering and the generation of more redundant global assumptions. In contrast, the IMM-PBP-TPMB method, based on particle confidence propagation, exhibits better tracking performance and a lower overall GOSPA error when targets approach.

[0341] The experiments described above demonstrate that the multi-model PBP-TPMB filtering method based on the correlation matrix provided in this application exhibits the best performance in estimating the state of multiple maneuvering extended targets. While estimating the state of multiple maneuvering extended targets, it can output complete trajectory information for each target from its appearance to its disappearance. To address the issue of increased error caused by the interactive output of estimated target sets by multiple motion models when a target maneuvers, the reverse smoothing method effectively reduces the error, achieving more accurate trajectory information estimation.

[0342] Some steps in the embodiments of the present invention can be implemented using software, and the corresponding software program can be stored in a readable storage medium, such as an optical disc or a hard disk.

[0343] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method of motorized extended object tracking, characterized in that, The method comprises the following steps of: in the framework of trajectory Poisson multiple Bernoulli filter (TPMB), firstly, target prediction is performed by using an interacting multiple model (IMM) method, and tracking of a maneuvering target is realized through prediction of multiple motion models; secondly, measurement data association is realized by particle belief propagation (PBP) based on an association matrix, and filter updating is performed; finally, target state is estimated, and reverse smoothing is performed, and complete target trajectory estimation results are output. The maneuvering extended target tracking method comprises the following steps of: Step one: assuming that the current time step is k, obtaining the posterior probability density of the target at the k-1 time step and a measurement set, performing multi-model prediction, and outputting the predicted target PPP components and MBM components under multiple motion models; Step two: the predicted target components obtained in step one and the measurement set are processed by using a particle belief propagation (PBP) method based on an association matrix, and the updated target posterior probability density is obtained; Step three: the updated target posterior probability density obtained in step two is processed by using the target state estimation, and an estimated trajectory set is obtained; Step four: the target state estimation set obtained in step three is processed by using a reverse smoothing method, and finally, a smoothed trajectory set is obtained; For the point target that is adjacent to or coincides with the extended target, only multi-model prediction is performed without updating, and after the target is separated, the position of the coincident point target is determined by matching the multi-model prediction (MBM) component and the new PPP component in the extended region, so that subsequent target tracking is realized, and the specific process comprises the following steps of: Step 1: assuming that the current time step is k, obtaining the posterior probability density of the target at the k-1 time step and a measurement set, determining whether the point target enters the coincident region of the extended target, and outputting the MBM component of the coincident point target; Step 2: using a multi-model fuzzy prediction method, processing the coincident point target MBM component obtained in step 1 to output a predicted point target component; Step 3: Prediction for the step 2 acquired prediction component, and the new PPP component is matched and updated, and the updated component is output Step 4: For the updated target components obtained in Step 3, output an estimated set of target trajectories. target components, output an estimated set of target trajectories.

2. The motorized dilation target tracking method of claim 1, wherein, The PPP prediction intensity of the target that is not detected in the monitoring region at the k time step in step one is as follows: wherein, and respectively represent the number of sampling particles corresponding to the potential target component and the nascent target component, in which the particle weight and are calculated as follows: The state transition mode of the target is as follows: Wherein, F(·) is the state transition equation expression of the uniform straight line motion; The process of the MBM component prediction comprises the following steps of: For the detected surviving target, the target state of the i-th MBM component at the k time step is represented as follows: The multi-model target state prediction calculation mode is as follows: where M is the number of motion models, is the target state transition matrix of the i-th target component under the n-th motion model at time k, is the transition probability between different motion models; The target component existence probability r and the particle weighted sum w of the surviving target are represented as follows: The target posterior density at k-1 time is taken as a potential target to operate, thereby ensuring the integrity of the trajectory; the number of particles meets and the survival target Since the target at the previous and subsequent time belongs to the same trajectory, it meets If i.e. considering the target alive, the target state at time k is predicted Join the trajectory set in: Among them, the predicted trajectory set During the prediction process, birth intensity is used as a means of prediction. The motion model F(·) performs particle sampling on the new target, and the motion model is used to perform particle sampling on the new target. Perform particle sampling on maneuvering targets. Let be the transition probability of different motion models transforming into the nth model at time k. Given the nth target motion state transition matrix, then under a total of M motion model state predictions, the following is generated: One predicted particle; At the k time step, considering the target extinction condition, the particle weight changes, all particles are copied at the next time step, and the weight is updated according to the survival probability; if it is determined that the target is extinct, the MBM component with an existence probability lower than a target survival threshold is reserved, and the multi-model prediction thereof is pruned, and only the particle generated by the single motion model prediction is reserved; If the target is extinct at the k time step, the target posterior information at the k-1 time step is reserved to the trajectory set: wherein, is the set of trajectories Posterior density of single target state at time k-1.

