CN116148837A

CN116148837A - Robust multi-sensor multi-target tracking method under heterogeneous clutter background

Info

Publication number: CN116148837A
Application number: CN202211412732.2A
Authority: CN
Inventors: 曾操; 刘敏提; 陶海红; 胡树林; 刘钰
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2022-11-11
Filing date: 2022-11-11
Publication date: 2023-05-23

Abstract

The invention relates to a robust multi-sensor multi-target tracking method under a non-uniform clutter background, which comprises the following steps: under the condition that no target exists in the observation area, the sensor with the limited detection range firstly estimates the clutter rate of the non-uniform clutter, then estimates the space density of the non-uniform clutter, and obtains the estimated clutter rate and the estimated space density; based on the echo amplitude characteristics of the target signal in the observation area, estimating the detection probability by integrating the amplitude likelihood function in the signal-to-noise ratio confidence interval, and obtaining the estimated detection probability; transmitting the estimated clutter rate, the estimated space density and the estimated detection probability into a standard TPMB filter to obtain a robust TPMB filter; the state of the multi-target track is estimated using a robust TPMB filter. According to the method, under the scene of unknown heterogeneous clutter and detection probability and limited detection distance of the sensor, multi-view fusion is utilized to achieve multi-target tracking of random disappearance, the problem that a fixed detection model is easy to mismatch is solved, and continuous target track information can be provided.

Description

Robust multi-sensor multi-target tracking method under heterogeneous clutter background

Technical Field

The invention belongs to the technical field of tracking, and particularly relates to a steady multi-sensor multi-target tracking method under a non-uniform clutter background.

Background

Multi-Object Tracking (MOT) refers to estimating the number of multiple objects and time-varying dynamics at the same time, and has been widely used in various application fields, such as autopilot, multi-row person Tracking, satellite video, and radar sensor networks. MOTs, however, are complicated by uncertainties in actual engineering scenarios, such as limited sensing range of individual sensors, false alarms, false detections, and data-related uncertainties. Under the background, researchers at home and abroad propose to use multiple sensors to obtain more information gain, so that uncertainty in a system can be reduced, and meanwhile, the performance of a tracking algorithm is improved. Currently, multi-sensor multi-target tracking has become a big hotspot problem in information fusion research.

In the field of multi-target tracking, commonly used tracking methods can be divided into three types: joint probability data association (Joint Probability Data Association, JPDA), multi-hypothesis tracking (Multiple Hypotheses Tracking, MHT), and random finite set (Random Finite Set, RFS) multi-objective tracking. Currently, various Multi-sensor Multi-target filters commonly employ Random Finite Set (RFS) filters, where unlabeled RFS filters include probabilistic hypothesis density (Probability Hypothesis Density, PHD), electromotive PHD (CPHD) filters, and Bernoulli (MeMBer). However, it is difficult to provide identity information of the object based on the unlabeled RFS filter. To this end, researchers have developed tag RFS filters that can provide continuous tracking of objects and identity information, such as delta-generalized tag Bernoulli (delta-Generalized Labeled Multi-Bernoulli, delta-GLMB) and tag Bernoulli (LMB) filters, by adding unique tags to the objects. It is noted that while tag RFS filters are suitable for many scenario scenarios, they are prone to the problem of ambiguity of the object-tag association for new objects of independent co-distributed cluster processes (Independent Identically Distributed Cluster, IIDC). To this end, researchers have proposed MOTs based on track sets, such as the track poisson Bernoulli filter (Trajectory Poisson Multi-Bernoulli, TPMB), that replace estimating a set of target states with tags to solve the ambiguity problem associated with the tags.

Aiming at the uncertainty problem in the target birth process, the adaptive measurement driving newly-generated is applied to the tag RFS filtering. For delta-GLMB and LMB filters, adaptive regeneration may significantly improve target track estimation for IIDC processes with greater spatial uncertainty. But the TPMB filter has better performance than the adaptive new tag RFS filter in terms of tracking accuracy and computational efficiency, and is selected to estimate the multi-target track in order to further improve tracking accuracy and computational efficiency.

In addition to the challenges described above, more practical challenges such as clutter and unknown prior information of detection can also degrade the performance of multi-target tracking. In response to the above problems, researchers have proposed robust algorithms for single sensor MOTs to accommodate clutter rate and detection mismatch. Mahler et al designed a Robust CPHD (R-CPHD) filter to obtain clutter rates and detection probabilities when filtering. In addition, an adaptive generalized signature, multiple Bernoulli (i.e., DP-GLMB), is developed to provide a target trajectory for clutter rate, detection probability, and unknown prior information of the birth model. On this basis, a Lu Bangduo sensor GLMB (R-MS-GLMB) filter is proposed, which has better performance in a scene of background fluctuation. Notably, the robust algorithm mentioned above generally assumes that clutter points are uniformly distributed in the monitored region, and multi-sensor multi-target tracking techniques involving limited sensing range, unknown non-uniform clutter, and fluctuating target detection characteristics background do not currently exist.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a robust multi-sensor multi-target tracking method under a uniform clutter background. The technical problems to be solved by the invention are realized by the following technical scheme:

the embodiment of the invention provides a robust multi-sensor multi-target tracking method under a non-uniform clutter background, which comprises the following steps:

s1, under the condition that a sensor with a limited detection range does not have a target in an observation area, firstly estimating the clutter rate of non-uniform clutter, and then estimating the space density of the non-uniform clutter based on an unsupervised learning method of model clustering to obtain the estimated clutter rate and the estimated space density;

s2, based on the echo amplitude characteristics of the target signal in the observation area, estimating the detection probability by integrating the amplitude likelihood function in a signal-to-noise ratio confidence interval, and obtaining the estimated detection probability;

s3, transmitting the estimated clutter rate, the estimated space density and the estimated detection probability into a standard TPMB filter to obtain a robust TPMB filter;

s4, estimating states of the multi-target track by using the robust TPMB filter.

