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

Abstract

The present invention relates to a robust multi-sensor multi-target tracking method in a non-uniform clutter background, comprising: first, when a sensor with a limited detection range has no targets within the observation area, estimating the clutter rate of the non-uniform clutter, then estimating the spatial density of the non-uniform clutter to obtain an estimated clutter rate and an estimated spatial density; estimating the detection probability by integrating the amplitude likelihood function within a signal-to-noise ratio confidence interval based on the target signal echo amplitude characteristics within the observation area to obtain an estimated detection probability; passing the estimated clutter rate, estimated spatial density, and estimated detection probability into a standard TPMB filter to obtain a robust TPMB filter; and estimating the state of the multi-target tracks using the robust TPMB filter. In scenarios with unknown non-uniform clutter and detection probability and limited sensor detection range, this method utilizes multi-field-of-view fusion to achieve tracking of multiple targets that appear and disappear randomly, addressing the problem of mismatch in fixed detection models and providing continuous target track information.

Description

Technical Field

[0001] The present invention belongs to the field of tracking technology, and in particular relates to a robust multi-sensor multi-target tracking method under a non-uniform clutter background. Background Art

[0002] Multi-Object Tracking (MOT) involves simultaneously estimating the number and time-varying dynamic states of multiple targets. It has been widely used in various applications, such as autonomous driving, multi-pedestrian tracking, satellite video, and radar sensor networks. However, MOT is complicated by the uncertainties inherent in real-world engineering scenarios, such as the limited sensing range of a single sensor, false alarms, misdetections, and data association uncertainty. Against this backdrop, researchers at home and abroad have proposed utilizing multiple sensors to obtain greater information gain, thereby reducing system uncertainty and improving the performance of tracking algorithms. Currently, multi-sensor multi-target tracking has become a hot topic in information fusion research.

[0003] In the field of multi-target tracking, commonly used tracking methods can be divided into three categories: Joint Probability Data Association (JPDA), Multiple Hypotheses Tracking (MHT), and Random Finite Set (RFS) multi-target tracking. Currently, various multi-sensor multi-target filters typically use Random Finite Set (RFS) filters. Unlabeled RFS filters include Probability Hypothesis Density (PHD), Cardinality PHD (CPHD) filters, and Multi-Bernoulli (MeMBer) filters. However, label-free RFS filters struggle to provide target identity information. To address this, researchers have developed labeled RFS filters by adding unique labels to targets. These filters, such as the δ-Generalized Labeled Multi-Bernoulli (δ-GLMB) and Labeled Multi-Bernoulli (LMB) filters, can provide both continuous target tracks and identity information. However, it is worth noting that although label RFS filters are applicable to many scenarios, they are prone to ambiguity in target-label association for newly generated targets in independent identically distributed cluster (IIDC) processes. To this end, researchers have proposed MOT based on trajectory sets, such as the Trajectory Poisson Multi-Bernoulli filter (TPMB), which replaces the use of labels to estimate the target state set to resolve the ambiguity in the target-label association.

[0004] To address the uncertainty in the target birth process, adaptive measurement-driven birth is applied to the tag RFS filter. For both the δ-GLMB and LMB filters, adaptive birth significantly improves target track estimation in the IIDC process with large spatial uncertainties. However, in terms of tracking accuracy and computational efficiency, the TPMB filter outperforms the adaptive birth RFS filter. To further improve tracking accuracy and computational efficiency, the TPMB filter is selected for multi-target track estimation.

[0005] In addition to the aforementioned challenges, more practical challenges such as clutter and unknown prior information about detection can also degrade the performance of multi-target tracking. To address these issues, researchers have proposed robust algorithms for single-sensor MOT that adapt to the mismatch between clutter rate and detection. Mahler et al. designed a robust CPHD (R-CPHD) filter to obtain the clutter rate and detection probability during filtering. Furthermore, they developed an adaptive generalized multi-Bernoulli (DP-GLMB) filter to provide target trajectories based on the unknown prior information about the clutter rate, detection probability, and birth model. Building on this, a robust multi-sensor GLMB (R-MS-GLMB) filter was proposed, which demonstrates good performance in scenarios with fluctuating backgrounds. It is worth noting that the aforementioned robust algorithms typically assume that clutter points are uniformly distributed across the surveillance area. Currently, no multi-sensor multi-target tracking technology addresses the challenges of limited sensing range, unknown non-uniform clutter, and fluctuating target detection characteristics. Summary of the Invention

[0006] In order to solve the above problems existing in the prior art, the present invention provides a robust multi-sensor multi-target tracking method in a uniform clutter background. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0007] An embodiment of the present invention provides a robust multi-sensor multi-target tracking method in a non-uniform clutter background, comprising the steps of:

[0008] S1. A sensor with a limited detection range, under the condition that no target exists in the observation area, first estimates the clutter rate of non-uniform clutter, and then estimates the spatial density of the non-uniform clutter using an unsupervised learning method based on model clustering to obtain an estimated clutter rate and an estimated spatial density;

[0009] S2. Based on the target signal echo amplitude characteristics in the observation area, the detection probability is estimated by integrating the amplitude likelihood function within the signal-to-noise ratio confidence interval to obtain an estimated detection probability;

[0010] S3. Passing the estimated clutter rate, the estimated spatial density, and the estimated detection probability into a standard TPMB filter to obtain a robust TPMB filter;

[0011] S4. Estimate the state of multiple target tracks using the robust TPMB filter.

[0012] In one embodiment of the present invention, step S1 includes:

[0013] S11. Under the condition that no target exists in the observation area, the sensor with limited detection range estimates the clutter rate by maximizing the fused clutter measurement likelihood function with respect to the clutter rate to obtain the estimated clutter rate;

[0014] S12. Based on a model clustering method, the spatial density of the non-uniform clutter is parameterized, and the number and parameter set of Gaussian mixture components in the parameterized representation are solved. The spatial density of the non-uniform clutter is calculated using the number and parameter set of the Gaussian mixture components to obtain the estimated spatial density.

