CN116630370A - Multi-model PBP-TPMB maneuver expansion target tracking method - Google Patents

Abstract

The invention discloses a multi-model PBP-TPMB maneuver expansion target tracking method based on an incidence matrix, and belongs to the field of target tracking. The method comprises the following steps: firstly, on the basis of a particle confidence propagation (PBP) data association mode, likelihood of traversing all measurement and targets is avoided by integrating an association matrix, calculation amount of data association is reduced, secondly, multi-target tracking during point target shielding is realized under a scene that a maneuvering point target and an expansion target are mutually close by a fuzzy processing method, and finally, complete track information during target movement is reserved by TPMB filtering based on a track set and integrated with reverse smoothing, so that a target track estimation set output by an algorithm is closer to a real target. The invention solves the problem of tracking maneuvering expansion targets in the close environment by filtering the multi-model PBP-TPMB, and achieves the effect of effectively tracking maneuvering point targets and expansion targets.

Description

Multi-model PBP-TPMB maneuver expansion target tracking method

Technical Field

The invention relates to a multi-model PBP-TPMB maneuvering expansion target tracking method, belonging to the field of target detection and tracking.

Background

The target tracking technology is widely applied along with the continuous development of modern software and hardware technologies. For example, in service technologies such as take-out delivery, sharing of bicycles, navigation positioning, etc., the most critical task is to obtain vehicle position information in real time through sensors, thereby planning an optimal driving route, etc. However, in order to obtain an optimal distribution route, not only receiving a signal returned from a mobile device by a satellite, a base station, or the like, but also high performance depending on a target tracking algorithm is required. The target tracking technology plays an irreplaceable role in civil field and military field, and has wide research space and development prospect in the fields of missile defense, underwater detection and tracking, automatic driving, industrial robot and the like.

Multi-target tracking (Multiple Target Tracking, MTT) refers to the process in which a sensor obtains noisy and unordered measurement sequences within a monitored area, iteratively estimates the state of a current plurality of targets, thereby forming a plurality of time-step target motion trajectories. Unlike single-target tracking, multi-target tracking needs to solve the problems of noise and clutter interference, filtering problems such as target omission and new generation, and the like, and also needs to consider the problems of reduced tracking precision caused by target maneuver or unclear target measurement distinction when a plurality of targets approach and cross, and the problems of target track maintenance and the like.

The target measurement data with clutter is collected from the monitoring area by using various sensors such as radar, sonar and infrared, and the targets can be divided into point targets and expanded targets according to the size of the targets and the number of returned measurement of the sensors. Unlike image targets, which have characteristic information, radar targets describe target information from measurement points. If the target size is small compared to the sensor resolution, it is often considered a point target, in which the target state usually contains motion information, such as position and velocity, and one point target at the same time produces at most one measurement. The point object only generates a single measurement, and cannot describe characteristic information such as the shape of the object, while the extended object is defined as an object which generates a plurality of measurements within the shape range of the object at each moment, and the object state generally comprises motion information and object shape range information. The problem that the point target tracking algorithm cannot accurately describe the shape of the target is well solved by the expanded target tracking technology.

In the moving process of the target, the original moving state changes, and the target with the changed moving mode is called a maneuvering target. For example, vehicles at the crossroad can be changed from uniform motion to motion states such as acceleration/deceleration or turning, or the unmanned aerial vehicle can be changed from motion states such as climbing or diving to stable uniform motion in the flight process. In the maneuvering target tracking problem, establishing a proper motion model for the target has extremely important significance for timely and accurately tracking the target, and the degree of adaptation of the establishment of the motion model and the real motion condition of the target directly influences the tracking effect of an algorithm.

The PMBM filtering algorithm fuses the advantages of the poisson random set and the bernoulli random set based on a Multi-hypothesis tracking concept, detects unknown targets by a poisson point process (Poisson Point Process, PPP) and detects surviving targets by a Multi-Bernoulli Mixture, MBM process. Compared to CPHD filtering and GLMB filtering, PMBM filtering estimates the centroid motion state of the target and the number of targets more accurately. The data association method of the filtering updating step is a two-step processing data association method: clustering and assignment (Clustering and Assignment, C & a). The method comprises the steps of firstly clustering the measurement based on factors such as density or distance, and secondly, realizing the corresponding relation between each measurement partition, namely the measurement cluster and the target through an effective allocation method. These C & a based data correlation methods tend to have good tracking effect with a more distributed distribution of targets, but when targets are closely adjacent or overlap, the target tracking performance is degraded.

PMBM filtering has a good effect on the estimation of the number of moving objects and the state of the objects, but cannot preserve the complete object track information. For the problem of maintaining a target track, the Xia and other scholars propose a Trajectory-PMBM filtering method for expanding the target in 2019, so that the PMBM filtering method for simultaneously estimating the target states and track information of multiple expanded targets is realized, the team of the PMBM filtering method proposes Trajectory-PMB filtering in 2020, PMB approximate estimation is performed through KL divergence minimization, and multi-target track estimation and maintenance are realized with lower calculation complexity.

Under the framework of a track Poisson Bernoulli (Trajectory Poisson Multi-Bernoulli, TPMB) filtering method, data association is realized by a particle confidence propagation method, and the edge association probability and Bernoulli density in a filtering updating step can be obtained, so that PMB approximation is realized, global assumption with too low weight is intercepted, and the calculation amount of the data association is reduced. The prediction step of PMBM filtering retains only one globally hypothesized mixture component, thereby approximating the estimated target state and reducing the computational effort. The updating step of the TPMB filtering is realized by executing Bayesian updating, the Bayesian updating generates PMBM distribution, then the edge density of the target state set is calculated by a PMB approximation mode, and the uncertainty of the global assumption is subjected to edge processing. For the implementation process of PMB approximation, first, a global hypothesis with low weight and negligible weight is pruned by a clustering and allocation method or a sampling-based method, and then, the edge association probability is approximately calculated by enumerating the pruned global hypothesis.

Both the multi-hypothesis tracking based C & a approach and the sampling based approach can avoid enumerating all data-associated hypotheses by pruning low-weight hypotheses. But as such, the performance of target tracking will be limited in cases where the data association uncertainty is high. One more efficient method of data correlation in extended target tracking that avoids enumerating all local correlation hypotheses is to directly calculate the posterior density probability of marginal multi-targets, where uncertainty of the data correlation will be marginalized. However, in the above method, for the situation that the targets are close to each other, since the metrology clustering generates more partitions, the tracking performance of the targets is reduced, and even the targets are close to or coincide with each other, the tracking is missed.

Disclosure of Invention

In order to solve the problem that tracking precision of the existing multi-mechanical expansion target is insufficient under the condition of close proximity, the invention provides a multi-model PBP-TPMB mechanical expansion target tracking method, which comprises the following steps:

under the framework of the TPMB (thermoplastic polyurethane) filtering of the Poisson Duobnoulli, firstly, performing target prediction by adopting an interactive multi-model method IMM, and realizing tracking of maneuvering targets through prediction of various motion models; secondly, realizing measurement data association by spreading PBP based on particle confidence coefficient of the association matrix, and carrying out filtering update; finally, estimating the target state, performing reverse smoothing, and outputting a complete target track estimation result;

the maneuvering extension target tracking method comprises the following steps:

step one: assuming the current time step is k, acquiring posterior probability density and a measurement set of a target at the moment k-1, carrying out multi-model prediction, and outputting predicted target PPP components and MBM components under a plurality of motion models;

step two: adopting a particle confidence propagation (PBP) method based on an incidence matrix to process the predicted target component and the measurement set obtained in the step one, and obtaining updated target posterior probability density;

step three: aiming at the updated target posterior probability density obtained in the second step, processing the updated target posterior probability density by utilizing the target state estimation to obtain an estimated track set;

Step four: and (3) processing the target state estimation set obtained in the step (III) by using a reverse smoothing method to finally obtain a smoothed track set.