In one embodiment of the present invention, step S1 includes:

s11, under the condition that a sensor with a limited detection range does not have a target in an observation area, estimating clutter rate by maximizing a fusion clutter measurement likelihood function related to the clutter rate, and obtaining the estimated clutter rate;

s12, carrying out parameterization representation on the space density of the non-uniform clutter based on a model clustering method, solving the number and the parameter set of Gaussian mixture components in the parameterization representation, and calculating the space density of the non-uniform clutter by utilizing the number and the parameter set of the Gaussian mixture components to obtain the estimated space density.

In one embodiment of the present invention, step S11 includes:

on the condition that no target exists in the multi-sensor observation area, based on the process of modeling clutter observed by a single sensor as poisson points and the process of clutter linearly combined by a plurality of sensors obeying the poisson points, a likelihood function that a fusion center acquires the fusion clutter measurement is expressed as:

wherein ,λ_C Is the clutter rate，W _J ＝|C _J I is the number of clutter, C _J The method comprises the steps of fusion clutter measurement sequences of J continuous time steps, wherein L is the number of sensors, and L is the first sensor;

maximizing the likelihood function of the fusion clutter measurement, and obtaining the estimated clutter rate as follows:

wherein ,

in one embodiment of the present invention, step S12 includes:

and carrying out parameterized representation on the space density of the heterogeneous clutter based on a model clustering method:

wherein Θ is a parameter set, θ _q For the q-th Gaussian component parameter, i.e.

Q is the number of Gaussian mixture components when the Gaussian mixture components approach the non-uniform clutter space density, +.>

The q-th partition cluster of the mixed clutter set, pi _q For the mixing ratio->

c _m For the m-th clutter sample,

is a parameter vector, ++>

For the weight of the q-th component, Θ= (α) ₁ ,…α _Q ；θ ₁ ,…,θ _Q ) Is an unknown set of parameters;

estimating the number of the Gaussian mixture components by using a Bayesian information criterion:

wherein ,

the number of the Gaussian mixture components;

estimating a parameter set of the gaussian mixture component by using a expectation maximization method:

wherein ,

to mix the component ratios, W _J For the clutter measurement, m is the mth clutter sample, +.>

For the posterior density of the mth clutter sample belonging to the qth cluster, n is the iteration number,/>

C is the mean vector of the Gaussian mixture component _m For the mth clutter sample,/th clutter sample>

The mean vector and covariance matrix are the mixed Gaussian components;

substituting the number of the Gaussian mixture components and the parameter set into the parameterized representation to obtain the estimated space density.

In one embodiment of the present invention, step S2 includes:

s21, based on the target signal echo amplitude characteristics in the observation area obey Rayleigh distribution, a detection probability model of the target signal echo amplitude characteristics is established:

wherein ,P_D (beta) is detection probability, beta is signal-to-noise ratio parameter, alpha is target signal echo amplitude characteristic, and T is threshold value;

s22, establishing a distribution model of signal-to-noise ratio parameters:

where p (β) is the distribution of the signal-to-noise ratio parameter, ρ is a proportionality constant that causes the probability density integral to be 1;

given signal-to-noise ratio interval value [ beta ] ₁ ,β ₂ ]Scaling factor ρ= (ln (1+β) ₂ )-ln(1+β ₁ )) ^-1 The amplitude likelihood function can be obtained by integrating the signal-to-noise ratio parameter beta, and the estimated detection probability is obtained by substituting the amplitude likelihood function into the detection probability model:

obtaining a numerical solution of the estimated detection probability through MATLAB built-in integral function:

wherein integral is the integral function and @ is the anonymous function symbol.

In one embodiment of the present invention, in the robust TPMB filter, the updated poisson component assumption and bernoulli component assumption include: updating undetected targets, updating missed targets, updating detected targets, updating nascent targets.

In one embodiment of the present invention, step S4 includes:

s41, using the robust TPMB filter, representing the gaussian mixture intensity of the multisensor on the new poisson component in the fusion measurement at the target moment as:

wherein ,n_k'|k Is the number of the components,

is the neonatal time, < >>

For the weight of the j-th component corresponding to the i-th target,

for mean value->

For covariance, k is the kth time step, k' e { k, k+1}, X is the multi-target track;

using the robust TPMB filter, the spatial density of the ith bernoulli component in the fusion measurement of the multisensor at the target moment is expressed as:

wherein ,bⁱ In order to start the time of the start-up,

is the mean value of the ith Bernoulli ingredient, < + >>

For covariance, k is track survival until the kth time step, +.>

n _x Is the dimension of the target state;

s42, reducing the mixed components of the multiple Bernoulli components to obtain a reduction result;

s43, taking the Bernoulli component with the existence probability exceeding a set threshold value in the reduction result as the state of the multi-target track.