[0015] In one embodiment of the present invention, step S11 includes:

[0016] Under the condition that there is no target in the multi-sensor observation area, based on modeling the clutter observed by a single sensor as a Poisson point process and the clutter of the linear combination of multiple sensors obeys the Poisson point process, the likelihood function of the fusion center obtaining the fused clutter measurement is expressed as:

[0017]

[0018] Among them, λ C is the clutter rate, W J =|C J | is the number of clutter, C J is a fusion clutter measurement sequence of J consecutive time steps, L is the number of sensors, and l is the lth sensor;

[0019] Maximizing the likelihood function of the fused clutter measurement yields the estimated clutter rate:

[0020]

[0021] in,

[0022] In one embodiment of the present invention, step S12 includes:

[0023] Based on the model clustering method, the spatial density of the non-uniform clutter is parameterized:

[0024]

[0025] Among them, Θ is the parameter set, θ q is the qth Gaussian component parameter, that is Q is the number of Gaussian mixture components when using Gaussian mixture components to approximate the non-uniform clutter spatial density, is the qth partition cluster of the mixed clutter set, π q is the mixing ratio, c m is the mth clutter sample, is the parameter vector, is the weight of the qth component, Θ=(α1,…α Q ;θ1,…,θ Q) is a set of unknown parameters;

[0026] The number of Gaussian mixture components is estimated using the Bayesian Information Criterion:

[0027]

[0028] in, is the number of Gaussian mixture components;

[0029] The parameter set of the Gaussian mixture components is estimated using the expectation maximization method:

[0030]

[0031]

[0032]

[0033] in, is the ratio of mixed components, W J is the number of clutter measurements, m is the mth clutter sample, is the posterior density of the mth clutter sample belonging to the qth cluster, n is the number of iterations, is the mean vector of the mixed Gaussian components, c m is the mth clutter sample, is the mean vector and covariance matrix of the mixed Gaussian components;

[0034] The number and parameter set of the Gaussian mixture components are substituted into the parameterized representation to obtain the estimated spatial density.

[0035] In one embodiment of the present invention, step S2 includes:

[0036] S21. Based on the fact that the target signal echo amplitude characteristics in the observation area obey the Rayleigh distribution, a detection probability model of the target signal echo amplitude characteristics is established:

[0037]

[0038] Among them, P D (β) is the detection probability, β is the signal-to-noise ratio parameter, α is the target signal echo amplitude characteristic, and T is the threshold value;

[0039] S22. Establish a distribution model of signal-to-noise ratio parameters:

[0040]

[0041] 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 equal to 1;

[0042] Given the signal-to-noise ratio interval value [β1,β2], the scaling factor ρ = (ln(1+β2)-ln(1+β1)) -1 , the amplitude likelihood function can be obtained by integrating the signal-to-noise ratio parameter β, and the amplitude likelihood function is substituted into the detection probability model to obtain the estimated detection probability:

[0043]

[0044] The numerical solution of the estimated detection probability is obtained by using the built-in integration function of MATLAB:

[0045]

[0046] Among them, integral is the integral function and @ is the anonymous function symbol.

[0047] In one embodiment of the present invention, in the robust TPMB filter, the updated Poisson component hypothesis and the Bernoulli component hypothesis include: updating undetected targets, updating missed targets, updating detected targets, and updating new targets.

[0048] In one embodiment of the present invention, step S4 includes:

[0049] S41. Using the robust TPMB filter, the Gaussian mixture intensity of the new Poisson component in the fusion measurement of multiple sensors at the target time is expressed as:

[0050]

[0051] Among them, n k'|k is the number of components, It's freshman time. is the weight of the jth component corresponding to the i-th target, is the mean, is the covariance, k is the kth time step, k'∈{k,k+1}, X is the multi-target track;

[0052] Using the robust TPMB filter, the spatial density of the i-th Bernoulli component in the fusion measurement of multiple sensors at the target time is expressed as:

[0053]

[0054] Among them, b i is the starting time, is the mean of the i-th Bernoulli component, is the covariance, k is the track survival until the kth time step, n x is the target state dimension;

[0055] S42, reducing a multi-Bernoulli mixture component formed by multiple Bernoulli components to obtain a reduction result;

[0056] S43: The existence of a Bernoulli component in the reduction result with a probability exceeding a set threshold is regarded as a state of the multi-target track.

[0057] In one embodiment of the present invention, step S42 includes:

[0058] A pruning operation, a merging operation, a limiting operation, and a recycling operation are performed on the multi-Bernoulli mixture components to obtain the reduction result.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] The tracking method of the present invention first estimates the clutter rate and spatial density of non-uniform clutter under the condition of no target, then estimates the detection probability based on the target signal echo amplitude characteristics, and finally estimates the status of multiple target tracks using a robust TPMB filter. In scenarios with unknown non-uniform clutter and detection probability and limited sensor detection range, the method not only achieves tracking of multiple targets that appear and disappear randomly using multi-field fusion, but also obtains detection information of unknown targets based on the target signal echo amplitude characteristics, solving the problem of easy mismatch of fixed detection models. At the same time, the robust TPMB filter's advantage in robustness to missed target detection can be used to provide continuous target track information, reducing missed detections and false alarms. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A flowchart of a robust multi-sensor multi-target tracking method under a non-uniform clutter background provided by an embodiment of the present invention;

[0062] Figure 2 A schematic diagram of the technical process of implementing multi-target tracking by fusing multiple limited-perception-range sensors provided by the present invention;

[0063] Figure 3 A schematic diagram of a multi-target tracking scenario provided by an example of the present invention;

