Self-adaptive new multi-extended target tracking method

[0028] The following describes in detail the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary, and are intended to explain the present invention and should not be construed as limiting the present invention.

[0029] In this application document, the following terms are used: 'std' means standard Poisson-Do Bernoulli mixing filtering based on fixed nascent distribution, 'tb' means filtering based on adaptive nascent distribution, 'gbs' means Gibb Sampling, 'BGGIW' means filtering based on unknown detection probability, 'ture value' means actual but unknown detection probability, 'PHD' means probability hypothesis density filtering.

[0030] see figure 1 , the present invention proposes an adaptive new-born multi-expansion target tracking method, comprising the following steps:

[0031] S1: Initialize system parameters and adapt to the new expansion target;

[0032] S2: forming an augmented vector of the expanded target in combination with the unknown detection probability;

[0033] S3: filter for prediction and correction;

[0034] S4: A Gibbs sampler is used to truncate the filter density to extract high-weight global hypotheses.

[0035] In the process of initializing the system parameters and adapting the new extended target, the Gaussian distribution and Euclidean metric are used to describe the likelihood and proximity between the target and the measurement, and then the likelihood function and proximity are used to represent the target and the measurement. The correlation between measurements is finally used to generate new targets near the measurements.

[0036] In the process of forming the augmented vector of the expanded target in combination with the unknown detection probability, the unknown detection probability is described by the beta distribution, the target state is described by the Gamma-Gaussian inverse Wishart distribution, and then combined to form the augmented state space.

[0037] Wherein, the augmented state space is formed by combining the unknown detection probability space and the extended target state space, and the transition density function of the augmented state is obtained by the product of the transition density function of the target and the evolution function of the unknown detection probability.

[0038] In the process of filtering prediction and correction, the Poisson-Do-Bernoulli mixture filter is used to recurse the new target, potential target and multi-Bernoulli mixture components, and the posterior information of the Poisson-Do-Bernoulli mixture density is obtained.

[0039] Further, in the recursive operation, the nascent target, the potential target and the multi-Bernoulli mixture are first predicted, and then the prediction result is corrected, which includes the nascent target, the potential target and the multi-Bernoulli mixture. Missing detections, nascent and potential targets detected for the first time, and updates to the DoBernoulli mix.

[0040] In the process of using the Gibbs sampler to truncate the filter density and extract high-weight global hypotheses, the cost matrix is ​​first generated according to the different sources of measurement, and then the disordered Gibbs sampler is obtained through the Markov chain-based Gibbs sampler. A collection of positive 1-1 vectors.

[0041] see figure 2 , each step is described in detail below:

[0042] S1. Initialize system parameters and adapt to the new extension target.

[0043] Specifically, initialize the system parameters, including: the cutoff parameter c of the reference distance, the penalty parameter p of the outliers, and the size N of the tracking scene plane x ×N y , transition matrix F, process noise Q, survival probability P s. New target adaptive using likelihood and proximity between measure and target where a i and beta i The parameters of the gamma distribution that describe the number of measurements produced by the target, m i and P i are the Gaussian distribution parameters describing the target centroid and covariance, v i and V i is the inverse Wishart distribution parameter describing the shape of the target, s i and t i is the beta distribution parameter describing the detection probability, λ exp is the mean of the number of new students.

[0044] Let the measurement received at the previous moment (here assumed to be the kth moment) be z k,1 =[x k,1 ,y k,1 ] T ,…,z k,N =[x k,N ,y k,N ] T ∈Z, N is the number of measurements. Set in the DoBernoulli Mixture (MBM) after correction, the centroid of the target is Calculate the likelihood between the measurement and the target through a Gaussian distribution

[0045]

[0046] where Σ represents the covariance corresponding to the target, det( ) represents the determinant of the matrix, and the likelihood truncation threshold λ is used g Pick out the corresponding measurement set Z g. Then the target centroid is calculated by the Euclidean metric and measure z k,g =[x k,g ,y k,g ]∈Z g proximity between

[0047]

[0048] Reuse the proximity cutoff threshold λ d Pick out the corresponding measurement set Z d.

[0049] Since the prior information of the target newborn is unknown, each measurement z k,d ∈Z d It is possible to generate new targets, that is, each measurement must generate a corresponding BGGIW component, and its weight is

[0050]

[0051] where w max represents the maximum weight of the nascent BGGIW component, λ exp Expected value for the number of ingredients in the freshman BGGIW.

[0052] S2. Combine the unknown detection probability to form the augmented vector of the expanded target, specifically, use the beta distribution to describe the unknown detection probability, use the Gamma-Gaussian inverse Wishard distribution to describe the target state, and then combine them into an augmented vector.