In one embodiment of the present invention, step S42 includes:

and pruning, combining, limiting and recycling the Bernoulli mixed components to obtain the reduction result.

Compared with the prior art, the invention has the beneficial effects that:

according to the tracking method, firstly, the clutter rate and the space density of non-uniform clutter are estimated under the condition that targets are not available, then the detection probability is estimated based on the echo amplitude characteristics of target signals, and finally the state of a multi-target track is estimated by using a robust TPMB filter, so that multi-target tracking for random disappearance is realized by using multi-field fusion under the conditions of unknown non-uniform clutter, detection probability and limited detection distance of a sensor; the detection information of an unknown target is obtained according to the echo amplitude characteristics of the target signal, so that the problem that a fixed detection model is easy to mismatch is solved; meanwhile, continuous target track information can be provided by utilizing the advantage of robustness of the robust TPMB filter on target missed detection, and missed detection and false alarm are reduced.

Drawings

FIG. 1 is a schematic flow chart of a robust multi-sensor multi-target tracking method in a non-uniform clutter background according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a technical flow for implementing multi-target tracking by fusion of a plurality of limited sensing distance sensors provided by the invention;

FIG. 3 is a schematic diagram of a multi-target tracking scenario provided by an example of the present invention;

FIG. 4 is a schematic illustration of an MBM structure according to an embodiment of the present invention;

FIG. 5 is a diagram of a real target motion trajectory in a linear scenario provided by an example of the present invention;

FIG. 6 is a graph of the detection probability and clutter rate estimation results in a linear scene provided by the example of the present invention;

FIG. 7 is a graph of the result of estimating the clutter component in a linear scene according to an embodiment of the present invention;

FIG. 8 is a graph of the result of estimating the clutter spatial density in a linear scene according to an embodiment of the present invention;

FIG. 9 is a graph of a multi-target track following result in a linear scenario provided by an example of the present invention;

FIG. 10 is a graph of the error result of multiple target number estimation in a linear scenario provided by an example of the present invention;

FIG. 11 is a graph of the result of multi-objective number estimation in a linear scenario provided by an example of the present invention;

FIG. 12 is a generalized optimal sub-pattern assignment error result graph for multi-target track tracking in a linear scenario provided by an example of the present invention;

FIG. 13 is a graph of two optimal sub-mode allocation error results for multi-target track tracking in a linear scenario provided by an example of the present invention;

FIG. 14 is a diagram of a real object motion trajectory in a nonlinear scenario provided by an example of the present invention;

FIG. 15 is a graph of detection probability and clutter rate estimation results in a nonlinear scenario provided by an embodiment of the present invention;

FIG. 16 is a graph of the result of estimating the clutter component count in a nonlinear scene provided by an example of the present invention;

FIG. 17 is a graph of the result of estimating the spatial density of clutter in a nonlinear scene according to an embodiment of the present invention;

FIG. 18 is a graph of the multi-objective track following results in a non-linear scenario provided by an example of the present invention;

FIG. 19 is a graph of the result of multiple target number estimation errors in a nonlinear scenario provided by an example of the present invention;

FIG. 20 is a graph of the result of multi-objective number estimation in a nonlinear scenario provided by an example of the present invention;

FIG. 21 is a generalized optimal sub-pattern assignment error result graph for multi-target track tracking in a nonlinear scenario provided by an example of the present invention;

FIG. 22 is a graph of distribution error results for two optimal sub-modes of multi-target track tracking in a nonlinear scenario provided by an example of the present invention.

Detailed Description

The present invention will be described in further detail with reference to specific examples, but embodiments of the present invention are not limited thereto.

Example 1

The embodiment provides a robust multi-sensor multi-target tracking method under a non-uniform clutter background, which comprises the following steps: the method comprises the steps of obtaining multi-target motion information under a global view field by utilizing the characteristic of complementation of multi-view field information of a sensor; the multi-target tracking robustness under a complex background is improved by adaptively estimating unknown priori detection and clutter model parameters; based on the track Poisson Bernoulli filter, the track missing detection and false alarm are reduced, and the continuity of the multi-target tracking track is improved; the validity of the invention is verified through tracking experimental results of a plurality of targets in linear and nonlinear typical scenes.

Referring to fig. 1, fig. 2 and fig. 3, fig. 1 is a schematic flow chart of a robust multi-sensor multi-target tracking method under a non-uniform clutter background according to an embodiment of the present invention, fig. 2 is a schematic flow chart of a technique for implementing multi-target tracking by fusion of a plurality of limited sensing distance sensors according to an embodiment of the present invention, and fig. 3 is a real target motion track diagram under a linear scene according to an embodiment of the present invention.