Optionally, in the first step, the PPP prediction strength of the undetected target in the monitored region at time k is:

wherein, and->Respectively representing the sampling particle numbers corresponding to the potential target component and the new target component, wherein the particle weight is +.>And->The calculation is as follows:

the state transition mode of the target is as follows:

wherein F (-) is a state transfer equation expression of uniform linear motion;

the MBM component prediction process includes:

for detected surviving targets, the target state of the ith MBM component at time k is expressed as:

the multi-model target state prediction calculation mode is as follows:

where M is the number of motion models,for the target state transition matrix under the ith target component nth motion model at k time,/th>Is a conversion outline between different motion modelsA rate;

the particle weighted sum w of the target component existence probability r and the surviving target is expressed as:

the posterior density of the target at the moment k-1 is used as a potential target to operate, so that the integrity of the track is ensured; the particle number satisfies+.>Since the targets belong to the same track before and after the moment, the +. >

If it isI.e. predicting the target state at time k, taking into account the situation of target survival +.>Add track set->In (a):

wherein the set of predicted trajectoriesIn the prediction process, the birth intensity is usedAnd a motion model F (-) for particle sampling of the nascent object by means of the motion model +.>Particle sampling of maneuver target->Transition probability for converting different motion models into nth model at k moment, +.>For the nth target motion state transition matrix, generating +.>A plurality of predicted particles;

at the moment k, considering the target extinction condition, the weight of the particles changes, copying all particles at the next moment, and updating the weight according to the survival probability; if the target is judged to die, the MBM component with the existence probability lower than the target survival threshold value is reserved, the multi-model prediction is pruned, and only particles generated by single motion model prediction are reserved;

if the target at the moment k is eliminated, retaining posterior information of the target at the moment k-1 to a track set:

wherein, is track set->Posterior density of single target states at time k-1.

Optionally, the second step includes:

(1) Initializing particle trajectories;

in the particle confidence propagation method, propagation information is optimized through P iterations, so that the confidence of all nodes is converged, and the label of each node is the optimal label;

Poisson strength is expressed asIs a collection of particles;

in the p=1 th iteration, the traceVariable node +.>Directional factor node _k sInformation of propagation->Is made up of a set of weighted particles->A representation;

updating the new and potential targets respectively to consider whether the target survives at the current moment;

(2) Evaluating measurement information;

calculate eachFactor node _k sVariable node for direction measurementInformation transferred->Factor node _k sInformation transfer process representing the survival trace and all measurements,

in P epsilon {1, …, P } iterations, information transmission between each target variable node and each measurement variable node is realized according to a factor graph formula;

introducing an association matrix, setting a gating threshold between the particle state and the measurement information, and calculating information in the gating when calculating the association likelihood matrix, wherein the particle likelihood calculation mode generated by the target is as follows:

where d (z, x) is the Euclidean distance between the particle generated by the surviving target and the existing measurement location, and δ is the gating threshold of the association of the particle with the measurement;

the data association mode and the measurement updating mode are realized by calculating and transmitting information according toThe target state update is denoted +.>

After one iteration is completed, the particlesThe weights are converged to values close to the real state of the target, and each variable node is used for the follow-up iteration process Directional factor node _k sInformation of propagation->All represent the un-normalized Bernoulli component density, other propagation information and particle weight parameters, when i.e {1, …, n _k|k-1 }，j∈{1,…,m _k Generating an update of the particle and existing measurements for each predicted surviving target:

when i epsilon { n } _k|k-1 +1,…,n _k|k }，j∈{1,…,i-n _k|k-1 At the time of }, i.e. for potential target and measurement updates, since the assumption of multiple motion models is removed when the target is determined to be dead, information is propagated by updating only particles generated by a single motion model prediction process with existing measurementsThe weight of the particles is as follows:

(3) Confidence calculation

Information sum calculated by multiple iterations of the above stepsParticle weight, the result of which converges to a value close to the true target state, confidence of the target state in each MBM componentCan be represented by the following bernoulli random set:

and calculating the particle weight and the Bernoulli component existence probability in the subsequent iteration to ensure the effectiveness of the track confidence, and finally carrying out particle weight normalization.

Optionally, the third step includes:

the updated target posterior probability density is stored in the form of MBM components, MBM components with existence probability higher than a threshold value are selected, the current k-moment target state is estimated from a group of weighted particle sets, and the current k-moment target state is taken as an output target track, and the output target track is expressed as follows:

Estimation of a new target is achieved through a poisson point process, the output new target generates a track set and tracks X are recorded ^b ＝(t ^b ,x ^1:v ) Wherein the birth time is t ^b For an unknown target trajectory, no particle sampling in the step of predicting the undetected target is required;

after each time step of outputting the estimated target trajectory set, the redundant MBM components are pruned and resampled to avoid the particle sample degradation problem.

Optionally, the fourth step includes:

after outputting the filtered set of estimated target trajectories, inverse smoothing may be performed by the estimated particle states. And (3) performing reverse particle smoothing with the length v on each track from the extinction moment e to the target occurrence moment t, wherein the target state at the moment k can be approximately calculated according to a weighted particle set obtained by filtering estimation, and the target marginal smoothing distribution is as follows:

wherein the method comprises the steps ofAnd->The filtering density and the forward filtering prediction density of the targets at the moment K of the track set are respectively obtained, all targets are monitored in K time steps, and the measurement information y appearing in all time steps is used for monitoring _1:k And performing reverse smoothing estimation.

Optionally, for a point target that is close to or coincides with the extended target, only multi-model prediction is performed without updating, after the target is separated, the position of the coincident point target is determined by matching the multi-model prediction MBM component with the new PPP component in the extended region, so as to realize subsequent target tracking, which specifically includes:

Step 1: assuming the current time step is k, acquiring posterior probability density and a measurement set of a target at the moment k-1, judging whether the point target enters a superposition area with the expansion target, and outputting an MBM component of the superposition point target;

step 2: processing the coincident point target MBM component obtained in the first step by adopting a multimode fuzzy prediction method, and outputting a predicted point targetA component;

step 3: prediction for step two acquisitionComponent, which is updated by matching with the nascent PPP component, and outputs the updated +.>A component;

step 4: updated for step three acquisitionAnd outputting the estimated target track set by the target component.

Optionally, the step 1 includes:

assuming that the current time is k, the ith survival target x _i The information propagated by the factor node of (a) is u _i,j Then the particle weight is w _i,j And meets i epsilon {1, …, n _k|k-1 }；

If the information u propagated by the target i _i,1 ,u _i,2 ,…,u _i,M In which there are a plurality of information u _i,e Information with highest weightSimilarly, the target i can correspond to a plurality of measuring points, and accords with the property of the expansion target, namely:

wherein delta _f To determine threshold values for likelihood closeness, each MBM component is based on the spatial model in which the point object and the extension object coexistDifferentiating the object type, if in the ith MBM component, the parameter c ^p =1, i.e. the target at time k-1 is determined to be a point target, point target x _i Information u propagated _i,j And (3) generating similar likelihood with a plurality of measuring points, wherein the likelihood indicates that the point target enters a superposition area shielded by the expansion target.

Optionally, the step 2 includes:

after the MBM component of the point target enters the overlapping area, stopping measuring and updating the point target, and only performing multi-mode fuzzy prediction;

assume that the current k moment is the starting time t of fuzzy processing of the point target _s End time t _e In the next consecutive a time steps, the MBM component corresponding to the point object is predicted by M motion models, denoted as

Keeping the existence probability of the multiple Bernoulli components unchanged and assuming that the coincident point target survives, the Gaussian distribution of the point target describing motion information is as followsThe multi-mode fuzzy prediction of the MBM component for a succession of a time steps within the overlap region is:

wherein, for the MBM component to have a normalization factor of probability in a time steps of the coincidence region,for the start time t of the blurring process _s To the end time t _e During this period, the state transition probability of the motion model at each moment:

wherein, for the motion model probability matrix of the ith MBM component at the k moment, in the fuzzy prediction of a point target, the target motion model is assumed not to change, and the point target is assumed to be Motion model probability +.>Motion model probability matrix obeying when entering the coincidence region>And is not updated;

the fuzzy prediction of the motion state of the point target only keeps the end time t _e The probability of the presence of Bernoulli components per time stepAnd the weights of the MBM components are predicted as:

after the fuzzy prediction of the MBM component is completed, the filtered prediction state of the survival point target is output,the components output M different motion model predicted bernoulli components.