[0053] Further, let X be the extended target state space, X (^) represents the unknown detection probability space, then the augmented state space is expressed as

[0054]

[0055] where × denotes the Cartesian product, each augmented state by extending the target state x ∈ X and increasing the detection probability η ∈ X (^) =[0,1] composition. The transfer density function can be expressed as

[0056]

[0057] where f k|k-1 (·|·) represents the target state transition density, is the evolution function of detection probability. The survival probability and detection probability of the augmented state are

[0058]

[0059]

[0060] S3: Predicting and correcting by filtering, specifically filtering the new target, the potential target and the Poisson-Do-Bernoulli mixture, respectively, to obtain the posterior information of the Poisson-Do-Bernoulli mixture density.

[0061] Further, the strength of the new target and potential target at time k-1 is mixed by BGGIW, respectively

[0062]

[0063]

[0064] Among them, B( ) is the beta distribution, which represents the change of the unknown detection probability, and s and t are its corresponding parameters. GGIW( ) is the GGIW distribution, which consists of a gamma probability density function, a multivariate Gaussian probability density function, and an inverse Schattter distribution. The function of the gamma probability density function is to describe the quantitative change of the measurement generated by the expansion target, and the multivariate Gaussian probability The function of the density function is to describe the change of the centroid of the expanded target and its corresponding covariance, while the inverse is the Schatt distribution, which represents the shape change of the expanded target, and α, β, m, P, v, and V are their corresponding parameters. Let the DoBernoulli mixing density at time k-1 be expressed as

[0065]

[0066]

[0067] in represents the probability density function of the nth Bernoulli in the sth multi-Bernoulli, is its corresponding existence probability, represents the weight of the s-th multi-Bernoulli, Π s represents the index set of Bernoulli in the s-th multi-Bernoulli.

[0068] First, the nascent target, potential target and multi-Bernoulli mixture are predicted. The prediction results of the nascent target and potential target are also the mixed form of BGGIW, and the prediction result of each Bernoulli in the multi-Bernoulli mixture is a single BGGIW. form, the overall prediction can also be represented by the hybrid form of BGGIW. The second is to correct the predicted results. The correction stage is divided into the following four steps:

[0069] 1) Missing detection of nascent targets and potential targets.

[0070] 2) New targets and potential targets are detected for the first time.

[0071] 3) Missing detection of Poisson-Do Bernoulli mixing.

[0072] 4) Correction for Poisson-Do Bernoulli mixing.

[0073] Also the components after the correction stage can be represented by a mixed form of BGGIW.

[0074] S4. A Gibbs sampler is used to truncate the filter density to extract high-weight global hypotheses.

[0075] Specifically, a cost matrix is ​​generated according to different sources of measurement

[0076]

[0077]

[0078] C miss,i =-ln(1-r k,i +r k,i (1-P d ))

[0079] where r k,m and r k,i is the existence probability of the surviving Bernoulli component, is its corresponding probability density function, l( ) is the predicted likelihood function, W n is the measurement cell obtained by the measurement division, represents the integral of a and b, is the probability density function of the potential target, κ C is the clutter intensity, P d is the detection probability.

[0080] After the cost matrix is ​​obtained, the global hypothesis of data association is obtained through the Gibbs sampler based on the Markov chain. The transfer kernel function of the Gibbs sampler is expressed as

[0081]

[0082] where υ' represents a global hypothesis of the joint assignment problem, and its physical meaning is the detection of n1 surviving Bernoulli components. represents an unordered set of positive 1-1 vectors representing the association between measurement cells and targets, and represents a positive 1-1 vector.

[0083] The present invention also verifies the adaptive new multi-expansion target tracking method through simulation experiments:

[0084] 1. Simulation conditions: The present invention uses MATLAB R2020a software to complete the simulation on a computer with Intel(R) Core(TM) i7-7700 CPU@3.60GHz and memory 8.0GB processor.

[0085] 2. Simulation scene setting: consider that in a two-dimensional scene of [-200,200]m×[-200,200]m, a total of 27 randomly generated targets move 100 time steps through a uniform motion model in the surveillance area, such as image 3 shown, its corresponding measurement distribution is in Figure 4 given in. Poisson rate λ x = 20, detection probability P d = 0.9, the number of measurements produced by each target obeys the mean λ x = 8 Poisson distribution. The transition matrix F and the process noise Q are respectively

[0086]

[0087] where T s =1 represents the time interval and σ=0.1 represents the noise driving parameter.

[0088] Fixed freshman distribution D b The intensity of (x) is expressed in the form of a GGIW mixture

[0089]

[0090] w b,1 =w b,2 =0.02,w b,3 =w b,4 =0.03

[0091] m b,1 =[-75,-75,0,0],m b,2 =[-75,75,0,0]

[0092] m b,3 =[75,75,0,0],m b,4 =[75,-75,0,0]

[0093] alpha b,i =32,β b,i =4,v b,i =12

[0094] P b,i =diag([1,1,1,1] T ) 2 ,V b,i =diag([12,12] T ), where i∈{1,2,3,4}.