[0064] Figure 4 A schematic diagram of an MBM structure provided in an embodiment of the present invention;

[0065] Figure 5 This is a real target motion trajectory diagram in a linear scenario provided by an example of the present invention;

[0066] Figure 6 This is a diagram showing the estimation results of detection probability and clutter rate in a linear scenario provided by an example of the present invention;

[0067] Figure 7 This is a diagram showing the estimation results of the number of clutter components in a linear scenario provided by an example of the present invention;

[0068] Figure 8 This is a diagram of the clutter spatial density estimation result in a linear scenario provided by an example of the present invention;

[0069] Figure 9 This is a diagram showing the multi-target tracking results in a linear scenario provided by an example of the present invention;

[0070] Figure 10 This is a graph showing the error results of multi-target number estimation in a linear scenario provided by an example of the present invention;

[0071] Figure 11 This is a diagram showing the result of multi-target number estimation in a linear scenario provided by an example of the present invention;

[0072] Figure 12 This is a diagram showing the generalized optimal sub-mode allocation error results for multi-target track tracking in a linear scenario provided by an example of the present invention;

[0073] Figure 13 The error result diagram of two optimal sub-mode allocations for multi-target track tracking in a linear scenario provided by the example of the present invention;

[0074] Figure 14 The actual target motion trajectory diagram in the nonlinear scenario provided by the example of the present invention;

[0075] Figure 15 This is a diagram showing the estimation results of detection probability and clutter rate in a nonlinear scenario provided by an example of the present invention;

[0076] Figure 16 This is a diagram showing the estimation results of the number of clutter components in a nonlinear scenario provided by an example of the present invention;

[0077] Figure 17 This is a diagram showing the clutter spatial density estimation results in a nonlinear scenario provided by an example of the present invention;

[0078] Figure 18 This is a diagram showing the multi-target tracking results in a nonlinear scenario provided by an example of the present invention;

[0079] Figure 19 This is a graph showing the error results of multi-target number estimation in a nonlinear scenario provided by an example of the present invention;

[0080] Figure 20 This is a graph showing the result of multi-target number estimation in a nonlinear scenario provided by an example of the present invention;

[0081] Figure 21 This is a diagram showing the error results of the generalized optimal sub-mode allocation for multi-target track tracking in a nonlinear scenario provided by an example of the present invention;

[0082] Figure 22This is a graph showing the error results of two optimal sub-mode allocations for multi-target track tracking in a nonlinear scenario provided by an example of the present invention. DETAILED DESCRIPTION

[0083] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0084] Example 1

[0085] This embodiment provides a robust multi-sensor multi-target tracking method in a non-uniform clutter background. The method is based on the following principles: utilizing the complementary characteristics of multi-field-of-view information of sensors to obtain multi-target motion information in the global field of view; improving the robustness of multi-target tracking in complex backgrounds by adaptively estimating unknown prior detection and clutter model parameters; reducing track missed detections and false alarms based on a track Poisson multi-Bernoulli filter, and improving the continuity of multi-target tracking tracks; and verifying the effectiveness of the present invention through experimental results of tracking multiple targets in typical linear and nonlinear scenarios.

[0086] See Figure 1 、 Figure 2 and Figure 3 , Figure 1 A flowchart of a robust multi-sensor multi-target tracking method in a non-uniform clutter background provided by an embodiment of the present invention is provided. Figure 2 This is a schematic diagram of the technical process of realizing multi-target tracking by fusing multiple limited-perception-range sensors provided by the present invention. Figure 3 This is a diagram of the actual target motion trajectory in a linear scenario provided by the example of the present invention.

[0087] Specifically, multi-target tracking scenarios such as Figure 3 As shown in Figure 2. Assume that there are L sensors in the detection area, each sensor has a limited sensing range, and assume that their observation data are independent of each other. Multiple sensors send measurements to the fusion center, and the fused measurement at time k can be expressed as:

[0088]

[0089] Among them, the target and clutter measurement sets observed by each local sensor l are and

[0090] Assume that the non-uniform clutter obeys the strength κ(C) = λ C f C Poisson process, where λ C and f Cwhere is the clutter rate and spatial clutter density, respectively, and the spatial distribution of clutter is assumed to be non-uniform. Furthermore, the time-varying detection range and the amplitude fluctuation model of the unknown target echo signal are considered to follow a Rayleigh distribution. To obtain the unknown clutter model and detection probability model, a clutter estimator and a detection estimator are first designed to avoid degradation of tracking performance due to mismatch between the clutter and detection models.

[0091] Based on the above multi-target tracking scenario, the tracking method includes the following steps:

[0092] S1. When a sensor with limited detection range does not have a target in its observation area, it first estimates the clutter rate of non-uniform clutter, and then estimates the spatial density of the non-uniform clutter using an unsupervised learning method based on model clustering to obtain an estimated clutter rate and an estimated spatial density. Specifically, the steps include:

[0093] S11. Under the condition that no target exists in the observation area, the sensor with limited detection range estimates the clutter rate by maximizing the fused clutter measurement likelihood function with respect to the clutter rate to obtain an estimated clutter rate.

[0094] Specifically, assuming that no target appears in the observation area, the clutter observed by a single sensor is modeled as a Poisson point process, and the clutter of the linear combination of multiple sensors still obeys the Poisson point process. Specifically, for each sensor, its clutter rate is constant during the scan period, and the fused clutter measurement sequence of J consecutive time steps is expressed as C k:k+j , abbreviated as C J , the number of clutter is W J =|C J |, the number of clutter obeys the parameter λ C Poisson distribution of :

[0095]

[0096] Therefore, the likelihood function of the fused clutter measurement obtained by the fusion center is expressed as:

[0097]

[0098] Among them, λ C is the clutter rate, W J =|C J | is the number of clutter, C J is a fusion clutter measurement sequence of J consecutive time steps, L is the number of sensors, and l is the lth sensor.