Optionally, the step 3 includes:

the new PPP component appearing in the expansion area of the overlapping area is detected and matched, so that the update and the subsequent tracking of the overlapping point target are realized;

the expansion area is t _e The expansion of the overlapping area of time instants is denoted asMatching the nascent targets in the region to determine the coincident point targets at t _e A state of time;

for t _e Updating the PBP-TPMB by all newly generated target PPP components appearing at the moment, wherein the predicted Poisson distribution intensity is as follows:

wherein the method comprises the steps ofRepresenting the desired number of potential targets, L ^b To represent the number of particles of the nascent object;

in all nascent target PPP components, located within the extension region and c ^p Point object of =1, take the posterior probability density and fuzzy prediction Matching and updating->As a priori condition of the trajectory of the output point target in the coincident region;

the posterior probability density of the new target PPP component is obtained through a multi-model PBP-TPMB method and is recorded asGet its updated target state +.>If the target state x of the component ^p Is located in the expansion area->In the interior, consider->I.e. is the coincident point target x ⁱ At t _e A target state of time;

optionally, the step 4 includes:

will be pre-madeMeasurement of MBM componentAnd corresponding nascent PPP component->After matching, the m-th predictive component of the match is used +.>As coincident point target x ⁱ Outputting a state estimation result of a time steps in the overlapping area, and judging a point target x if the state estimation result is not matched with the PPP component ⁱ Death in the coincident region;

x ⁱ at t _e The estimation result of the target state at the moment is thatParameters of the component->For time steps k e { t } coincident with the expansion target _s ,…,t _e -1, the estimation result of the target state is +.>In the component, the parameter set of the target state

To sum up, if target x ⁱ At t _e The time survives, the estimation result of the target state isSatisfy->

The invention has the beneficial effects that:

(1) On the basis of TPMB filtering, the invention integrates an interactive multi-model algorithm to realize maneuvering target tracking, and provides a factor graph representation of an extended target posterior variable and an associated variable so as to realize data association of particle confidence propagation;

(2) Under the multi-model TPMB filtering framework of the maneuvering target, the confidence coefficient propagation based on the incidence matrix is operated on the constructed factor graph, so that a message transmission equation based on a random finite set is derived, the particle filtering experiment of IMM-PBP-TPMB is realized, and the effectiveness of the method for tracking the immediately adjacent multi-maneuvering expansion target is proved;

(3) The invention provides a mode of blurring processing of the overlapping area aiming at the overlapping condition of the point target and the expansion target, and solves the problem that the point target cannot be effectively tracked when being shielded by the expansion target.

The problem that the clustering and distribution data association mode is difficult to effectively track the adjacent maneuvering expansion targets is solved through the data association mode based on the particle confidence propagation of the association matrix, the effect of effectively tracking a plurality of adjacent maneuvering expansion targets is achieved, and the detection and tracking of the adjacent maneuvering expansion targets and the expansion targets are further achieved under the scene that the point targets and the expansion targets coexist.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

Fig. 1 is a flow chart of a PMBM filtering algorithm.

FIG. 2 is a factor graph representation of a confidence propagation process.

FIG. 3 is a schematic flow chart of the method of the application.

Fig. 4 is a schematic diagram of the overlap region and the blur region.

Fig. 5 is a real track diagram of a target of a multi-extended target experimental scenario.

FIG. 6 is a graph comparing the tracking results of multiple extended targets experimental scenes.

FIG. 7 is a comparison of root mean square GOSPA error for multiple extended target experiments.

Fig. 8 is a real track of a scene of a multi-point target and an extended target.

FIG. 9 is a graph comparing the tracking results of a multi-point target and an extended target.

Fig. 10 is a root mean square GOSPA error comparison of a multi-point target and an extended target scene.

Detailed Description

For the purpose of making the objects, technical solutions and advantages of the present application more apparent, the embodiments of the present application will be described in further detail with reference to the accompanying drawings.

First, the basic knowledge related to the present application is described as follows:

1. PMBM filtering principle

In the target tracking problem, at each moment, the positions and the numbers of the targets change due to the states of new generation, disappearance, derivation, continuous survival and the like of the targets, and the measurement obtained by the sensor at each moment also changes simultaneously, so that uncertainty exists. Similar to point-target poisson-multiple-bernoulli hybrid filtering (PMBM), the extended-target PMBM model is also based on a multi-hypothesis tracking concept, consisting of a poisson-point process (PPP) random finite set and a multiple-bernoulli hybrid (MBM) random finite set. The overall flow of extended target tracking through PMBM filtering algorithm is shown in fig. 1.

Compared with an expansion target represented by GGIW density in the filtering recursion process, the point target is filtered through Gaussian density without considering information such as target expansion state, but the point target is different from the expansion target in the measurement generation model and the filtering recursion process. The measurement values of the point target and the expansion target are generated by selecting different measurement likelihood functions f (z|x), respectively.

The PMBM model consists of two independent RFS models, one of which is PPP RFS, describing the distribution of undetected potential targets, i.e. the set of new targets that may occur in the monitored area, and the other of which is MBM RFS, describing the presenceDistribution of living targets, that is, targets that are detected at least once within a monitoring time. Assume thatRepresenting the set of targets that were not detected, +.>Representing the target set detected at least once, then the complete target set at time k +.>The PMBM filtering process for the target set is expressed as:

wherein, representing the prior probability density, lambda, of undetected targets _k|k-1 (x) Poisson intensity of potential target x, which is not currently detected,/>A mixed representation of bernoulli showing the survival targets at time k.

PMBM filtering performs data correlation through multi-hypothesis ideas at PMBM probability density f _k|k-1 (X _k ) In the presence of n _k|k-1 A plurality of Bernoulli components, each Bernoulli component being at most likely to be generated A local hypothesis corresponding to the measurement set. Selecting for each Bernoulli component the corresponding local hypothesis +.>Get a global hypothesis +.> Wherein A is _k|k-1 A set of all global hypotheses for time k.

Each global hypothesis represents a type of bernoulli distribution, then corresponding to local hypothesis a ⁱ The i-th bernoulli component density of (c) is:

wherein, is the probability of the presence of Bernoulli components, +.>Is the Bernoulli component probability distribution, the global assumption a weights +.>The weight is proportional to n _k|k-1 Local hypothesis a ⁱ The product of the weights and->Multiple global hypotheses may occur during the data correlation process because multiple metrology clustering results may be generated by distance-based clustering algorithms when objects are in close proximity in the presence of multiple extended objects.

The PMBM filtering algorithm realizes target tracking through two steps of prediction and updating.

(1) PMBM prediction

Assume that the probability density of the multi-target state at the moment k-1 is f _k|k-1 (X _k ) The predicted probability density still consists of a poisson Random Finite Set (RFS) and an MBM random finite set. Wherein the predicted intensity of poisson RFS is

λ _k|k-1 (x)＝λ _b (x)+∫p _s (y)f _k|k-1 (x|y)λ _k-1 (y)dy

Wherein p is _s (. Lambda.) is the target survival probability _k-1 (. Cndot.) is the posterior intensity of the poisson RFS target at time k-1.

For the predicted intensity of MBM RFS, assume that the posterior parameters of the target at time k-1 are expressed as And->The corresponding predicted intensity is expressed as

(2) PMBM update

The PMBM filtering form is the same as the multi-objective Bayesian filtering, and the joint probability density of the PMBM filtering at the current k moment is expressed as

Wherein g ^p (. Cndot. Cndot.). Cndot.and g ^mbm (. |.) likelihood functions of Poisson RFS and MBM RFS, respectively, can beSimplified into

2. TPMB filtering principle

Unlike the PMBM filtering method based on the target set, the TPMB filtering indicates the target component including the birth and death moments and the target states during the target component, so that the complete track information of the target can be effectively recorded. By passing throughAndthe method respectively represents a random finite set of target states and a random finite set of measurement at the moment k. Wherein the target x _k Single object state information such as motion information (position and velocity), and expansion state information (shape and size) if the object is an expansion object. z _1:k Is the measurement sequence at time k and all times before. The track information of the object is a finite sequence of states of the object in continuous time steps, expressed as

X＝(t,x ^1:v )

Wherein t is the initial time of the track, v is the time length from the track movement to the current moment, and x ^1:v ＝(x ¹ …, x) is a finite sequence of target states. The variable (t, v) belonging to set I _(k) = { (t, v) < 0.ltoreq.t.ltoreq.k, 1.ltoreq.v.ltoreq.k-t+1 }. Thus, the single track space representation containing the complete time information and the target state information at time k is represented as

Wherein the method comprises the steps ofFor the intersection union operation, the formula describes the target x at time k _k Birth time, survival time, and target status per moment. />

The new generation target appearing in the monitoring area at the moment k is determined as the birth intensityIs detected for the poisson point process of the detected target x _k-1 Which is expressed in terms of survival probability P ^S (x _k-1 ) Markov transition Density g _k (x _k |x _k-1 ) Evolution, the process being independent of other targets within the monitored area; otherwise the target track is in 1-P ^S (x _k-1 ) Probability of death of (c). The survival probability in the model determines whether the track is ended at the current time step k, and the eliminated track can be reserved as a potential target component in consideration of the conditions of shielding and the like of the target. To ensure track maintenance effectiveness, all target tracks remain in the track set regardless of whether the track has ended. The bernoulli RFS transfer density of the single target trajectory is:

f _k|k-1 ＝π ^x (x _t:e |t,e,x _t′:e′ )×π ^e (e|t,x _t′:e′ )Δ _t′ (t)

wherein delta (·) is the kronecker delta function.