[0095] In scenario 1, such as Figure 5 and Image 6 shown that the base estimates for the adaptive and fixed birth distributions are nearly equal, except for a few time steps after the target birth. In addition, after the birth of a new target, the estimated value of the cardinality of the fixed birth distribution is larger than the estimate of the cardinality of the adaptive birth distribution, because the expected target births of the adaptive birth distribution are allocated to more BGGIW components . Therefore, the weight of the new target is lower, and the potential estimate will grow at a slower rate. In the time steps before and after the target birth, relative to the fixed birth distribution, the OSPA distance and GOSPA distance (including LE, ME, and FE) adapted to the birth distribution were larger, while at other times, they were almost equal. For the adaptive birth distribution, all estimates start at the second time step, because the measurements from the first time step are used to generate new targets. The estimated mean values ​​are given in Table 1, and it can be seen that the use of the Gibbs sampler has no obvious effect on the estimation accuracy, but can greatly improve the estimation efficiency.

[0096] Table 1: Estimated Means

[0097] filter std PMBM-tb PMBM-tb-gbs OSPA 0.918 1.150 1.171 GOSPA 7.506 8.744 8.884 LE 5.631 5.844 6.124 ME 0.229 0.362 0.335 FE 0.146 0.218 0.217 Time 245.827 775.073 413.713

[0098] In scenario 2, such as Figure 7As shown, the OSPA distance and potential estimates of the robust PMBM filter are very close to the standard PMBM filter. also, Figure 8 The comparison of the GOSPA distance in the middle also reflects similar conclusions to the OSPA distance. The robustness to ME is slightly stronger than that of the standard PMBM filter due to the online adaptive adjustment capability of the robust PMBM filter. As can be seen from Table 2, as expected, the Gibbs sampler can greatly improve the estimation efficiency without changing the estimation accuracy.

[0099] Table 2: Estimated Means

[0100] filter std BGGIW-PMBM BGGIW-PMBM-gbs OSPA 0.918 0.942 0.991 GOSPA 7.506 7.657 7.989 LE 5.631 5.772 5.959 ME 0.229 0.077 0.099 FE 0.146 0.301 0.307 Time 245.827 1022.45 564.494

[0101] In scenario 3, such as Figure 9 and Figure 10 shown, similar to the previous conclusions, except for the moment near the birth of the new target, the estimates of the filter using the adaptive birth distribution are very close to those of the filter using the fixed birth distribution. The estimated value of the unknown probability filter is also close to the estimated value of the known probability filter. The estimated mean values ​​are given in Table 3, and it can be seen that the Gibbs sampling method greatly reduces the computation time of the filter.

[0102] Table 3: Estimated Means

[0103] filter std BGGIW-PMBM BGGIW-PMBM-tb BGGIW-PMBM-tb-gbs PMBM-tb OSPA 0.821 0.936 1.108 1.162 1.118 GOSPA 6.513 7.217 8.744 8.752 8.075 LE 5.533 5.472 5.659 5.707 5.410 ME 0.084 0.212 0.312 0.324 0.395 FE 0.112 0.317 0.305 0.285 0.138 Time 217.44 248.035 1119.091 618.319 389.277

[0104] In scenario 4, such as Figure 11 and Figure 12 shown, it can be seen that the performance of the BGGIW-PHD-tb filter is much worse than the other filters, which can be well explained as the PHD filter is less tolerant when the number of targets is large. The BGGIW-PMBM-tb filter has the best performance in all aspects.

[0105] Aiming at the multi-expanded target tracking problem of unknown detection probability and unknown birth position, the present invention proposes a BGGIW-PMBM algorithm, wherein the unknown detection probability is described by Beta distribution, and the target birth intensity is modeled by adaptive newborn distribution. Adopt Gibbs sampler to reduce the computational burden caused by data association. Four scenarios are used to verify the superiority of the proposed algorithm. Scenario 1 proves the high efficiency of the filter under Gibbs sampling and the stability of target adaptive regeneration; Scenario 2 proves the performance of the filter when the unknown detection probability is described by the beta distribution. Effectiveness; Scenario 3 gives the efficiency of the filter under the conditions of the combination of adaptive new algorithm, unknown detection probability algorithm and Gibbs sampling; Scenario 4 is a combination of PMBM filter and other filters. Comprehensive comparison, thus proving the accuracy of PMBM algorithm.

[0106] The above disclosure is only a preferred embodiment of the present invention, and of course, it cannot limit the scope of rights of the present invention. Those of ordinary skill in the art can understand that all or part of the process for realizing the above-mentioned embodiment can be realized according to the rights of the present invention. The equivalent changes required to be made still belong to the scope covered by the invention.