[0099] Maximizing the likelihood function of the fused clutter measurement yields the estimated clutter rate:

[0100]

[0101] in,

[0102] S12. Based on a model clustering method, the spatial density of the non-uniform clutter is parameterized, and the number and parameter set of Gaussian mixture components in the parameterized representation are solved, and the spatial density of the non-uniform clutter is calculated using the number and parameter set of the Gaussian mixture components.

[0103] Specifically, based on the model clustering method, the spatial density of the non-uniform clutter is parameterized:

[0104]

[0105] Among them, Θ is the parameter set, θ q is the qth Gaussian component parameter, i.e. θ q =(m q ,Σ q ),q∈{1,2,…,Q}, Q is the number of Gaussian mixture components when using Gaussian mixture components to approximate the non-uniform clutter spatial density, is the qth partition cluster of the mixed clutter set, π q is the mixing ratio, π q is the logistic regression function of the observed clutter c, that is, c m is the mth clutter sample, is the parameter vector, is the weight of the qth component, Θ=(α1,…α Q ;θ1,…,θ Q ) is the unknown parameter set.

[0106] In practical applications, the number of components Q is generally unknown and needs to be estimated. The Bayesian information criterion (BIC) is used for estimation, namely:

[0107]

[0108] in, is the number of Gaussian mixture components.

[0109] Furthermore, the clutter log-likelihood can be expressed in terms of finite mixture components as,

[0110]

[0111] Then, the expectation maximization method is used to estimate the parameter set Θ of the Gaussian mixture component, and the parameter set Θ includes the mixing ratio Mean vector of Gaussian mixture components and the covariance matrix

[0112] 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:

[0113]

[0114] in, and The mth clutter sample c is defined respectively m The mixture ratio and density function of the qth component at the nth iteration, with the denominator being the normalization factor.

[0115] For the above formula, first find the conditional expectation likelihood function. The conditional expectation likelihood of complete data can be expressed as:

[0116]

[0117] Then maximize the conditional expected likelihood function, specifically using the n+1th iteration to solve the following two equations:

[0118]

[0119]

[0120] Furthermore, the model parameters can be obtained:

[0121]

[0122]

[0123]

[0124] in, is the ratio of mixed components, W J is the number of clutter measurements, m is the mth clutter sample, is the posterior density of the mth clutter sample belonging to the qth cluster, n is the number of iterations, is the mean vector of the mixed Gaussian components, c m is the mth clutter sample, is the mean vector and covariance matrix of the mixed Gaussian components.

[0125] Finally, the number Q of the Gaussian mixture components and the parameter set are substituted into the parameterized formula to obtain the estimated spatial density of the non-uniform clutter.

[0126] According to the above theoretical derivation process, the clutter intensity function can be further expressed as:

[0127]

[0128] S2. Based on the target signal echo amplitude characteristics in the observation area, the detection probability is estimated by integrating the amplitude likelihood function within the signal-to-noise ratio confidence interval to obtain an estimated detection probability. Specifically, the steps include:

[0129] S21. Based on the fact that 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.

[0130] Specifically, the target signal echo amplitude characteristic is assumed to obey the Rayleigh distribution with parameter α, that is,

[0131]

[0132] Where 1+β is the expected signal-to-noise ratio (SNR), SNR (dB) = 10log 10 (1+β). Given a threshold T, the detection probability can be expressed as,

[0133]

[0134] Among them, P D (β) is the detection probability, β is the signal-to-noise ratio parameter, α is the target signal echo amplitude characteristic, and T is the gate threshold.

[0135] S22. Estimate the detection probability.

[0136] Specifically, first, in general, due to the target's distance and RCS flicker, the detection probability of the target is usually a random variable. Assuming that the data association is known, the distribution of the signal-to-noise ratio parameter β can be modeled as:

[0137]

[0138] Where p(β) is the distribution of the signal-to-noise ratio parameter, and ρ is the proportionality constant that makes the integral of the probability density equal to 1.

[0139] Given the signal-to-noise ratio (SNR) interval [β1, β2], the scaling factor ρ = (ln(1+β2)-ln(1+β1)) -1 , the amplitude likelihood function can be obtained by integrating the signal-to-noise ratio parameter β, and the amplitude likelihood function is substituted into the detection probability model. The estimated detection probability can be expressed as:

[0140]

[0141] From the above formula, we can see that there is no analytical solution for the integral. The numerical solution of the estimated detection probability can be obtained through the built-in integral function of MATLAB, that is,

[0142]

[0143] Among them, integral is the integral function and @ is the anonymous function symbol.

[0144] S3. Pass the estimated clutter rate, the estimated spatial density, and the estimated detection probability into a standard TPMB filter to obtain a robust TPMB filter.

[0145] Specifically, the mathematical description of the standard TPMBM filter is: the two non-intersecting multi-target tracks RFS are represented as X U and X T , the probability density of TPMBM can be expressed as PPP probability density f Poisson (X U ) and TMBM probability density f mbm (X T ) of the convolution, i.e.

[0146]

[0147] The probability density of PPP is:

[0148]

[0149] where v(·) is the intensity, which is the undetected target geometry |X U The probability density of a random finite set of MBM is,

[0150]

[0151] Where the symbol ‘∝’ indicates that it is proportional to, j is the index of the Multi-Bernoulli Mixture (MBM), n is the number of potential detection targets, and the weight and density of the i-th Bernoulli Component (BC) in the j-th MBM mixture are denoted as and X i is the state of target i, and the density of a single Bernoulli component can be written as:

[0152]

[0153] Among them, ε j,i and p j,i (x) are the target existence probability (EP) and state density (SD) of the i-th BC in the j-th MBM mixture component, respectively, and x is the state of a single target. Further, we can get:

[0154]

[0155] Observe the above formula, each summation term corresponds to a global association hypothesis (GAH).