Specifically, a multi-target tracking scenario is shown in FIG. 3. It is assumed that there are L sensors in the detection area, each sensor having a limited perceived distance, and that their observations are independent of each other. The multisensor sends measurements to the fusion center, and the fusion measurements at time k can be expressed as:

wherein the observed target and clutter measurement set of each local sensor are respectively

and />

Assume that the non-uniform clutter compliance intensity is kappa (C) =lambda _C f _C Wherein lambda is _C and f_C Clutter rates and clutter spatial densities, respectively, and assume that the clutter distribution in space is non-uniform. In addition, the detection distance of time variation and the unknown target echo signal fluctuation amplitude model are considered to follow Rayleigh distribution. In order to obtain an unknown clutter model and a detection probability model, a clutter estimator and a detection estimator are designed firstly to avoid the reduction of tracking performance caused by the mismatch of clutter and the detection model.

Based on the multi-target tracking scene, the tracking method comprises the following steps:

s1, under the condition that a sensor with a limited detection range does not have a target in an observation area, firstly estimating the clutter rate of non-uniform clutter, and then estimating the space density of the non-uniform clutter based on an unsupervised learning method of model clustering to obtain the estimated clutter rate and the estimated space density. The method specifically comprises the following steps:

s11, under the condition that no target exists in the observation area, the sensor with the limited detection range estimates the clutter rate by maximizing the fusion clutter measurement likelihood function about the clutter rate, and the estimated clutter rate is obtained.

Specifically, assuming no target is present in the observation region, modeling clutter observed by a single sensor as a poisson point process, multiple sensors are linearThe combined clutter remains subject to the poisson point process. Specifically, for each sensor, the clutter rate is constant during the scan, and the fusion clutter measurement sequence of J consecutive time steps is denoted as C _k:k+j Abbreviated as C _J The clutter number is W _J ＝|C _J I, clutter number compliance parameter is lambda _C Poisson distribution of (c):

thus, the likelihood function of the fusion clutter measurement acquired by the fusion center is expressed as:

wherein ,λ_C Is clutter rate, W _J ＝|C _J I is the number of clutter, C _J The fusion clutter measurement sequence is J continuous time steps, L is the number of sensors, and L is the first sensor.

Maximizing the likelihood function of the fusion clutter measurement to obtain an estimated clutter rate:

wherein ,

s12, carrying out parameterization representation on the space density of the non-uniform clutter based on a model clustering method, solving the number and parameter set of Gaussian mixture components in the parameterization representation, and calculating the space density of the non-uniform clutter by utilizing the number and parameter set of the Gaussian mixture components.

Specifically, based on a model clustering method, the spatial density of the heterogeneous clutter is parameterized and represented:

wherein Θ is a parameter set, θ _q For the q-th Gaussian component parameter, i.e. θ _q ＝(m _q ,Σ _q ) Q is {1,2, …, Q }, Q is the number of Gaussian mixture components when the Gaussian mixture components approach the non-uniform clutter spatial density,

the q-th partition cluster of the mixed clutter set, pi _q For the mixing ratio, pi _q Is a logistic regression function with respect to the observation clutter c, i.e

c _m For the mth clutter sample,/th clutter sample>

Is a parameter vector, ++>

For the weight of the q-th component, Θ= (α) ₁ ,…α _Q ；θ ₁ ,…,θ _Q ) Is an unknown set of parameters. />

In practical application, the general component number Q is unknown and needs to be estimated, and the bayesian information criterion (Bayesian information criteria, BIC) is adopted for estimation, namely:

wherein ,

the number of the Gaussian mixture components.

Further, the clutter log-likelihood may be expressed as a finite mixture of components,

then, estimating a parameter set Θ of the gaussian mixture component using a desired maximization method, the parameter set Θ comprising a mixture ratio

Mixed Gaussian component mean vector->

And covariance matrix->

Specifically, given the clutter measurement and gaussian mixture components of the nth iteration, the posterior density of the mth clutter belonging to the qth component can be expressed as:

wherein ,

and->

Respectively define the mth clutter samples c _m The mixing ratio and density function of the q-th component in the nth iteration, and the denominator is a normalization factor.

For the above equation, the conditional desired likelihood function is first found, and the conditional desired likelihood of the complete data can be expressed as:

then maximizing the conditional expectation likelihood function, and solving the following two equations with the n+1th iteration:

further, the model parameters can be found:

/>

wherein ,

Is the mean vector and covariance matrix of the mixture Gaussian components.

And finally, substituting the number Q of the Gaussian mixture components and the parameter set into the parameterized expression formula to obtain the estimated spatial density of the non-uniform clutter.

According to the theoretical derivation process described above, further clutter intensity functions can be expressed as,

s2, based on the echo amplitude characteristics of the target signal in the observation area, the amplitude likelihood function is integrated in a signal-to-noise ratio confidence interval to estimate the detection probability, and the estimated detection probability is obtained. The method specifically comprises the following steps:

s21, based on the target signal echo amplitude characteristics in the observation area obeying Rayleigh distribution, a detection probability model of the target signal echo amplitude characteristics is established.

Specifically, the Rayleigh distribution with the characteristic compliance parameter alpha of the echo amplitude of the target signal is set, namely

Wherein 1+β is a desired signal-to-noise ratio (SNR), SNR (dB) =10log ₁₀ (1+beta). Given a threshold value T, the probability of detection can be expressed as,

wherein ,P_D And (beta) is the detection probability, beta is a signal-to-noise ratio parameter, alpha is the echo amplitude characteristic of the target signal, and T is a gate threshold.