3. The motorized dilation target tracking method of claim 2, wherein, The step two comprises the following steps of: (1) particle trajectory initialization; In the particle belief propagation method, the optimization of the propagation information is realized through P iterations, so that the confidence of all nodes converges, and the label of each node at this time is the optimal label; The Poisson intensity is expressed as in the form of a set of particles; In the p = 1st iteration, the variable nodes of the trajectory propagate information s k to the factor nodes represented by a set of weighted particles ; The update of the new target and the potential target and the surviving target respectively considers whether the target is alive at the current time step; (2) measurement information evaluation; Computing individual factor nodes s k Vector-measured variable nodes Transmitted information Factor nodes s k Representation of the information transfer process of surviving trajectories with all measurements, In p In each iteration, information propagation between each target variable node and measurement variable node is implemented according to the factor graph formula. The correlation matrix is introduced, and the information within the gate is calculated when calculating the correlation likelihood matrix by setting a gating threshold between the particle state and the measurement information. The particle likelihood calculation method generated by the target is: Where d(z, x) is the Euclidean distance between the surviving target generated particle and the existing measurement position, and δ is the gating threshold of the particle and measurement correlation degree. The data association mode and the measurement update mode are both realized by calculating the transfer information, according to The target state update is expressed as After one iteration, the particle weights converge to values close to the true state of the target, and in the subsequent iterations, each variable node to factor nodes s k propagated messages all represent unnormalized Bernoulli component densities, and other parameters such as particle weights and messages, when i e {1,..., n k|k-1}, j e {1,..., m k}, i.e., for each predicted surviving target, generate particles and update existing measurements: when i ∈ {n k|k-1 + 1,..., n k|k} and j ∈ {1,..., i - n k|k-1}, i.e. for the update of potential targets and measurements, since the hypothesis of multiple motion models is removed when a target is declared to be killed, here the particles generated by the single motion model prediction process are only updated with existing measurements, then the propagated information and the particle weights are: (3) Confidence calculation The information and particle weights computed by the above steps are iterated multiple times, and the results converge to values close to the true target state, and the confidence of the target state in each MBM component are represented by the following Bernoulli random set: Considering the calculation of particle weight and Bernoulli component probability in subsequent iterations to ensure the effectiveness of the track confidence, the particle weight is finally normalized.

4. The motorized dilation target tracking method of claim 3, wherein, The step three includes: The updated target posterior probability density is stored in the form of MBM components, and the MBM components with a probability higher than a threshold are selected to estimate the target state at the current k time from a set of weighted particle collection, which is the output target trajectory, denoted as: The estimation of the new target is realized by a Poisson point process, and the output is a set of generated trajectories of the new target, denoted as X b = (t b , x 1:v ), where the birth time is t b = k, and the trajectory length v = 1. For the unknown target trajectory, there is no need to perform particle sampling in the prediction step of the undetected target; After outputting the estimated target trajectory set at each time step, the redundant MBM components are pruned and resampled to avoid the problem of particle sample degradation.

5. The motorized dilation target tracking method of claim 4, wherein, The step four includes: After outputting the filtered estimated target trajectory set, the estimated particle state can be used for backward smoothing; each trajectory is smoothed by backward particle smoothing from the extinction time e to the target appearance time t, and the target state at time k can be approximately calculated according to the weighted particle set obtained by filtering estimation, and the target marginal smoothing distribution is: where and are the filtered density of targets at time k and the predicted density of the forward filter, respectively, for a set of tracks k, all targets are monitored for K time steps, with measurement information y 1:K backward smoothing estimation is performed.