[0156] Further, to clearly describe the MBM structure, see Figure 4 , Figure 4 This is a schematic diagram of an MBM structure provided by an embodiment of the present invention, in which MmTt represents the mth measurement at time t, Mis represents missed detection, and NE represents that the target does not exist or is not detected. Figure 4 It can be seen that at time step 2, the three single-target association hypotheses (STH) correspond to three global association hypotheses: GAH1, GAH2 and GAH3.

[0157] Furthermore, to improve computational efficiency, the auxiliary variable method is introduced to approximate the MBM with a single MB component, resulting in the mathematical description of the TPMB filter as follows:

[0158]

[0159] Observing the above formula, it is obvious that the posterior density of the TPMB filter only contains one global hypothesis component.

[0160] Furthermore, the clutter rate of the non-uniform clutter estimated in step S1, the spatial density of the non-uniform clutter, and the detection probability estimated in step S2 are input into the standard TPMB filter to obtain a robust TPMB filter.

[0161] Standard TPMB generally consists of four parts: prediction, update, pruning, and estimation. The robust TPMB filter differs from standard TPMB primarily in the measurement update phase, which takes into account three complex scenario factors: the sensor's limited field of view, fluctuating detection probabilities, and non-uniform clutter.

[0162] Since the estimated parameters only affect the update step, this embodiment only describes the detailed steps of the update process. k|k-1 、Number of targets n k|k-1 And the fused measurement data set Z at the kth time step k ,The updated Poisson component hypothesis and Bernoulli component hypothesis can be divided into the following four parts: updating undetected targets, updating missed targets, updating detected targets, and updating new targets.

[0163] ① Update the undetected targets:

[0164]

[0165] ② Update the missed targets. Specifically, for the Bernoulli component i∈{1,…,n k|k-1}, given In the case of , the missed target update can be expressed as:

[0166]

[0167]

[0168]

[0169] Among them, 〈f,h〉=∫f(x)h(x)dx is the inner product, and the prediction parameter of the i-th Bernoulli component is

[0170] ③ Update the detected target. Specifically, given the fusion measurement data set at the kth time step

[0171] Then the update of the i-th Bernoulli is:

[0172]

[0173]

[0174] ④ Update the new target. Specifically, for the new Bernoulli component i∈{n k|k-1 +j|j∈{1,…,m k}}, which is fused with the measurement data set Initialization, local hypothesis h i =2, the new target update can be expressed as,

[0175]

[0176]

[0177]

[0178]

[0179] Among them, the collection represents the measurement index of the i-th Bernoulli component in the j-th local hypothesis.

[0180] The global assumed data association set is:

[0181]

[0182]

[0183] in, a i is the global hypothesis corresponding to the i-th target.

[0184] S4. Using the robust TPMB filter to estimate the state of multiple target tracks. Specifically including:

[0185] S41. Using the robust TPMB filter, the Gaussian mixture intensity of the new Poisson component in the fusion measurement of multiple sensors at the target time is expressed as:

[0186]

[0187] Among them, n k'|k is the number of components, It's freshman time. is the weight corresponding to the jth component of the i-th target, is the mean, is the covariance, k is the kth time step, k'∈{k,k+1}, and X is the multi-target track.

[0188] Using the robust TPMB filter, the spatial density of the i-th Bernoulli component in the fusion measurement of multiple sensors at the target time is expressed as:

[0189]

[0190] Among them, b i is the starting time, is the mean of the i-th Bernoulli component, is the covariance, k is the track survival until the kth time step, X is the multi-target track, n x is the target state dimension.

[0191] S42. Reduce the multi-Bernoulli mixed component formed by the multiple Bernoulli components to obtain a reduction result.

[0192] Specifically, in order to reduce computational complexity, a pruning operation, a merging operation, a limiting operation, and a recycling operation are performed on a multi-Bernoulli mixture component formed by multiple Bernoulli components, that is, a global hypothesis, to obtain the reduction result.

[0193] Among them, the pruning operation is to discard the Bernoulli components whose detection probability is lower than a given threshold.

[0194] Merge operation: Merge similar Bernoulli components of MBM.

[0195] Limitation operation: only retain the global hypothesis with the largest weight before Hmax for data association.

[0196] Recycling operation: Approximate the Bernoulli component with very small probability to a Poisson component. Furthermore, the approximation error can be measured by minimizing the KL divergence:

[0197]

[0198] in, is the density of the i-th Bernoulli component, is the probability of the existence of the i-th Bernoulli component.

[0199] Furthermore, the PPP intensity for the undetected target after recovery becomes:

[0200]

[0201] Among them, v k′ | k (X) is the predicted multi-target intensity, is the probability of the existence of the i-th Bernoulli component in the h-th local hypothesis, Γ T is the existence probability threshold, is the single target hypothesis at the kth time step, for the prior MB hypothesis a and data association o k , the standardized posterior weights is the weight corresponding to the global hypothesis a.

[0202] S43: The existence of a Bernoulli component in the reduction result with a probability exceeding a set threshold is regarded as a state of the multi-target track.

[0203] Specifically, according to the TPMB posterior equation, the threshold Γ is set T , for the tracks that survive at the kth moment, the probability of existence in the reduction result exceeding the set threshold Γ T The Bernoulli component of is used as the state of the multi-target track, and the estimated track set can be expressed as It means that there is a probability greater than Γ T The mean of the Bernoulli components is the estimated state of the target track.