S22, estimating detection probability.

Specifically, first, in general, the probability of detection of an object is typically a random variable due to the distance of the object and the RCS flickering. Assuming that the data correlation is known, the distribution of the signal-to-noise ratio parameter β can be modeled as:

where p (β) is the distribution of the signal-to-noise ratio parameter and ρ is the proportionality constant that makes the probability density integral 1.

Given signal-to-noise ratio SNR interval value [ beta ] ₁ ,β ₂ ]Scaling factor ρ= (ln (1+β) ₂ )-ln(1+β ₁ )) ^-1 The estimated detection probability can be expressed as:

from the above equation, the integral does not have an analytical solution, and the numerical solution of the estimated detection probability can be obtained by MATLAB built-in integral function, i.e.

And S3, transmitting the estimated clutter rate, the estimated space density and the estimated detection probability into a standard TPMB filter to obtain a robust TPMB filter.

Specifically, the standard TPMBM filter is described mathematically as: two mutually disjoint multi-target tracks RFS are respectively denoted as X _U and X_T The probability density of the TPMBM may be expressed as PPP probability density f ^Poisson (X _U ) And TMBM probability density f ^mbm (X _T ) Is (are) convolved, i.e

The probability density of PPP is:

where v (·) is the intensity, which is the undetected target geometry |X _U First order statistical moment of i. The probability density of the MBM random finite set is,

where the symbol' ≡indicates that j is proportional to the index of the multiple Bernoulli mixture (Multi-Bernoulli Mixture, MBM), n is the number of potential detection targets, and the weight and density of the ith Bernoulli component (Bernoulli Component, BC) in the jth MBM mixture is recorded as

and />

X _i For the state of target i, the individual Bernoulli composition densities can be written as:

/>

wherein ,ε_j,i and p_j,i (x) The target existence probability (Existence Probability, EP) and State Density (SD) of the ith BC in the jth MBM blend component, x is a single target State, respectively. Further, the finishing may be:

looking at the above, each summation term corresponds to a global correlation hypothesis (Global Association Hypothesis, GAH).

Further, for a clear description of the MBM structure, please refer to fig. 4, fig. 4 is a schematic diagram of the MBM structure provided in the embodiment of the invention, wherein mt in the figure represents the mth measurement at the t-th moment, mis represents omission, and n.e. represents absence of the target or absence of the target detected. As can be seen from fig. 4, at time step 2, three Single-target association hypotheses (STH) correspond to three global association hypotheses: GAH1, GAH2 and GAH3.

Further, to improve the computational efficiency, the mathematical description of the TPMB filter is obtained by approximating MBM with a single MB component by introducing an auxiliary variable method:

looking at the above equation, it is apparent that the a posteriori density of the TPMB filter contains only one globally hypothesized component.

Further, the clutter rate of the non-uniform clutter estimated in the step S1, the space density of the non-uniform clutter and the detection probability estimated in the step S2 are transmitted into a standard TPMB filter, and a robust TPMB filter is obtained.

Standard TPMBs generally contain four parts: prediction, updating, pruning and estimation. The robust TPMB filter differs from the standard TPMB mainly in the measurement update part, where three complex scene factors are mainly considered: the limited field of view of the sensor, the probability of detection of float, and non-uniform clutter.

Since the estimated parameters only have an influence on the update step, the present embodiment describes only the detailed steps of the update process. At a given predicted intensity v _k|k-1 Number of targets n _k|k-1 And a fused metrology data set Z at the kth time step _k The updated poisson and bernoulli component hypotheses may be divided into four parts: updating undetected targets, updating missed targets, updating detected targets, updating nascent targets.

(1) Updating undetected targets is:

(2) updating the missed detection target. Specifically, for Bernoulli ingredient i ε {1, …,n _k|k-1 In a given state }

In the case of (2), the missed target update may be expressed as:

wherein < f, h > = jc f (x) h (x) dx is the inner product, and the prediction parameter of the ith bernoulli component is

(3) Updating the detected object. Specifically, a fused set of metrology data at a kth time step is given

The update of the ith bernoulli is:

(4) updating the new target. Specifically, for the new Bernoulli composition i ε { n _k|k-1 +j|j∈{1,…,m _k }, it isFusing measurement data sets

Initializing, locally supposing h _i =2, further new target updates can be expressed as,

wherein, the collection

Representing the index of the measurement in the j-th local hypothesis for the i-th bernoulli element.

The global hypothesis data association set is:

wherein ,

a _i is the global hypothesis corresponding to the ith target.

S4, estimating states of the multi-target track by using the robust TPMB filter. The method specifically comprises the following steps:

wherein ,n_k'|k Is the number of the components,

is the neonatal time, < >>

For the weight corresponding to the jth component of the ith target,/for the jth component>

For mean value->

For covariance, k is the kth time step, k' e { k, k+1}, X is the multi-target track.

/>

wherein ,bⁱ In order to start the time of the start-up,

is the mean value of the ith Bernoulli ingredient, < + >>

For covariance, k is track survival until the kth time step, +.>

X is a multi-target track, n _x Is the target state dimension.