6. The motorized dilation target tracking method of claim 5, wherein, The step 1 includes: Assume that the current is k time, the i-th surviving target x i The factor node propagated information u i,j , then the particle weight w i,j , and satisfy i∈{1,…,n k|k-1} If the target i spreads the information u i,1 , i,2 , …, u i,M , i,e , Among them, there are multiple information u Close to the highest weight information, target i can correspond to multiple measurement points, in line with the nature of the extended target, that is: where δ r is the threshold value for determining the likelihood proximity, in the spatial model where point targets and extended targets coexist, each MBM component is according to distinguishing target types, if the parameter c p = 1, i.e. the target is determined as a point target at the k-1 moment, the point target x i propagated information u i,j and multiple measurement points have generated similar likelihoods, indicating that the point target has entered the overlapping area blocked by the extended target.

7. The motorized dilation target tracking method of claim 6, wherein, The step 2 includes: After the MBM component of the point target enters the overlapping area, the measurement update is stopped, and only the multi-model fuzzy prediction is performed; Assume that the current k moment is the start time t s of the coincident point target blur processing e , and the end time t e =k+a, then in the next a consecutive time steps, the MBM component corresponding to the point target is predicted by M motion models, denoted as Keeping the existence probability of the multi-Bernoulli components unchanged, and assuming that the coalesced point-mass survives, the Gaussian distribution describing the motion information of the point-mass is The multi-model fuzzy prediction of the MBM component in the coalesced region for a consecutive a time steps is wherein, is a normalization factor for the probability of presence of the MBM component in the a time steps of the coincidence region, is the start time of the blurring process t s is the end time of the blurring process t e is the state transition probability of the motion model at each time instant during the blurring process. wherein, is the motion model probability matrix of the ith MBM component at time k, in the fuzzy prediction of point targets, it is assumed that the motion model of the target does not change, and the motion model probability of the point target obeys the motion model probability matrix and is no longer updated; The fuzzy prediction of the motion state of the point target only retains the multi-model prediction result at the end time t e The existence probability of the Bernoulli component at each time step and the weight prediction of the MBM component are: After the completion of the fuzzy prediction of the MBM component, the filtered prediction state output of the surviving point targets, The component outputs M different motion model predictions of the multinomial Bernoulli component.

8. The motorized dilation target tracking method of claim 7, wherein, The step 3 includes: By detecting and matching the new-born PPP component appearing in the extended area of the overlapping area, the update and subsequent tracking of the overlapping point target are realized; The expansion of the region of coincidence at time t is denoted as e The expansion of the region of coincidence at time t is denoted as The new target is matched within this region, and the state of the coincidence point target at time t is determined e The expansion of the region of coincidence at time t is denoted as For t e PBP-TPMB update is performed for all new target PPP components emerging at time t, with the predicted Poisson distribution intensity: wherein represents the desired number of potential targets, L b is the number of particles representing newly born targets; Among all the new-born target PPP components, the point targets located in the extended area and with c p = 1 take their posterior probability density and the fuzzy predicted are matched, and the motion model probability of is updated as the prior condition of the trajectory of the output point target in the overlap area; The new target PPP component posterior probability density is obtained by the multi-model PBP-TPMB method, and is denoted as The updated target state is taken If the target state x p of the component is located in the extended area , it is considered that The target x i at the time t e is the coincidence point.

9. The motorized dilation target tracking method of claim 8, wherein, The step 4 includes: The predicted MBM component is matched with the corresponding newborn PPP component After matching, the matched mth prediction component is used as the coincidence point target x i The state estimation output result in the coincidence area for a time step, if not matched with the PPP component, is determined as the point target x i is eliminated in the coincidence area; x i At time instant t e , the target state estimate is The parameter of the component For time steps k e {t s ,…,t e -1} coinciding with the extended target, the estimate of the target state is The parameter set of the target state in the component In summary, if the target x i At time t e Survives, the estimate of the target state is Satisfies

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