The multi-target track set TPMB component densities including the undetected target and the detected target are:

wherein A is _k|k-1 Is a global assumption that is generated from the measurement set and all MBM components.

3. Belief propagation principle

For methods that require complex global functions that handle many variables, a given function may be decomposed into products of multiple local functions, each of which depends on a subset of the variables. Such decomposition may be represented by a bipartite graph, referred to as a factor graph. The particle belief propagation method is a message passing method described on a factor graph that follows a simple calculation rule that can accurately or approximately calculate various edge functions derived from a global function.

Measurement-oriented factor nodes are expressed asWherein j is {1, …, m _k },If and only if the j-th measurement +.>May be associated with the ith Bernoulli component, < >>This is true. I e {1, …, n corresponding to surviving targets _k|k-1 The Bernoulli component and all m in the current time step _k The association of individual measurements may be represented by a messaging process between the factor node and the variable node. Based on the local assumption of the Bernoulli component, the j-th measurement is known>Can not be combined with i E { n _k|k-1 +1,…,n _k|k-1 Bernoulli component of +j-1}, then variable node +.>Satisfy->{0,1,…,n _k|k-1 ,n _k|k-1 +j,…,n _k|k }. Then the target state set is associated with the measurement-oriented directionThe combined posterior of the amounts is

Wherein, to ∈>Target posterior probability density obtained by poisson point procedure,/>And->Confidence of the respective surviving and potential targets, prior information predicted by the targetAnd (5) calculating to obtain the product. N and M are the number of targets and measurements, respectively.

FIG. 2 illustrates the belief propagation relationship of information between each factor node of a target state set and a measurement set, propagating informationAnd->Obtained from the following formula.

Wherein r is the probability of the presence of Bernoulli components,a likelihood of the measurement is generated for the target.

Embodiment one:

the embodiment provides a multi-model PBP-TPMB maneuver expansion target tracking method based on an incidence matrix, which comprises the following steps: under the framework of the track Poisson Bernoulli filtering (TPMB), firstly, an interactive multi-model method (IMM) is adopted to predict a target, tracking of a maneuvering target is realized through prediction of various motion models, and secondly, measurement data association is realized through particle confidence propagation (PBP) based on an association matrix, filtering update is carried out, the calculation complexity of a data association step is reduced, and the overall performance of the target tracking method is improved. And finally, estimating the state of the target, performing reverse smoothing, and outputting a complete target track estimation result.

Step one: assuming the current time step is k, acquiring posterior probability density and a measurement set of a target at the moment k-1, carrying out multi-model prediction, and outputting predicted target components (including PPP components and MBM components) under a plurality of motion models;

the specific processing process comprises the following steps:

(1) PPP component prediction

In the filtering process, track information is needed to be considered, so that whether the target dies or not needs to be judged in each time step, namely, the relation between the current moment and the target die moment is compared, and the single-target track density is expressed as:

where t is the time of birth of the target, L is the number of particles generated by the target, v is the track length of the target x (i.e., the size of the target time step of survival),as a dirac function, if v ^(l) =v, then->Otherwise->By->To indicate whether the particle track length is consistent with the target, thereby judging whether the target is eliminated at the current moment. Calculating a target track x ^1:v The track density of the target is determined by judging whether the corresponding birth time and target duration v are consistent with the target according to the generated particles of all targets, so that the particles meeting the conditions are reserved for weighted summation, and the weighted summation is used as a single-target track density representation. The complete target trajectory represented by the particles is +.>w ^(l) Represents the weight of particle l, satisfying w ^(l) >0, the above formula represents a single target trajectory described by L particles. Wherein->Indicating that the first particle is generated at the target birth moment, < >>Indicating that the first particle can match the complete target trajectory x ^1:v ，t ^(l) Represents the first particleCorresponding birth time, x ^(l) Representing the first particle sampled by the target x.

In the TPMB filtering framework, the PPP process is used for detecting a potential target, and considering the prediction of a single motion model, the PPP prediction strength of the undetected target in the k-time monitoring area is as follows:

wherein the method comprises the steps ofAnd->Representing the sample particle numbers corresponding to the potential target component and the new target component respectively, wherein the potential target component corresponds to the situation that the target does not normally generate measurement, the possibility of the target to survive should be considered at the moment,representing the number of potential targets expected. />Indicating that the first particle is identical to the potential target x birth moment,/i>Indicating that the track length of the first particle is the same as the track length of the potential target x, +.>Representing the current trajectory x ^1:v Corresponding to the potential target. The new target component corresponds to a randomly new target track delta in the monitoring area _k [t]The current time k is the birth time t delta of the new generation target ₁ [v]Indicating that the length of the new-born target is 1,/and->For the new track->The first target component of (a) is target x _k 。

Weight of medium particlesAnd->The calculation is as follows:

wherein, express goal->Survival probability of->Representing the poisson intensity of the new target at time k, L ^b Representing the number of sampling particles corresponding to the nascent target component.

The state transition mode of the target is as follows:

wherein F (·) is a state transfer equation expression of uniform linear motion.

(2) MBM component prediction

For detected surviving targets, the target state of the ith MBM component at time k is expressed as:

the multi-model target state prediction calculation mode is as follows:

where M is the number of motion models,for the target state transition matrix of the ith target component at time k under the nth motion model,/>Is the probability of transition between different motion models. The particle weighted sum w of the target component existence probability r and the surviving target is expressed as:

and calculating the posterior density of the target at the moment k-1 as a potential target, thereby ensuring the integrity of the track. The particle number satisfies+.>Since the targets of the previous and subsequent moments belong to the same track, the birth moment of particle l satisfies +.>

If it isI.e. predicting the target state at time k, taking into account the situation of target survival +.>Add track set->In (a)

Wherein the set of predicted trajectoriesIn the above prediction step, the birth intensity is used And a motion model F (-) for particle sampling of the nascent object by means of the motion model +.>Particle sampling of the maneuver target is performed. Then generate +.>And predicting particles. At time k, considering the target extinction condition, the weight of the particles will change, and all the particles will be replicated at the next time, according toAnd (5) updating the weight of the survival probability. If the target is judged to die, the MBM component with the existence probability lower than the target survival threshold value is reserved, the multi-model prediction is pruned, and only particles generated by single motion model prediction are reserved. />

If the target at the moment k is eliminated, retaining the posterior information of the target at the moment k-1 to the track set

Wherein, representing track set +.>Posterior Density of Single target State at time k-1,/-)>Representing particle weights.

Step two: adopting a particle confidence propagation (PBP) method based on an incidence matrix to process the predicted target component and the measurement set obtained in the step one, and obtaining updated target posterior probability density;

the specific processing process comprises the following steps:

(1) Particle trajectory initialization

In the particle confidence propagation method, propagation information is optimized through P iterations, so that the confidence of all nodes is converged, and the label of each node is the optimal label.

The target track is expressed asIn the form of particle sets. Wherein, representing the single target state extracted at trace set at time k, < >>For a poisson distribution of potential targets,represents the complete set of potential target trajectories by +.>The initialization of the trajectory is achieved by individual particles.

TrackVariable node +.>Directional factor node _k sInformation of propagation->From a group of weighted particles And (3) representing. Wherein->Is the information transmitted by the vector measurement node j of the target node i in the p-th iteration process. />The first particle weight representing p iterations, +.>And->The birth time information and the trajectory information of the particle i generated by the target i at the time k are respectively shown.

The new and potential targets are updated to take into account whether the target survives at the current time, respectively.

(2) Measurement information assessment

Measurement and evaluation need to calculate each factor node _k sVariable node for direction measurementInformation transferred->Factor node _k sInformation transfer process representing the survival trace and all measurements,

/>

wherein the method comprises the steps ofPoisson intensity of clutter at time k, +.>For the j-th measurement at time k, L _i Representing the number of particles generated by target i->Indicating the length of survival of the first particle generated by object i at the current moment +.>And particle track length->Whether or not the target i is matched, i.e. whether or not the target i is still alive at time k is judged, +. >Poisson intensity representing target i for calculating likelihood of target generation measure +.>

In P epsilon {1, …, P } iterations, information propagation between each target variable node and each measurement variable node is realized according to a factor graph formula, and in the process, the calculation complexity of the particle weight is high. Therefore, the method introduces the correlation matrix, sets the gating threshold between the particle state and the measurement information, and only needs to calculate the information in the gating without considering the information transmitted among all variable nodes when calculating the correlation likelihood matrix, thereby reducing the complexity of calculating the particle weight. The particle likelihood calculation mode of target generation is as follows:

where d (z, x) is the Euclidean distance between the particle generated by the surviving target and the existing measurement location, and δ is the gating threshold for the correlation of the particle and the measurement.