S42, reducing the mixed components of the multiple Bernoulli components to obtain a reduction result.

Specifically, in order to reduce the computational complexity, pruning operation, merging operation, limiting operation and recycling operation are performed on a mixed multi-Bernoulli component formed by a plurality of Bernoulli components, namely, a global hypothesis, so as to obtain the reduction result.

Wherein, pruning operation: discarding is performed for bernoulli components whose detection probability is below a given threshold.

Combining: MBM-like Bernoulli ingredients were pooled.

Defining operation: only the global hypothesis of the maximum weight of the front Hmax is reserved for data association.

Recovery operation: the bernoulli ingredient whose existence probability is very small is approximated as a poisson ingredient. Further, approximation error can be measured by minimizing KL divergence:

wherein ,

for the density of the ith Bernoulli ingredient, < >>

The presence probability of the ith Bernoulli ingredient.

Further, the target PPP intensity for which no detection is made becomes after recovery:

wherein ,v_k′ | _k (X) for predicting the multi-target intensity,

for the probability of the presence of the ith Bernoulli element in the h partial hypothesis, Γ _T For the presence probability threshold, <' > for>

For a single target hypothesis at the kth time step, a is associated with omicron for a priori MB hypothesis a and data _k Normalized posterior weight +.>

The weight corresponding to the global hypothesis a.

Specifically, according to the TPMB posterior equation, a set threshold Γ is given _T For the tracks surviving at the kth moment, the existence probability in the reduced result exceeds the set threshold gamma _T The estimated set of tracks can be expressed as

It indicates that the existence probability exceeds Γ _T The mean of the bernoulli components of (c) is the estimated state of the target track.

The tracking method of the embodiment firstly estimates the clutter rate and the space density of the non-uniform clutter under the condition of no target, then estimates the detection probability based on the echo amplitude characteristics of the target signal, and finally estimates the state of a multi-target track by utilizing a steady TPMB filter, so that multi-target tracking for the disappearance of random occurrence is realized by utilizing multi-field fusion under the scene of unknown non-uniform clutter and the detection probability and the limited detection distance of a sensor, and the multi-target tracking performance under the complex non-uniform clutter scene is improved; the detection information of an unknown target is obtained according to the echo amplitude characteristics of the target signal, so that the problem that a fixed detection model is easy to mismatch is solved; meanwhile, continuous target track information can be provided by utilizing the advantage of robustness of the robust TPMB filter on target missed detection, and missed detection and false alarm are reduced.

Further, the embodiment evaluates the multi-target tracking performance of the robust TPMB filter based on the tracking method described above.

Specifically, target tracking performance is evaluated using generalized optimal sub-mode allocation criteria (Generalized Optimal Sub-Pattern Assignment, GOSPA). Given the parameters c, p, and v=2, in the target set x= { x ₁ ,…,x _n And y= { y ₁ ,…,y _n The GOSPA error between } can be expressed as,

where χ is the allocation between the two target sets. Ω is a set of all possible allocations, then there is χ εΩ. The first term above is used to measure the position error of the target, and the second two terms are used to measure the false alarm error and omission of the target. According to the conventional parameter setting rules, parameters c=100 and p=2 are set in experimental simulation of the technology.

1) A linear Gaussian uniform target motion scene.

In the sensor detection range of the set area 2000m×2000m, 11 targets in total appear in 100 scanning periods. The length of time that the ith target is active in the area is tau _i ∈[b,d]s, i.epsilon.N. The multi-target real motion track is shown in fig. 5, and fig. 5 is a real target motion track diagram in a linear scene provided by the embodiment of the invention. In the kth scanning period, the target state and position are x _k ＝[p _x,k ,v _x,k ,p _y,k ,v _y,k ] ^T The measurement vector of the corresponding target is z _k ＝[z _x,k ,z _y,k ] ^T . The motion model of the object is a linear gaussian model, and the transfer function about the state of the object is:

wherein the transfer matrix F and the process noise V are respectively,

wherein the scanning period ts=1.

The measurement likelihood is also Gaussian, and the probability density function (Probability Density Function, PDF) is

Wherein the observation matrix H and the measurement noise R are respectively

Setting survival probability P of target _s =0.99. For PHD type filter and R-TPMB filter, 4 new targets were modeled as Poisson RFS with intensity of

wherein ,

weight ω _b =0.03. For Labeled-type filters, the new parametric model is +.>

wherein />

The maximum number of hypotheses is set to 1000.