[0204] The tracking method of this embodiment first estimates the clutter rate and spatial density of non-uniform clutter in the absence of a target. It then estimates the detection probability based on the target signal echo amplitude characteristics. Finally, it uses a robust TPMB filter to estimate the status of multiple target tracks. This method not only uses multi-field fusion to track multiple targets that randomly appear and disappear in scenarios with unknown non-uniform clutter and detection probability, and limited sensor detection range, improving multi-target tracking performance in complex non-uniform clutter scenarios, but also obtains detection information of unknown targets based on the target signal echo amplitude characteristics, solving the problem of mismatch in fixed detection models. Furthermore, the robust TPMB filter's robustness to missed target detections provides continuous target track information, reducing missed detections and false alarms.

[0205] Furthermore, based on the above tracking method, this embodiment evaluates the multi-target tracking performance of the robust TPMB filter.

[0206] Specifically, the generalized optimal sub-pattern assignment criterion (GOSPA) is used to evaluate the target tracking performance. Given parameters c, p, and v = 2, in the target set x = {x1, ..., x n} and y={y1,…,y n The GOSPA error between} can be expressed as,

[0207]

[0208] Where χ is the allocation between the two target sets. Ω is the set of all possible allocations, so χ∈Ω. The first term in the above equation measures the target's position error, while the next two terms measure the target's missed detection and false alarm errors. Following conventional parameter setting rules, in the experimental simulations of the present invention, the parameters c=100 and p=2 were set.

[0209] 1) Linear Gaussian uniform target motion scene.

[0210] In the sensor detection range of the set area 2000m×2000m, a total of 11 targets appeared in 100 scanning periods. The length of time that the i-th target survives in the area is τ i ∈[b,d]s,i∈N. The real motion trajectory of multiple targets is as follows Figure 5 As shown, Figure 5 This is a real target motion trajectory diagram in a linear scenario provided by the present invention. In the kth scanning cycle, the target state and position are x k =[p x,k ,v x,k ,p y,k ,v y,k ] T, the measurement vector corresponding to the target is z k =[z x,k ,z y,k ] T The target motion model is a linear Gaussian model, and the transfer function of the target state is:

[0211]

[0212] Among them, the transfer matrix F and process noise V are,

[0213]

[0214] Wherein, the scanning period Ts=1.

[0215] The measurement likelihood is also Gaussian distributed, and the probability density function (PDF) is

[0216]

[0217] Among them, the observation matrix H and the measurement noise R are

[0218]

[0219] Set the target's survival probability P s = 0.99. For PHD filters and R-TPMB filters, the four new targets are modeled as Poisson RFS, and their strength is

[0220]

[0221] in, Weight ω b = 0.03. For Labeled filters, the new parameter model is in The maximum number of hypotheses is set to 1000.

[0222] First, for the ideal filters Ideal-LMB and Ideal-CPHD, the detection probability p 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 filter, it is necessary to estimate the clutter filtering and detection probability. According to the estimation method described above, compared with the advanced DP-GLMB filter, the estimation results of the detection probability and clutter rate are as follows: Figure 6 As shown, Figure 6The results of the detection probability and clutter rate estimation in a linear scenario provided by the present invention are shown in Figure 2. Next, the non-uniform spatial density of the clutter is estimated. The Gaussian mixture model is used to represent the actual spatial density of the clutter, which is mathematically described as:

[0223]

[0224] Among them, θ i ={m i ,Σ i},i∈{1,2,3,4},m1=[-500,0] T ,Σ1=diag([300 2 ,700 2 ] T ),m2=[-900,0] T ,Σ2=diag([700 2 ,500 2 ] T ),m3=[250,0] T ,Σ3=diag([200 2 ,600 2 ] T ),m4=[600,600] T ,Σ4=diag([300 2 ,300 2 ] T ). The estimated results of the number of clutter components and the spatial distribution of clutter are as follows: Figure 7 、 Figure 8 As shown, Figure 7 This is a diagram showing the estimation results of the number of clutter components in a linear scenario provided by an example of the present invention. Figure 8 This is a diagram of the clutter spatial density estimation result in a linear scenario provided by an example of the present invention.

[0225] Further, if Figure 9 As shown, Figure 9 The figure shows the multi-target tracking results in a linear scenario provided by the example of the present invention. Under non-uniform clutter and unknown detection probability, the advanced R-CPHD, DP-GLMB, R-MS-GLMB, and R-TPMB robust multi-target tracking technology proposed in this embodiment are given. The results show that the proposed technical solution has a low level of missed detection and false alarm for multi-target tracking. Next, as Figure 10 and Figure 11 As shown, Figure 10 This is a graph showing the error in estimating the number of multiple targets in a linear scenario provided by an example of the present invention. Figure 11 This is a graph showing the estimation results of the number of multiple targets in a linear scenario provided by the example of the present invention. Figure 10 and Figure 11Results on target number estimation using this embodiment and five other tracking techniques are presented. The experimental results show that the target number estimated by the proposed solution, DP-GLMB, and R-MS-GLMB techniques is close to the actual target number, and the proposed solution has a lower estimation error.

[0226] To further measure the performance advantages of the proposed technical solution in terms of tracking accuracy, such as Figure 12 As shown, Figure 12 This is a diagram showing the generalized optimal sub-mode allocation error results for multi-target track tracking in a linear scenario provided by an example of the present invention. Figure 12 The results of 200 Monte Carlo (MC) simulation experiments are given to quantitatively describe the tracking performance of each technical solution under the GOSPA error metric. The experimental results show that when the local sensors have small clutter differences, the proposed R-TPMB technical solution has a slight advantage over the DP-GLMB technology, but is slightly worse than the R-MS-GLMB technology. It is worth noting that the proposed R-TPMB (2) Technical solution (robust tracking implementation of the second type TPMB filter), using the Optimal Sub-Pattern Assignment (OSPA) and Track-to-Track Optimal Sub-Pattern Assignment (OSPA) (2) ) The multi-target tracking accuracy obtained by it still has the best tracking performance when the local sensor differences are small. The experimental results are as follows Figure 13 As shown, Figure 13 This is a graph showing the error results of two optimal sub-mode allocations for multi-target track tracking in a linear scenario provided by an example of the present invention.