The data association mode and the measurement updating mode are realized by calculating and transmitting information according to the calculated informationThe target state update may be expressed as +.>The updating of the target state is based on the correlation method, and the particle weight meter is reduced by setting gating between the particle state and the measurement information and only calculating information in the gating range And (5) calculating complexity. After the information transfer iteration is completed, the particle weight converges to a numerical value close to the real state of the target.

After one iteration is completed, the particle weight converges to a value close to the true state of the target. In the subsequent iteration process, each variable nodeDirectional factor node _k sInformation of propagation->The unnormalized bernoulli component densities are indicated.

When i epsilon {1, …, n _k|k-1 }，j∈{1,…,m _k When, for each predicted surviving target, an update of the particle and the existing measurements is generated,

wherein the method comprises the steps ofRepresenting information propagated by a target variable node i 'to a vector-measured variable node j', n _k|k Representing the number of targets at time k.

When i epsilon { n } _k|k-1 +1,…,n _k|k }，j∈{1,…,i-n _k|k-1 At the time of }, i.e. for potential target and measurement updates, since the assumption of multiple motion models is removed when the target is determined to be dead, information is propagated by updating only particles generated by a single motion model prediction process with existing measurementsThe weight of the particles is->

(3) Confidence calculation

The information and particle weight calculated by the above steps are iterated for several times, and the result is converged to a value close to the real target state, and the confidence of the target state in each MBM componentCan be represented by the following Bernoulli random set

Its calculation mode and information Similarly, in addition, the calculation of the particle weight and the probability of the existence of the bernoulli component in the subsequent iteration still needs to be considered to ensure the effectiveness of the track confidence, and finally the particle weight normalization is performed.

Step three: aiming at the updated target posterior probability density obtained in the second step, processing the updated target posterior probability density by utilizing the target state estimation to obtain an estimated track set;

the specific processing process comprises the following steps:

the updated target posterior probability density is stored in the form of MBM components, MBM components with existence probability higher than a threshold value are selected, the current k-moment target state is estimated from a group of weighted particle sets, and the current k-moment target state is taken as an output target track, and the output target track is expressed as follows:

by poisson point processEstimation of new target, generation of track set by output new target and recording of track X ^b ＝(t ^b ,x ^1:v ) Wherein the birth time is t ^b =k, track length v=1. For an unknown target trajectory, no particle sampling is required in the prediction step of the undetected target. After each time step of outputting the estimated target trajectory set, the redundant MBM components are pruned and resampled to avoid the particle sample degradation problem.

Step four: processing the target state estimation set obtained in the step three by using a reverse smoothing method to finally obtain a smoothed track set;

The specific process comprises the following steps:

after outputting the filtered set of estimated target trajectories, inverse smoothing may be performed by the estimated particle states. Performing inverse particle smoothing with length v on each track from extinction time e to target occurrence time t, wherein the target state at k time can be calculated approximately according to the weighted particle set obtained by filtering estimation, and the target marginal smoothing distribution is that

Wherein the method comprises the steps ofAnd->The filtering density and the forward filtering prediction density of the targets at the moment K of the track set are respectively obtained, all targets are monitored in K time steps, and the measurement information y appearing in all time steps is used for monitoring _1:K And performing reverse smoothing estimation.

Embodiment two:

the present embodiment provides for supplementing and expanding the multi-model PBP-TPMB method provided in the first embodiment in a scenario where the point target coincides with the expansion target.

The multi-model PBP-TPMB method in the first embodiment solves the problem of target tracking when multiple motorized expanded targets are in close proximity, however, when the motorized point target is in close proximity or even coincident with the expanded target, a situation may occur in which the point target is occluded by the expanded target. The measurement generated by two targets is judged to be a cluster, and the point targets generating single measurement cannot be matched and tracked for a plurality of time steps whether the measurement is based on a clustering and distribution mode or a data association mode based on confidence propagation. Particularly, when the point target moves flexibly, a plurality of continuous time steps are blocked by the expansion target, and the point target cannot be updated according to the measurement generated by the point target, so that heel leakage is easy to occur.

In order to solve the problem, the embodiment provides a method for blurring a target overlapping region. According to the method, on the basis of multi-model PBP-TPMB filtering, only multi-model prediction is performed on point targets which are close to or coincide with an expansion target, and after the targets are separated, matching is performed on multi-model prediction MBM components and new PPP components in the expansion region, so that the position of the coincident point target is judged, and subsequent target tracking is realized.

Step one: assuming the current time step is k, acquiring posterior probability density and a measurement set of a target at the moment k-1, judging whether the point target enters a superposition area with the expansion target, and outputting an MBM component of the superposition point target;

the specific processing process comprises the following steps:

in the method provided by the invention, when the target distribution is scattered or a plurality of expansion targets are close to each other, the plurality of maneuvering expansion targets can be effectively detected and tracked by the multi-model PBP-TPMB maneuvering expansion target tracking method disclosed by the embodiment I. The expansion example mainly solves the problem that the point target cannot be accurately detected and tracked when the point target coincides with the expansion target, and the specific flow is shown in fig. 3, and determining whether the moving point target enters the coinciding area with the expansion target is the first step of executing the method.

According to the TPMB filtering method based on the particle confidence propagation data association mode, when a point target is close to an extension target, likelihood that the information propagated by the point target is higher and similar in value to a plurality of measured variable nodes is generated. When more similar values appear in the likelihood matrix of the point target, the point target is considered to enter a superposition area with the expansion target, and blurring processing of a plurality of time steps in the superposition area is needed to realize subsequent tracking of the blocked point target.

Assuming that the current time is k, the ith survival target x _i The information propagated by the factor node of (a) is u _i,j Then the particle weight is w _i,j And meets i epsilon {1, …, n _k|k-1 }. If the information u propagated by the target i _i,1 ,u _i,2 ,…,u _i,M In which there are a plurality of information u _i,e Information with highest weightIf the target i is similar, the target i can correspond to a plurality of measuring points and accords with the property of the expansion target, namely

Wherein delta _f To determine threshold values for which likelihood is similar. In the spatial model in which the point object and the extension object coexist, each MBM component is based onDifferentiating the object type, if in the ith MBM component, the parameter c ^p =1, i.e. the target at time k-1 is determined to be a point target, point target x _i Information u propagated _i,j And (3) generating similar likelihood with a plurality of measuring points, wherein the likelihood indicates that the point target enters a superposition area shielded by the expansion target.

And positioning the extended target state information overlapped with the target positions of the other MBM components by comparing Euclidean distances with the target positions of the ith MBM component according to the target state information of the ith MBM component. Assuming that the c-th MBM component is an extension target with coincidence, the target state isThe overlapping area is denoted +.>The overlapping area is time dependentMoving toward the direction of motion of the coincident extended target.

Step two: processing the coincident point target MBM component acquired in the first step by adopting the multimode fuzzy prediction method, and outputting a predicted point targetA component;

the specific processing process comprises the following steps:

if the MBM component of the coincident point target is updated, multiple high-weight information likelihoods occur, thereby generating multiple local hypotheses, resulting in redundant and invalid target estimation hypotheses. Furthermore, the fusion of multiple predictive MBM components of the interactive multi-model can confuse the metrology update step, resulting in an inability to accurately track the motion trajectories of the maneuver point targets.

The method is provided by the invention, after the MBM component of the point target enters the overlapping region, the measurement update is stopped, and only multi-model fuzzy prediction is performed. Assume that the current k moment is the starting time t of fuzzy processing of the point target _s End time t _e In the next consecutive a time steps, the MBM component corresponding to the point object is predicted by M motion models, denoted asThe probability of presence of the bernoulli component is kept unchanged and the coincident point target is assumed to survive. The point object describes the gaussian distribution of motion information as +.>The multi-mode fuzzy prediction of the MBM component for a succession of a time steps within the overlap region is:

wherein, for the MBM component to have a normalization factor of probability in a time steps of the coincidence region,for the start time t of the blurring process _s To the end time t _e During this period, the state transition probability of the motion model at each moment:

wherein, the motion model probability matrix at k moment for the ith MBM component. In the fuzzy prediction of point targets, it is assumed that the target motion model does not change. Motion model probability of point object->Motion model probability matrix obeying when entering the coincidence region>And is not updated.