First, for Ideal filters Ideal-LMB and Ideal-CPHD filters, the probability p is detected _D =0.97 and clutter rate

Is a known quantity. For the robust filters R-CPHD, DP-GLMB, R-MS-GLMB and the proposed R-TPMB filters, the clutter filtering and detection probabilities need to be estimated. According to the estimation method described above, compared with an advanced DP-GLMB filter, the estimation results of the detection probability and the clutter rate are shown in fig. 6, and fig. 6 is a graph of the detection probability and the clutter rate estimation result in the linear scene provided by the embodiment of the present invention. Next, a non-uniform spatial density of clutter is estimated. The actual clutter space density is represented by a Gaussian mixture model, which is mathematically described as:

wherein ,θ_i ＝{m _i ,Σ _i },i∈{1,2,3,4},m ₁ ＝[-500,0] ^T ,Σ ₁ ＝diag([300 ² ,700 ² ] ^T ),m ₂ ＝[-900,0] ^T ，Σ ₂ ＝diag([700 ² ,500 ² ] ^T ),m ₃ ＝[250,0] ^T ,Σ ₃ ＝diag([200 ² ,600 ² ] ^T ),m ₄ ＝[600,600] ^T ,Σ ₄ ＝diag([300 ² ,300 ² ] ^T ). As shown in fig. 7 and 8, fig. 7 is a graph of the estimation result of the clutter component number in the linear scene provided by the embodiment of the invention, and fig. 8 is a graph of the estimation result of the clutter space density in the linear scene provided by the embodiment of the invention.

Further, as shown in fig. 9, fig. 9 is a graph of a multi-target track tracking result in a linear scenario provided by an embodiment of the present invention. Under the conditions of non-uniform clutter and unknown detection probability, the track tracking results of the R-CPHD, DP-GLMB and R-MS-GLMB and the R-TPMB robust multi-target tracking technology provided by the embodiment are given out in advance, and the observation results can obtain the technical scheme, so that the track tracking method has lower omission and false alarm for tracking the multi-target track. Next, as shown in fig. 10 and fig. 11, fig. 10 is a graph of the multi-target number estimation error in the linear scene provided by the example of the present invention, fig. 11 is a graph of the multi-target number estimation error in the linear scene provided by the example of the present invention, and fig. 10 and fig. 11 show the results of the present embodiment and the other five tracking techniques with respect to the target number estimation. The experimental result shows that the number of targets estimated by the technical proposal and the DP-GLMB and R-MS-GLMB technologies is close to the real target number, and the technical proposal has lower estimation error.

For further measuring the performance advantage of the technical scheme in the aspect of tracking precision, as shown in fig. 12, fig. 12 is a generalized optimal sub-mode distribution error result diagram of multi-target track tracking in a linear scene provided by the example of the present invention, and fig. 12 shows the result of a simulation experiment using 200 Monte Carlo (MC), and quantitatively describes the tracking performance result of each technical scheme under the GOSPA error measurement. Experimental results show that when each local sensor has smaller clutter difference, the provided R-TPMB technical scheme has a slight advantage compared with the DP-GLMB technology and has poorer performance compared with the R-MS-GLMB technology. Notably, the proposed R-TPMB ⁽²⁾ Technical solution (robust tracking implementation of second class TPMB filter), optimal Sub-mode allocation (Optimal Sub-Pattern Assignment, OSPA) and Track-Track Optimal Sub-mode allocation (Track-to-Track Optimal Sub-Pattern Assignment, OSPA) ⁽²⁾ ) The obtained multi-target tracking precision still has the best tracking performance under the condition of smaller difference of the local sensors, the experimental result is shown in fig. 13, and fig. 13 is a graph of two optimal sub-mode distribution error results of multi-target track tracking in a linear scene provided by the embodiment of the invention.

2) Nonlinear distance and azimuth target motion scene.

Under the nonlinear target motion scene, assuming that 7 targets appear in total in 100 scanning periods in the region of 3500m×2000m of the detectable region, the real track information of the targets is shown in fig. 14, and fig. 14 is a true view of the nonlinear scene provided by the embodiment of the inventionAnd a real target motion trail graph. Setting survival probability P of target _s =0.99, single target state transition model is:

x _k ＝F(ω _k-1 )x _k-1 +G

ω _k ＝ω _k-1 +u _k-1

wherein ,

T _s ＝1s,σ _ω ＝10m/s ² ,σ _u the state transition matrix F is pi/180 rad/s with the process noise matrix G: />

The metrology model for a single target is expressed as:

wherein the position of the first sensor is

Taking two sensors as an example, the position of the sensor 1 is set to be [ -1500,0]The position of the sensor 2 is [1000,0 ]]Measuring noise vector

wherein σ_r ＝10m,σ _θ ＝π/180rad。

First, for CPHD-like and R-TPMB multi-eye tracking techniques, the target neonatal distribution model is known and the same for all sensors. Assuming that the number of the new targets is 4, the new positions of all the new targets are respectively

For the Ideal-LMB filter, the new density is

Wherein survival probability->

PDF of a single labeled Bernoulli ingredient

Then, for robust R-CPHD, DP-GLMB, R-MS-GLMB multi-target tracking techniques, the detection model for each target is modeled as a beta distribution. For DP-GLMB and R-MS-GLMB, the new model adopts measurement to drive the new model, and the maximum new probability is set as R _B,max =0.02, neocovariance p _B ＝Σ _b . Assuming that two local sensors have the same clutter rate, i.e

For Ideal Ideal-CPHD and Ideal-LMB, the local sensor knows the clutter rate and the detection probability P _D =0.97. For a robust multi-target tracking technique, as shown in fig. 15, fig. 15 is a graph of the estimated detection probability and clutter rate in a nonlinear scenario provided by the embodiment of the present invention, regarding the estimated detection probability and clutter rate.