[0227] 2) Non-linear distance and orientation target motion scenarios.

[0228] In the nonlinear target motion scenario, assuming that the detectable area is 3500m×2000m, a total of 7 targets appear in 100 scanning cycles. The target's real track information is as follows: Figure 14 As shown, Figure 14 The real target motion trajectory diagram in the nonlinear scenario provided by the present invention. Set the target survival probability P s =0.99, the single target state transition model is:

[0229] x k =F(ω k-1 )x k-1 +G

[0230] ω k =ωk-1 +u k-1

[0231] in, T s =1s,σ ω =10m / s 2 ,σ u =π / 180rad / s, the state transfer matrix F and the process noise matrix G are:

[0232]

[0233] The measurement model of a single target is expressed as:

[0234]

[0235] Among them, the position of the lth sensor is Taking two sensors as an example, set the position of sensor 1 to [-1500,0] and the position of sensor 2 to [1000,0], and measure the noise vector where σ r =10m,σ θ =π / 180rad.

[0236] First, for CPHD and R-TPMB multi-target tracking technologies, the target new distribution model is known and the same for all sensors. Assume that there are 4 new targets and the new positions of all new targets are For the Ideal-LMB filter, the newborn density is The survival probability The PDF of a single label Bernoulli component is

[0237] Then, for the robust R-CPHD, DP-GLMB, and 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 uses a measurement-driven new model, and the maximum new probability is set to r B,max =0.02, the newborn covariance is p B =Σ b Assume that the two local sensors have the same clutter rate, that is For the ideal Ideal-CPHD and Ideal-LMB, the local sensor has known clutter rate and detection probability P D =0.97. For robust multi-target tracking technology, the estimation results of detection probability and clutter rate are as follows: Figure 15 As shown, Figure 15This is a diagram of the detection probability and clutter rate estimation results in a nonlinear scenario provided by an example of the present invention.

[0238] Next, the spatial probability density of non-uniform clutter is modeled using a Gaussian mixture model, namely

[0239]

[0240] Among them, θ i ={m i ,Σ i}, i∈{1,2,3,4}, m1=[-1300,1200] T ,Σ1=diag([500 2 ,500 2 ] T ), m2=[-1000,700] T ,Σ1=diag([600 2 ,400 2 ] T ), m3=[200,1200] T ,Σ3=diag([500 2 ,350 2 ] T ), m4=[800,900] T ,Σ4=diag([200 2 ,700 2 ] T ). Next, regarding the estimation results of the number of clutter components and the spatial distribution of clutter probability, if Figure 16 and Figure 17 As shown, Figure 16 This is a diagram showing the estimation results of the number of clutter components in a nonlinear scenario provided by an example of the present invention. Figure 17 The figure shows the clutter spatial density estimation result in a nonlinear scenario provided by the example of the present invention. The experimental results show that compared with the DP-GLMB technology, the clutter spatial density estimator designed in this embodiment can better estimate the spatial distribution of non-uniform clutter.

[0241] Finally, the estimated clutter and detection probability are used as inputs to conventional CPHD, GLMB and TPMB filters to achieve robust multi-target track tracking. For nonlinear scenarios, the RFS filter is implemented using the Unscented Kalman Filter (UKF). The track estimation results obtained under different multi-target tracking technologies are as follows: Figure 18 As shown, Figure 18This figure shows the results of multi-target tracking in a nonlinear scenario using an example of the present invention. The experimental results show that the R-TPMB robust multi-target tracking technique proposed in this embodiment has fewer false tracks and missed detections than the R-CPHD robust tracking technique. Furthermore, the resulting track integrity and smoothing are superior compared to the DP-GLMB and R-MS-GLMB robust tracking techniques.

[0242] Furthermore, in order to quantitatively evaluate the advantages of the technology of the present invention in terms of target number estimation and track tracking accuracy, the present invention uses 200 MC experiments and adopts six different multi-target tracking technologies to obtain the experimental results of target number and track tracking accuracy respectively. The experimental results are as follows: Figure 19-21 As shown, Figure 19 This is a graph showing the error results of multi-target number estimation in a nonlinear scenario provided by the example of the present invention. Figure 20 This is a graph showing the result of multi-target number estimation in a nonlinear scenario provided by the example of the present invention. Figure 21 This figure shows the generalized optimal sub-pattern assignment error results for multi-target track tracking in a nonlinear scenario, as provided by the present invention. The experimental results show that this embodiment's technology achieves low mean square error (MSE) in target number estimation and low GOSPA error in track estimation accuracy, demonstrating the robustness and high tracking accuracy of this embodiment's technology in multi-target tracking.

[0243] Furthermore, in order to better evaluate the advantages of this embodiment in terms of track continuity, the OSPA (2) The error metric criterion is given in OSPA through 200 MC experiments. (2) The error is the track tracking accuracy evaluation result under the OSPA error metric, such as Figure 22 As shown, Figure 22 The two optimal sub-mode allocation error results of multi-target track tracking in nonlinear scenarios provided by the present invention are shown in the figure. (2) The conclusions of the two error measurement criteria are consistent, that is, compared with other multi-target tracking technologies, the errors obtained by the technology of this embodiment are the smallest, and the track tracking accuracy obtained is relatively high, thereby verifying the good application value of this embodiment in terms of robustness and tracking accuracy in multi-target tracking.

[0244] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A robust multi-sensor multi-target tracking method in a non-uniform clutter background, characterized by: Including steps: S1. A sensor with a limited detection range, under the condition that no target exists in the observation area, first estimates the clutter rate of non-uniform clutter, and then estimates the spatial density of the non-uniform clutter using an unsupervised learning method based on model clustering to obtain an estimated clutter rate and an estimated spatial density; S2. Based on the target signal echo amplitude characteristics in the observation area, the detection probability is estimated by integrating the amplitude likelihood function within the signal-to-noise ratio confidence interval to obtain an estimated detection probability; S3. Passing the estimated clutter rate, the estimated spatial density, and the estimated detection probability into a standard TPMB filter to obtain a robust TPMB filter; S4. Estimate the state of multiple target tracks using the robust TPMB filter.

2. The robust multi-sensor multi-target tracking method in a non-uniform clutter background according to claim 1 is characterized in that: Step S1 includes: S11. Under the condition that no target exists in the observation area, the sensor with limited detection range estimates the clutter rate by maximizing the fused clutter measurement likelihood function with respect to the clutter rate to obtain the estimated clutter rate; S12. Based on a model clustering method, the spatial density of the non-uniform clutter is parameterized, and the number and parameter set of Gaussian mixture components in the parameterized representation are solved. The spatial density of the non-uniform clutter is calculated using the number and parameter set of the Gaussian mixture components to obtain the estimated spatial density.

3. The robust multi-sensor multi-target tracking method under non-uniform clutter background according to claim 2 is characterized in that: Step S11 includes: Under the condition that there is no target in the multi-sensor observation area, based on modeling the clutter observed by a single sensor as a Poisson point process and the clutter of the linear combination of multiple sensors obeys the Poisson point process, the likelihood function of the fusion center obtaining the fused clutter measurement is expressed as: Among them, λ C is the clutter rate, W J =|C J | is the clutter measurement number, C J is a fusion clutter measurement sequence of J consecutive time steps, L is the number of sensors, and l is the lth sensor; Maximizing the likelihood function of the fused clutter measurement yields the estimated clutter rate: in, 4. The robust multi-sensor multi-target tracking method in a non-uniform clutter background according to claim 2 is characterized in that: Step S12 includes: Based on the model clustering method, the spatial density of the non-uniform clutter is parameterized: Among them, Θ is the parameter set, θ q is the qth Gaussian component parameter, i.e. θ q =(m q ,Σ q ),q∈{1,2,…,Q}, Q is the number of Gaussian mixture components when using Gaussian mixture components to approximate the non-uniform clutter spatial density, is the qth partition cluster of the mixed clutter set, π q is the mixing ratio, c m is the mth clutter sample, is the parameter vector, is the weight of the qth component, Θ=(α1,…α Q ;θ1,…,θ Q ) is a set of unknown parameters; The number of Gaussian mixture components is estimated using the Bayesian Information Criterion: in, is the number of Gaussian mixture components; The parameter set of the Gaussian mixture components is estimated using the expectation maximization method: in, is the ratio of mixed components, W J is the number of clutter measurements, m is the mth clutter sample, is the posterior density of the mth clutter sample belonging to the qth cluster, n is the number of iterations, is the mean vector of the mixed Gaussian components, c m is the mth clutter sample, is the mean vector and covariance matrix of the mixed Gaussian components; The number and parameter set of the Gaussian mixture components are substituted into the parameterized representation to obtain the estimated spatial density.

5. The robust multi-sensor multi-target tracking method in a non-uniform clutter background according to claim 1 is characterized in that: Step S2 includes: S21. Based on the fact that the target signal echo amplitude characteristics in the observation area obey the Rayleigh distribution, a detection probability model of the target signal echo amplitude characteristics is established: Among them, P D (β) is the detection probability, β is the signal-to-noise ratio parameter, α is the target signal echo amplitude characteristic, and T is the threshold value; S22. Establish a distribution model of signal-to-noise ratio parameters: 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 equal to 1; Given the signal-to-noise ratio interval value [β1,β2], the scaling factor ρ = (ln(1+β2)-ln(1+β1)) -1 , the amplitude likelihood function can be obtained by integrating the signal-to-noise ratio parameter β, and the amplitude likelihood function is substituted into the detection probability model to obtain the estimated detection probability: The numerical solution of the estimated detection probability is obtained by using the built-in integration function of MATLAB: Among them, integral is the integral function and @ is the anonymous function symbol.

6. The robust multi-sensor multi-target tracking method in a non-uniform clutter background according to claim 1, characterized in that: In the robust TPMB filter, the updated Poisson component hypothesis and the Bernoulli component hypothesis include: updating undetected targets, updating missed targets, updating detected targets, and updating new targets.

7. The robust multi-sensor multi-target tracking method in a non-uniform clutter background according to claim 1, characterized in that: Step S4 includes: S41. Using the robust TPMB filter, the Gaussian mixture intensity of the new Poisson component in the fusion measurement of multiple sensors at the target time is expressed as: Among them, n k'|k is the number of components, It's freshman time. is the weight of the jth component corresponding to the i-th target, is the mean, is the covariance, k is the kth time step, k'∈{k,k+1}, X is the multi-target track; Using the robust TPMB filter, the spatial density of the i-th Bernoulli component in the fusion measurement of multiple sensors at the target time is expressed as: Among them, b i is the starting time, is the mean of the i-th Bernoulli component, is the covariance, k is the track survival until the kth time step, n x is the target state dimension; S42, reducing a multi-Bernoulli mixture component formed by multiple Bernoulli components to obtain a reduction result; S43: The existence of a Bernoulli component in the reduction result with a probability exceeding a set threshold is regarded as a state of the multi-target track.

8. The robust multi-sensor multi-target tracking method in a non-uniform clutter background according to claim 7, characterized in that: Step S42 includes: A pruning operation, a merging operation, a limiting operation, and a recycling operation are performed on the multi-Bernoulli mixture components to obtain the reduction result.

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