The fuzzy prediction of the motion state of the point target only keeps the end time t _e The probability of the presence of Bernoulli components per time stepAnd the weights of the MBM components are predicted as:

after the fuzzy prediction of the MBM component is completed, the filtered prediction state of the survival point target is output, The components output M different motion model predicted bernoulli components.

Step three: prediction for step two acquisitionComponent, which is updated by matching with the nascent PPP component, and outputs the updated +.>A component;

the specific processing process comprises the following steps:

after the coincident objects are separated, the measurements generated by the outlier objects are detected as PPP components of the nascent objects based on the properties of the TPMB filtering. In the method, the new PPP component appearing in the expansion area of the overlapping area is detected and matched, so that the updating and the subsequent tracking of the overlapping point target are realized.

The expansion area is t _e The expansion of the overlapping area at the time is shown in FIG. 4 asMatching the nascent targets in the region to determine the coincident point targets at t _e A state of time.

For t _e Updating the PBP-TPMB by all newly generated target PPP components appearing at the moment, wherein the predicted Poisson distribution intensity is as follows:

in all nascent target PPP components, located within the extension region and c ^p Point object of=1, take itPosterior probability density and fuzzy predictionMatching and updating->As a priori condition of the trajectory of the output point target within the region of coincidence. Obtaining new target PPP component posterior probability density by a multi-model PBP-TPMB method, and marking the new target PPP component posterior probability density as +. >Get its updated target state +.>If the target state x of the component ^p Located in the extended areaIn the interior, consider->I.e. is the coincident point target x ⁱ At t _e The target state of the moment.

Step four: updated for step three acquisitionA target component outputting an estimated target trajectory set;

the specific processing process comprises the following steps:

through fuzzy prediction and updating processing of the coincident point target, MBM components are predictedAnd corresponding nascent PPP component->After matching, the m-th predictive component of the match is used +.>As coincident point target x ⁱ And outputting results through state estimation of a time steps in the overlapping area. If the point object x is not matched with the PPP component, determining the point object x ⁱ And die in the overlapping area.

x ⁱ At t _e The estimation result of the target state at the moment is thatParameters of the component->For time steps k e { t } coincident with the expansion target _s ,…,t _e -1, the estimation result of the target state is +.>In the component, the parameter set of the target state

To sum up, if target x ⁱ At t _e The time survives, the estimation result of the target state isSatisfy->

In order to verify the effect of the multi-model PBP-TPMB maneuvering expansion target tracking method based on the incidence matrix, the application has the following specific experiments:

1. experimental metrics

In order to verify the effectiveness of the proposed multi-model PBP-TPMB method, an experimental part is compared with the traditional CA-PMBM filtering and the multi-model CA-PMBM filtering, and an experiment of three expansion target scenes which are in maneuvering motion and are close to each other and an experiment of maneuvering targets which are close to the expansion targets are respectively carried out. Experimental results were measured by generalized optimal sub-mode allocation (GOSPA). In the experimental scene, three motion modes of the target are assumed, namely, left turn and right turn of uniform linear motion (CV) and turning motion (CT), and the corresponding motion model transfer matrix and process noise are as follows:

/>

Sampling time interval t=1s, motion noise standard deviation sigma=0.01, target detection probability pd=0.95, survival probability ps=0.99, clutter obeys poisson distribution with mean value of λ=8, and model transition probability of motion models a to b is

Assuming that the real target set and the output estimated target set are random finite sets:

then in each set, a single real targetAnd estimate target->The distance between them is

Wherein w is _γ +w _x +w _X =1, constant c _γ 、c _x And c _X Maximum expected errors for measuring velocity, motion state and extended state, respectively, and

wherein I and II ₂ And II _F Absolute, euclidean and fei Luo Beiniu s norms, respectively.

The GOSPA error does not simply take into account euclidean distance errors between the real target set and all targets of the estimated target set, but emphasizes the accuracy of the target number estimation by miss-detection errors and false-detection errors. Let it be assumed that the real target set G _k Comprising a target number of N _s,k Estimating the target set E _k Comprising a target number ofIf->GOSPA error of

/>

If it isThe GOSPA method divides the error difference into three parts,for the target distanceError (S)>For detecting target error, the method is->Is a false detection target error. C is a cut-off value of the baseline distance, and represents the allowable maximum position error, if the maximum position error is exceeded, the target mismatch is considered, and the condition is judged to be missed detection or false detection, and the target error is represented by the missed detection or false detection; p is the degree of penalty for outliers, with greater p values being more penalized for outliers. The experimental part of the invention is provided with p=2 and c=10, and simulation experiments are respectively carried out under 3 mutually-approaching maneuvering expansion targets, 5 coexistence point targets and expansion target scenes, and 50 Monte Carlo (MC) simulations are carried out.

2. Experiment and result analysis

The specific experiment of the application evaluates the performance of the method under two experimental scenes, namely: the three maneuvering expansion targets are close to each other, and a maneuvering point target and an expansion target scene coexist, and experimental results are as follows.

Experiment one: multi-extension target scene

(1) Scene setting

The method of the application mainly solves the problem that multiple maneuvering expansion targets are close to each other, so that 3 maneuvering expansion targets are arranged in the scene in total. The monitoring area is [ -100,100] m× [ -100,100] m, and the total monitoring time is k=100 s.

The object 1 appears at k=1s, (0 m, -80 m), makes a uniform linear motion in the y-axis forward direction at a speed of 1.5m/s, makes a clockwise turning motion at an angular speed θ=pi/30 at k=40s, converts the object into a uniform linear motion at k=60deg.s, and disappears from a constant speed to k=100deg.s. The object 2 and the object 3 appear at (-40, 50) m and (50, 50) m, respectively, and do uniform linear motion at the speeds of (1, -1) m/s and (-1, -1) m/s, respectively. In the course of the movement, the situation that the target is maneuvered is similar to that of the target 1, firstly, uniform linear movement is performed at k=1s, then, clockwise turning movement with the angular velocity of θ=pi/30 is performed at k=40s, and finally, uniform linear movement is converted at k=60deg.s until the target disappears at k=100deg.S.

In the experimental scene, three targets simultaneously appear in a monitoring area, jointly move towards the center of the monitoring area, start to move flexibly at k=40s, then move to the center position of the monitoring area at k=50s, and are in close proximity. The target motion trajectory is shown in fig. 5.

(2) Analysis of experimental results

In this experimental scenario, the number of measurements for three targets obeys the gamma distribution, each yielding about 10 measurements. Clutter rate lambda at each moment ^C The actual target state and measurement is taken every 10 times, and the target state estimation results of the three filtering methods are taken. In order to show the effect of target tracking in the close proximity of multiple extended targets, fig. 6 shows extended targets with ovals, and shows measurement generated by each target, clutter in the monitored area, real states of the targets, and target state estimation results of different filtering methods. As is apparent from fig. 6, in the tracking scenario of three extended targets, the proposed multi-model PBP-PMBM filtering method has the highest estimation accuracy for the target state.

In fig. 6 (a), the conventional CA-PMBM filtering method based on the clustering and the distributed data correlation method gradually causes heel missing when three targets turn (about k=40s), and the method predicts the target state through a single motion model, so that heel missing is easily caused when the targets maneuver. And IMM-CA-PMBM filtering integrated with the interactive multi-model method can realize tracking of maneuvering targets when the distribution among different targets is more dispersed. However, in the experimental scene, when three extended targets move to the central position of the monitoring area (about k=50s), the targets are closely adjacent to each other or even coincide with each other, which is unfavorable for measurement division, and thus the problems of time complexity rise of data association and inaccurate measurement clustering are caused. And the matching between the target and the measurement fails, so that the problems of false detection or missing detection and the like can be generated. The method has good tracking effect when three expansion targets are in maneuvering motion and are close to each other.

Fig. 6 (b) and (c) illustrate that the tracking effect of the proposed method is better than that of other methods in the scene where the targets are immediately adjacent by comparing the tracking results of the IMM-CA-PMBM filtering and IMM-PBP-TPMB filtering when the three extended targets are immediately adjacent by k=51s. The CA-PMBM filtering has missed at this time due to the maneuver of the target. As can be seen from the figure, at k=51s, the ca-PMBM method generates multiple global hypotheses, and the output estimation result has 4 extended targets, which are more than the number of real targets, and causes a large false detection error. In the right graph, under the same condition of target state and measurement distribution, the IMM-PBP-TPMB filtering method accurately distinguishes the state information of three extended targets, and no missed detection or false detection is caused under the condition that the targets are in close proximity, so that the method has good effect.

In the experimental scenario of three maneuver expansion targets, the GOSPA error of the target detection result is shown in fig. 7. As can be seen from comparison of the target filtering results in fig. 6, in this experimental scenario, the CA-PMBM filter has a missing heel during the target turning motion, which results in an increase in missing detection error and distance error, and thus, in the error result in fig. 7, after k=40 s, the root mean square GOSPA value of the CA-PMBM filter suddenly increases. And when the IMM-CA-PMBM method is used for moving a target in k=40s, the target track can be accurately tracked when the target moves due to the integration of the interactive multi-model. However, as three extended targets come closer, the density-based metrology clustering DBSCAN method divides a large number of metrology clusters after the metrology generated by each target comes closer, resulting in a redundant global assumption. And the matching failure of the measurement cluster can cause larger false detection/missing detection OSPA errors. Thus, the IMM-CA-PMBM method produces a large root mean square GOSPA error after target approach.

The IMM-PBP-TPMB filtering method provided by the invention can realize the tracking of the immediate maneuvering expansion target, does not cause the target tracking missing, has good data association effect when three targets with k=50s are close, and has relatively stable and good tracking effect in the whole target movement process.

Comparison of the operating speeds of the methods of Table 1

Table 1 shows the operation speed of each method in the scene operation process, and compares the operation time of the CA-PMBM filtering, the IMM-PBP-TPMB filtering without the incidence matrix and the proposed IMM-PBP-TPMB filtering method. The CA-PMBM filtering and the IMM-CA-PMBM filtering are realized by Kalman filtering based on a clustering and distribution data association method, the overall operation time is shorter, and the tracking effect is good in a scene with more dispersed target distribution. The IMM-PBP-TPMB filtering is realized by particle filtering based on a confidence propagation data association mode, and the larger calculated amount is caused by calculating the particle weight through multiple iterations. On the basis of the same tracking effect, the method reduces the calculation amount of particle likelihood in the process of matching the target and measurement by comparing with an IMM-PBP-TPMB method which is not integrated with the incidence matrix, thereby reducing the time complexity of the whole method.

Experiment II: multi-point target and extension target coexistence scene

(1) Scene setting

In a simulation experiment in which a plurality of point targets coexist with an extension target, consider the scenes of two point targets (T1 and T2) and three extension targets (T3, T4 and T5). Table 2 shows the movement state information of the object.

TABLE 2 Multi-target simulation scenario target motion information

The complete multi-target motion trajectories are plotted according to the target information described in the table as shown in fig. 8.

(2) Analysis of experimental results

The IMM-PBP-TPMB filtering method provided by the invention is respectively compared with the results of CA-PMBM filtering and IMM-CA-PMBM filtering, and under the condition of more dispersed multiple targets, the tracking effect of three filtering results is better; when the target is maneuvered, the CA-PMBM filtering generates a heel leakage; when multiple targets are in close proximity, the IMM-PBP-TPMB filtering method can estimate states and motion tracks of the point targets and the expansion targets respectively, and has good target tracking effect.

Fig. 9 (a) shows that in a coexistence scene of a multipoint target and an extended target, the IMM-CA-PMBM filtering is compared with the result of the proposed method, and as can be seen from the figure, the extended targets T3, T4 and T5 are distributed more dispersedly with the point target T1 for 1 to 50 seconds, the tracking effect is good, then the extended targets are adjacent, the IMM-CA-PMBM filtering tracking effect is reduced, and the proposed method outputs complete tracks of the extended targets and the point targets.

As is apparent from fig. 9 (b) and (c), the conventional CA-PMBM filtering method based on the clustering and the assignment data association method uses a single motion model at k=38s, and causes heel missing when the targets T2, T3 and T4 are maneuvered, and only outputs the estimation results of the two targets; the IMM-CA-PMBM method integrated with multiple models has good tracking effect when all targets are scattered at the current moment; the IMM-PBP-TPMB filtering method provided by the invention has good tracking effect when targets T1, T3, T4 and T5 are in close proximity.

Fig. 9 (d) and (e) are comparisons of the estimation results of the three filtering methods of k=55s with the real scene. As can be seen from table 2, the targets gradually approach between 35 seconds and 55 seconds, and the CA-PMBM filter can only track the target T5 moving at constant speed, and leak heel for other point targets and extended targets due to the approach of multiple targets; compared with the IMM-CA-PMBM filtering which has excessive target state estimation, the IMM-PBP-TPMB filtering provided by the invention has good estimation effect when multiple targets are in close proximity, the number of targets is estimated correctly, the target is divided and is very similar to the real target state, and a good target tracking effect is shown.

Fig. 9 is a root mean square GOSPA error comparison of three filtering results in a coexisting scene of a multi-point target and a maneuver expansion target. In a multi-target scene, when target distribution is more dispersed, the methods CA-PMBM and IMM-CA-PMBM based on the clustering and distribution data association mode have good target state estimation effect; after 31 seconds to 40 seconds of target approach, the method based on the CA data association mode generates more redundant global assumptions due to difficult measurement clustering, so that GOSPA errors are increased. In contrast, the IMM-PBP-TPMB method based on the particle confidence propagation method exhibits better tracking performance when the target approaches, and the GOSPA error is generally lower.

According to the experiment, the multi-model PBP-TPMB filtering method based on the incidence matrix has the optimal multi-mobile expansion target state estimation performance, and can output complete track information from occurrence to extinction of each target when carrying out state estimation on the multi-mobile expansion targets. Aiming at the problem that when the target moves, the multi-motion model interactively outputs an estimated target set to cause error increase, the error can be effectively reduced by a reverse smoothing method, and more accurate track information estimation is realized.

Some steps in the embodiments of the present application may be implemented by using software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.

The foregoing description of the preferred embodiments of the application is not intended to limit the application to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the application are intended to be included within the scope of the application.

Claims (10)

1. A motorized extended target tracking method, the method comprising: under the framework of the TPMB (thermoplastic polyurethane) filtering of the Poisson Duobnoulli, firstly, performing target prediction by adopting an interactive multi-model method IMM, and realizing tracking of maneuvering targets through prediction of various motion models; secondly, realizing measurement data association by spreading PBP based on particle confidence coefficient of the association matrix, and carrying out filtering update; finally, estimating the target state, performing reverse smoothing, and outputting a complete target track estimation result;

The maneuvering extension target tracking method comprises the following steps:

step one: assuming the current time step is k, acquiring posterior probability density and a measurement set of a target at the moment k-1, carrying out multi-model prediction, and outputting predicted target PPP components and MBM components under a plurality of motion models;

step two: adopting a particle confidence propagation (PBP) method based on an incidence matrix to process the predicted target component and the measurement set obtained in the step one, and obtaining updated target posterior probability density;

step three: aiming at the updated target posterior probability density obtained in the second step, processing the updated target posterior probability density by utilizing the target state estimation to obtain an estimated track set;

step four: and (3) processing the target state estimation set obtained in the step (III) by using a reverse smoothing method to finally obtain a smoothed track set.

2. The method of claim 1, wherein the PPP prediction strength of the undetected target in the monitored region at time k in the first step is:

wherein, and->Respectively representing the sampling particle numbers corresponding to the potential target component and the new target component, wherein the particle weight is +.>And->The calculation is as follows:

the state transition mode of the target is as follows:

wherein F (-) is a state transfer equation expression of uniform linear motion;

The MBM component prediction process includes:

for detected surviving targets, the target state of the ith MBM component at time k is expressed as:

the multi-model target state prediction calculation mode is as follows:

where M is the number of motion models,for the target state transition matrix under the ith target component nth motion model at k time,/th>The transition probability between different motion models;

the particle weighted sum w of the target component existence probability r and the surviving target is expressed as:

the posterior density of the target at the moment k-1 is used as a potential target to operate, so that the integrity of the track is ensured; the particle number satisfies+.>Since the targets belong to the same track before and after the moment, the +.>

If it isI.e. predicting the target state at time k, taking into account the situation of target survival +.>Add track set->In (a):

wherein the set of predicted trajectoriesIn the course of prediction, by birth intensity +.>And a motion model F (-) for particle sampling of the nascent object by means of the motion model +.>Performing manoeuvresParticle sampling of objects>Transition probability for converting different motion models into nth model at k moment, +.>For the nth target motion state transition matrix, generating +. >A plurality of predicted particles;

at the moment k, considering the target extinction condition, the weight of the particles changes, copying all particles at the next moment, and updating the weight according to the survival probability; if the target is judged to die, the MBM component with the existence probability lower than the target survival threshold value is reserved, the multi-model prediction is pruned, and only particles generated by single motion model prediction are reserved;

if the target at the moment k is eliminated, retaining posterior information of the target at the moment k-1 to a track set:

wherein, is track set->Posterior density of single target states at time k-1.

3. The multi-machine-operated extended target tracking method according to claim 2, wherein the second step comprises:

(1) Initializing particle trajectories;

in the particle confidence propagation method, propagation information is optimized through P iterations, so that the confidence of all nodes is converged, and the label of each node is the optimal label;

poisson strength is expressed asIs a collection of particles;

in the p=1 th iteration, the traceVariable node +.>Directional factor node _k sInformation of propagation->Is made up of a set of weighted particles->A representation;

updating the new and potential targets respectively to consider whether the target survives at the current moment;

(2) Evaluating measurement information;

calculating each factor node _k sVariable node for direction measurementInformation transferred->Factor node _k sInformation transfer process representing the survival trace and all measurements,

in P epsilon {1, …, P } iterations, information transmission between each target variable node and each measurement variable node is realized according to a factor graph formula;

introducing an association matrix, setting a gating threshold between the particle state and the measurement information, and calculating information in the gating when calculating the association likelihood matrix, wherein the particle likelihood calculation mode generated by the target is as follows:

where d (z, x) is the Euclidean distance between the particle generated by the surviving target and the existing measurement location, and δ is the gating threshold of the association of the particle with the measurement;

the data association mode and the measurement updating mode are realized by calculating and transmitting information according toThe target state update is denoted +.>

After one iteration is completed, the particle weight converges to a numerical value close to the real state of the target, and in the subsequent iteration process, each variable node is formedDirectional factor node _k sInformation of propagation->All represent the un-normalized Bernoulli component density, other propagation information and particle weight parameters, when i.e {1, …, n _k|k-1 }，j∈{1,…,m _k Generating an update of the particle and existing measurements for each predicted surviving target:

When i epsilon { n } _k|k-1 +1,…,n _k|k }，j∈{1,…,i-n _k|k-1 At the time of }, i.e. for potential target and measurement updates, since the assumption of multiple motion models is removed when the target is determined to be dead, information is propagated by updating only particles generated by a single motion model prediction process with existing measurementsThe weight of the particles is as follows:

(3) Confidence calculation

The information and particle weight calculated by the above steps are iterated for several times, and the result is converged to a value close to the real target state, and the confidence of the target state in each MBM componentCan be represented by the following bernoulli random set:

and calculating the particle weight and the Bernoulli component existence probability in the subsequent iteration to ensure the effectiveness of the track confidence, and finally carrying out particle weight normalization.

4. The multi-machine extended target tracking method according to claim 3, wherein the third step comprises:

the updated target posterior probability density is stored in the form of MBM components, MBM components with existence probability higher than a threshold value are selected, the current k-moment target state is estimated from a group of weighted particle sets, and the current k-moment target state is taken as an output target track, and the output target track is expressed as follows:

estimation of a new target is achieved through a poisson point process, the output new target generates a track set and tracks X are recorded ^b ＝(t ^b ,x ^1:v ) Wherein the birth time is t ^b For an unknown target trajectory, no particle sampling in the step of predicting the undetected target is required;

after each time step of outputting the estimated target trajectory set, the redundant MBM components are pruned and resampled to avoid the particle sample degradation problem.

5. The multi-machine extended target tracking method according to claim 4, wherein the fourth step comprises:

after outputting the filtered set of estimated target trajectories, inverse smoothing may be performed by the estimated particle states. And (3) performing reverse particle smoothing with the length v on each track from the extinction moment e to the target occurrence moment t, wherein the target state at the moment k can be approximately calculated according to a weighted particle set obtained by filtering estimation, and the target marginal smoothing distribution is as follows:

wherein the method comprises the steps ofAnd->The filtering density and the forward filtering prediction density of the targets at the moment K of the track set are respectively obtained, all targets are monitored in K time steps, and the measurement information y appearing in all time steps is used for monitoring _1:K And performing reverse smoothing estimation.

6. The multi-machine-driven extended target tracking method according to any one of claims 1 to 5, wherein for a point target that is close to or coincides with an 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 a multi-model predicted MBM component with a new PPP component in the extended region, and the method specifically comprises:

Step 1: assuming the current time step is k, acquiring posterior probability density and a measurement set of a target at the moment k-1, judging whether the point target enters a superposition area with the expansion target, and outputting an MBM component of the superposition point target;

step 2: processing the coincident point target MBM component obtained in the first step by adopting a multimode fuzzy prediction method, and outputting a predicted point targetA component;

step 3: prediction for step two acquisitionComponent, which is updated by matching with the nascent PPP component, and outputs the updated +.>A component;

step 4: updated for step three acquisitionAnd outputting the estimated target track set by the target component.

7. The multi-machine extended target tracking method according to claim 6, wherein the step 1 comprises:

assuming that the current time is k, the ith survival target x _i The information propagated by the factor node of (a) is u _i,j Then the particle weight is w _i,j And meets i epsilon {1, …, n _k|k-1 }；

If the information u propagated by the target i _i,1 ,u _i,2 ,…,u _i,M In which there are a plurality of information u _i,e Information with highest weightSimilarly, the target i can correspond to a plurality of measuring points, and accords with the property of the expansion target, namely:

wherein delta _f To determine threshold values for likelihood closeness, each MBM component is based on the spatial model in which the point object and the extension object coexist Differentiating the object type, if in the ith MBM component, the parameter c ^p =1, i.e. the target at time k-1 is determined to be a point target, point target x _i Information u propagated _i,j And (3) generating similar likelihood with a plurality of measuring points, wherein the likelihood indicates that the point target enters a superposition area shielded by the expansion target.

8. The multi-machine extended target tracking method according to claim 7, wherein the step 2 comprises:

after the MBM component of the point target enters the overlapping area, stopping measuring and updating the point target, and only performing multi-mode fuzzy prediction;

assume that the current moment i is the starting time t of fuzzy processing of the point target _s End time t _e =k+a, then in the next consecutive a time steps, the point targets the corresponding MBM componentThe prediction of M motion models is respectively carried out and is recorded as

Keeping the existence probability of the multiple Bernoulli components unchanged and assuming that the coincident point target survives, the Gaussian distribution of the point target describing motion information is as followsThe multi-mode fuzzy prediction of the MBM component for a succession of a time steps within the overlap region is:

wherein, for the MBM component to have a normalization factor of probability in a time steps of the coincidence region,for the start time t of the blurring process _s To the end time t _e During this period, the state transition probability of the motion model at each moment:

wherein, in the fuzzy prediction of the point target, the motion model probability of the point target is +.>Motion model probability matrix obeying when entering the coincidence region>And is not updated;

the fuzzy prediction of the motion state of the point target only keeps the end time t _e The probability of the presence of Bernoulli components per time stepAnd the weights of the MBM components are predicted as:

after the fuzzy prediction of the MBM component is completed, the filtered prediction state of the survival point target is output,the components output M different motion model predicted bernoulli components.

9. The multi-machine extended target tracking method according to claim 8, wherein the step 3 includes:

the new PPP component appearing in the expansion area of the overlapping area is detected and matched, so that the update and the subsequent tracking of the overlapping point target are realized;

the expansion area is t _e The expansion of the overlapping area of time instants is denoted asMatching the nascent targets in the region to determine the coincident point targets at t _e A state of time;

For t _e Updating the PBP-TPMB by all newly generated target PPP components appearing at the moment, wherein the predicted Poisson distribution intensity is as follows:

wherein the method comprises the steps ofRepresenting the desired number of potential targets, L ^b To represent the number of particles of the nascent object;

in all nascent target PPP components, located within the extension region and c ^p Point object of =1, take the posterior probability density and fuzzy predictionMatching and updating->As a priori condition of the trajectory of the output point target in the coincident region;

the posterior probability density of the new target PPP component is obtained through a multi-model PBP-TPMB method and is recorded asGet its updated target state +.>If the target state x of the component ^p Is located in the expansion area->In the interior, consider->I.e. is the coincident point target x ⁱ At t _e The target state of the moment.

10. The multi-machine extended target tracking method according to claim 9, wherein the step 4 includes:

will predict MBM componentAnd corresponding nascent PPP component->After matching, the m-th predictive component of the match is used +.>As coincident point target x ⁱ Outputting a state estimation result of a time steps in the overlapping area, and judging a point target x if the state estimation result is not matched with the PPP component ⁱ Death in the coincident region;

x ⁱ At t _e The estimation result of the target state at the moment is thatParameters of the component->For time steps k e { t } coincident with the expansion target _s ,…,t _e -1, the estimation result of the target state is +.>In the component, the parameter set of the target state

To sum up, if target x ⁱ At t _e The time survives, the estimation result of the target state isSatisfy->