Next, the spatial probability density of non-uniform clutter is modeled using a Gaussian mixture model, i.e

wherein ,θ_i ＝{m _i ,Σ _i }，i∈{1,2,3,4}，m ₁ ＝[-1300,1200] ^T ，Σ ₁ ＝diag([500 ² ,500 ² ] ^T )，m ₂ ＝[-1000,700] ^T ，Σ ₁ ＝diag([600 ² ,400 ² ] ^T )，m ₃ ＝[200,1200] ^T ，Σ ₃ ＝diag([500 ² ,350 ² ] ^T )，m ₄ ＝[800,900] ^T ，Σ ₄ ＝diag([200 ² ,700 ² ] ^T ). Next, regarding the estimation results of the number of clutter components and the spatial distribution of the clutter probability, if fig. 16 and 17 show, fig. 16 is a graph of the estimation results of the number of clutter components in the nonlinear scene provided by the embodiment of the present invention, and fig. 17 is a graph of the estimation results of the spatial density of clutter in the nonlinear scene provided by the embodiment of the present invention. As shown by experimental results, compared with the DP-GLMB technology, the clutter space density estimator designed by the embodiment can better estimate the space distribution of non-uniform clutter.

Finally, the estimated clutter and detection probability are used as inputs of conventional CPHD, GLMB and TPMB filters to realize robust multi-target track tracking. For nonlinear scenarios, RFS filter implementations are implemented using unscented kalman filters (Unscented Kalman Filter, UKF). Under different multi-target tracking technologies, the obtained track estimation results are shown in fig. 18, and fig. 18 is a graph of multi-target track tracking results in a nonlinear scene provided by the embodiment of the invention. As shown by experimental results, the R-TPMB robust multi-target tracking technology provided by the embodiment has less false tracks and missed detection compared with the R-CPHD robust tracking technology. In addition, compared with the DP-GLMB in the R-MS-GLMB robust tracking technology, the obtained track has higher integrity and smoothing effect.

Further, in order to quantitatively evaluate the advantages of the technology in terms of target number estimation and track tracking precision, the invention utilizes 200 MC experiments and adopts six different multi-target tracking technologies to respectively obtain experimental results of target number and track tracking precision, the experimental results are shown in figures 19-21, figure 19 is a multi-target number estimation error result graph in a nonlinear scene provided by the embodiment of the invention, figure 20 is a multi-target number estimation result graph in the nonlinear scene provided by the embodiment of the invention, and figure 21 is a generalized optimal sub-mode distribution error result graph of multi-target track tracking in the nonlinear scene provided by the embodiment of the invention. The experimental result shows that the technology of the embodiment has lower mean square error in the aspect of target number estimation and lower GOSPA error in the aspect of flight path estimation precision, and the advantages of strong robustness and high tracking precision in the aspect of multi-target tracking are verified.

Still further, to better assess the advantages of the present embodiment in terms of flight path continuity, OSPA was utilized ⁽²⁾ Error metric criteria, given in OSPA by 200 MC experiments ⁽²⁾ As shown in FIG. 22, FIG. 22 is a graph of error results of two optimal sub-mode allocation error results for multi-target track tracking in a nonlinear scenario provided by the example of the present invention. As is clear from the experimental results, the R-TPMB of the present example ⁽²⁾ The conclusion of the technology under the two error measurement criteria is consistent, namely, compared with other multi-target tracking technologies, the error obtained by the technology of the embodiment is minimum, and the obtained track tracking precision is relatively high, so that the better application value of the embodiment in the aspects of multi-target tracking, namely robustness and tracking precision, is verified.

The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.

Claims

1. A robust multi-sensor multi-target tracking method under a non-uniform clutter background is characterized by comprising the following steps:

2. The robust multi-sensor multi-target tracking method in non-uniform clutter background of claim 1, wherein step S1 comprises:

3. The robust multi-sensor multi-target tracking method in non-uniform clutter background of claim 2, wherein step S11 comprises:

wherein ,λ_C Is clutter rate, W _J ＝|C _J I is the number of clutter, C _J The method comprises the steps of fusion clutter measurement sequences of J continuous time steps, wherein L is the number of sensors, and L is the first sensor;

wherein ,

4. the robust multi-sensor multi-target tracking method in non-uniform clutter background of claim 2, wherein step S12 comprises:

c _m For the m-th clutter sample,

is a parameter vector, ++>

wherein ,

the number of the Gaussian mixture components;

wherein ,

C is the mean vector of the Gaussian mixture component _m Is the mth impurityWave sample,/->

The mean vector and covariance matrix are the mixed Gaussian components;

5. The robust multi-sensor multi-target tracking method in non-uniform clutter background of claim 1, wherein step S2 comprises:

/>

s22, establishing a distribution model of signal-to-noise ratio parameters:

6. The robust multi-sensor multi-target tracking method in non-uniform clutter background of claim 1, wherein in the robust TPMB filter, updated poisson and bernoulli component hypotheses comprise: updating undetected targets, updating missed targets, updating detected targets, updating nascent targets.

7. The robust multi-sensor multi-target tracking method in non-uniform clutter background of claim 1, wherein step S4 comprises: