A multi-Bernoulli multi-target tracking method with multiple radar labels under low detection probability

Abstract

The present invention provides a multi-radar label multi-Bernoulli multi-target tracking method under low detection probability, comprising: S1: using label multi-Bernoulli distribution to describe multi-target state; S2: obtaining label multi-Bernoulli distribution of multi-target state prediction according to label multi-Bernoulli posterior distribution of multi-target state at the previous moment; S3: using a two-step greedy measurement partitioning mechanism, measuring and partitioning according to label Bernoulli distribution of multi-target state prediction; S4: updating label multi-Bernoulli density function of multi-target state according to the result of measurement partitioning, obtaining label multi-Bernoulli posterior distribution of multi-target state at the current moment; S5: pruning and merging all label Bernoulli items representing multi-target state, extracting multi-target state according to label multi-Bernoulli posterior distribution, and generating target track. The present invention solves the problem that it is difficult for a medium-multi radar system to stably track targets with low detection probability.

Description

Technical Field

[0001] The invention relates to the field of multi-radar multi-target tracking. Background Art

[0002] Multi-target tracking is to estimate the state information of unknown targets using the measurement data of sensors. Traditional multi-target tracking associates measurements with targets, but as the number of targets increases, combinatorial explosion will occur. Mahler introduced finite set statistics on the basis of multi-target tracking theory and proposed the random finite set (RFS) theory, which modeled the state and measurement of multiple targets in the form of RFS, effectively solving the combinatorial explosion problem in the multi-target tracking process based on multiple hypothesis tracking (MHT) and joint probabilistic data association (JPDA). Later, Vo et al. introduced the concept of labeled finite sets. The multi-target filter based on random sets of labels models the target state information as a finite set of labels and calculates and transmits it in a recursive process, which can easily realize the establishment of target tracks. After research by many scholars, the RFS theory has been widely used in radar, sonar, mobile communications, robotics and other fields.

[0003] In actual tracking scenarios, due to interference from natural environment or human factors, as well as the increasing mobility of targets, radars cannot obtain complete information, resulting in target tracking based on a single radar failing to meet the requirements of higher tracking performance. Therefore, the use of multiple radars for target tracking has become a research hotspot for many experts and scholars. Mutual cooperation between multiple radars can effectively overcome the limitations of a single radar. Vo et al. proposed a generalized label multi-Bernoulli (GLMB) filter based on Gibbs sampling, which can realize prediction and update joint truncation approximation, and the computational complexity increases linearly with the number of measurements. Later, Vo et al. extended the GLMB filter to the multi-sensor field. Reuter et al. used the first-order approximate matching criterion to approximate the GLMB distribution to the label multi-Bernoulli (LMB) distribution, and obtained the LMB filter, which can be easily extended to the multi-sensor field. The multi-sensor label multi-Bernoulli (MS-LMB) filter is used in the tracking method provided by the present invention.

[0004] At present, the GLMB filter and LMB filter of multi-sensors generally use Gibbs sampling to solve the measurement partitioning problem. However, when a multi-radar system tracks a target with a low detection probability, the radar has a relatively low detection probability of the target, and it is easy to be in a missed detection state. If Gibbs sampling is still used, the likelihood weight calculation during measurement allocation will be affected, and then the state estimation of the target and the number of targets in the monitoring area will be wrong. To solve this problem, it is necessary to specifically consider the measurement set containing missed detection items when performing measurement partitioning to ensure that the correct measurement partition hypothesis will not be discarded due to a small likelihood weight. Summary of the invention

[0005] The present invention provides a multi-radar tag multi-Bernoulli multi-target tracking method under low detection probability, which can solve the problem in the prior art that multi-radar systems are difficult to stably track targets with low detection probability.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0007] Step S1: Initialize the target state: use label multi-Bernoulli distribution to describe the multi-target state;

[0008] Step S2: target state prediction: obtain the label multi-Bernoulli distribution of the multi-target state prediction according to the label multi-Bernoulli posterior distribution of the multi-target state at the previous moment;

[0009] Step S3: measurement partitioning: a two-step greedy measurement partitioning mechanism is used to perform measurement partitioning according to the multi-Bernoulli distribution of labels for multi-target state prediction;

[0010] Step S4: target state update: update the label multi-Bernoulli density function of the multi-target state according to the measurement division result to obtain the label multi-Bernoulli posterior distribution of the multi-target state at the current moment;

[0011] Step S5: Generate track: Prune and merge all label Bernoulli items representing multi-target states, extract multi-target states according to label multi-Bernoulli posterior distribution, and generate multi-target tracks.

[0012] The multi-radar tag multi-Bernoulli multi-target tracking method under low detection probability proposed by the present invention has the following beneficial effects: the present invention adopts a multi-sensor tag multi-Bernoulli filter, and adopts a two-step greedy measurement partitioning mechanism to solve the measurement partitioning problem in filtering. Compared with the conventional multi-sensor tag multi-Bernoulli filter using Gibbs sampling, it can effectively avoid the situation where the likelihood weight calculation is affected during measurement partitioning under low detection probability and the target state estimation is wrong; the two-step greedy measurement partitioning mechanism adopted by the tracking method described in the present invention separately retains the measurement set containing missed items when searching for the measurement set with the largest weight, avoiding the measurement partitioning error when there are many missed items of the low detection probability target, and improving the tracking performance of the multi-radar system under low detection probability. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 A schematic diagram of the first step of the two-step greedy measurement partitioning mechanism provided by the present invention, where R1, R2, R3, and R4 represent radar numbers;

[0014] Figure 2A schematic diagram of the second step partitioning of the two-step greedy measurement partitioning mechanism provided by the present invention, where B1, B2, B3, and B4 represent the sequence numbers of the label Bernoulli items;

[0015] Figure 3 The present invention provides a flowchart of a multi-radar tag multi-Bernoulli tracking method under low detection probability. DETAILED DESCRIPTION

[0016] The specific embodiments of the present invention are described in detail below with reference to the accompanying drawings, but are not intended to limit the present invention.

[0017] The present invention provides a multi-radar tag multi-Bernoulli multi-target tracking method under low detection probability, which is described in detail one by one in the following embodiments.

[0018] Step S1: Initialize the target state: use label multi-Bernoulli distribution to describe the multi-target state;

[0019] The multi-target state is represented by a label random set X, where X = {x1,…,x i ,…,x |X|}, x i =(m i ,l i ) is the label single target state, represents the motion state of the target, and |X| represents the potential of the set;

[0020] According to the target's motion scene, the state parameters of the target at the initial moment are set, including the number of targets, position speed, intensity, existence probability and the variance of the target's motion state;

[0021] Use the parameters set above as the target initial distribution and express it in the form of parameter set of label multi-Bernoulli random set;

[0022] Step S2: target state prediction: obtain the label multi-Bernoulli distribution of the multi-target state prediction according to the label multi-Bernoulli posterior distribution of the multi-target state at the previous moment;

[0023] Assuming that the previous moment is k-1, the label multi-Bernoulli posterior density at this moment is

[0024]

[0025] The Gaussian mixture form of the probability density function of the multi-Bernoulli term label is

[0026]

[0027] Assuming that the probability density of new targets at time k satisfies the label multi-Bernoulli distribution, it can be expressed as

[0028]

[0029] The Gaussian mixture form of the multi-Bernoulli probability density function of the label of the new target is:

[0030]

[0031] Then the predicted probability density is still in the form of labeled multi-Bernoulli, which is

[0032]

[0033] The label of the surviving target is a multi-Bernoulli distribution parameter They are

[0034]

[0035]

[0036] where f k-1 (·|x,l) represents the target state transfer function. Under the Gaussian mixture model, the target state transfer function satisfies the Gaussian distribution f k|k-1 (·|x,l)=N(·|F k-1 x,Q k-1 ), where F k-1 is the target state transfer matrix, Q k-1 is the process noise covariance matrix; is the survival probability of the target. Given the survival probability of the target, the Gaussian mixture form of the multi-Bernoulli term probability density function of the label of the surviving target is

[0037]

[0038] in:

[0039]

[0040]

[0041] The target state prediction is still in the label multi-Bernoulli form, so it can be expressed as

[0042]

[0043] The total label set L + =L∪B, weight And the probability density function p k|k-1 (x,l) are

[0044]

[0045] p k|k-1 (x,l)=1L (l)p S,k|k-1 (x,l)+1 B (l)p B,k|k-1 (x,l)

[0046] Then the Gaussian mixture form of the multi-Bernoulli probability density function of the predicted labels of multiple targets is

[0047]

[0048] Step S3: measurement partitioning: a two-step greedy measurement partitioning mechanism is used to perform measurement partitioning according to the label Bernoulli distribution of multi-target state prediction;

[0049] Assume that at time k, there are M labeled multi-Bernoulli items and the measurement set generated by V radars is Then the mapping relationship between the label multi-Bernoulli term and the measurement partition result can be expressed as

[0050]

[0051] where θ (m,s) Represents the index of the measurement of radar s that is assigned to the mth label Multi-Bernoulli term among all the measurements of radar s.

[0052] The computational complexity of finding all the measurement partitioning hypotheses is very large, so a finite number of measurement partitioning hypotheses with higher weights are used as the measurement partitioning results to obtain an approximate solution to the filter. The weight of the measurement partitioning hypothesis θ is calculated as follows:

[0053]

[0054] in Represents the measurement of θ (l,s) The cost allocated to target x.

[0055] In general LMB filters and GLMB filters, Gibbs sampling is used to obtain measurement partition hypotheses with larger weights. However, in the tracking of targets with low detection probability, radars are easily in a missed detection state due to their low detection probability of the target. When most radars are in a missed detection state, the likelihood weight of the target is small due to too many missed detection items, so it is difficult to obtain the target using Gibbs sampling. In addition, in multi-target tracking, if one of the targets can only be detected by fewer radars, the likelihood weight calculated for the target is smaller than that of other targets. Therefore, it is difficult to track the target with low detection probability in these cases. To solve such problems, a two-step greedy measurement partitioning mechanism is used to solve the measurement partitioning problem in the filter. In addition, in order to ensure that multiple radars can obtain correct measurement partitioning results when they are in a missed detection state, when obtaining several measurement sets with the largest weight for each target in turn, the measurement set containing the missed detection item is retained.

[0056] Figure 1 and Figure 2 This is the specific process of the greedy measurement partitioning method. Assume that the measurement data of 4 radars are received, and there are 4 predicted label Bernoulli items. Figure 1 As shown in , we first find the local optimal solution for each label Bernoulli term, that is, to find the measurement set with larger weight. The solution process is carried out in sequence according to the radar order, where Indicates that radar s is in a missed detection state. To ensure that the actual measurement division results can be obtained even when multiple radars are in a missed detection state, when obtaining several measurement sets with larger weights in order of radars, W should be retained. max -1 measurement set with the largest weight excluding the missed items and the measurement set including the missed items. Figure 2 For the second step of greedy measurement partitioning, the W of each label Bernoulli item is max The final measurement partitioning result is obtained by combining the measurement sets with larger weights. The solution process is carried out in the order of the labeled Bernoulli terms, where Indicates that the case where the label Bernoulli term is not associated with a measurement is considered. Because a single measurement can only be assigned to a single target, when combining measurement sets with different label Bernoulli terms, it is necessary to avoid repeatedly assigning a measurement to different targets.

[0057] Step S4: target state update: update the label multi-Bernoulli density function of the multi-target state according to the measurement division result to obtain the label multi-Bernoulli posterior distribution of the multi-target state at the current moment;

[0058] The posterior density of the multi-objective state after the measurement partitioning is updated follows the GLMB distribution, which is:

[0059]

[0060] Where F(L + ) is the label set L + The space formed; To divide the results for measurement; Represents a set of hypothesized labels; weight and the probability density function They are

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] in represents the measurement likelihood function of radar s. Under the Gaussian mixture model, the measurement likelihood function satisfies the Gaussian distribution g(z|x)=N(z|H k x,R k ), where H k is the measurement matrix of a single radar, R k is the measurement noise covariance matrix of a single radar; κ (s) (·) represents the clutter intensity function in radar s; is the detection probability of radar s to target x.

[0067] To ensure continuous updating, the LMB distribution is used to approximate the GLMB distribution, and the updated multi-objective posterior density can be approximately written as

[0068]

[0069] in:

[0070]

[0071]

[0072] Then the probability density function of the multi-Bernoulli item of the updated multi-target state label is the following Gaussian mixture form:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] Step S5: Generate track: Prune and merge the label Bernoulli items representing the multi-target states, extract the multi-target states according to the label multi-Bernoulli posterior density function, and generate the multi-target track.

[0085] Eliminate the probability that the target label exists in the multi-Bernoulli random set after the update is lower than r min The target of the merged target label is less than d in the Euclidean distance of the multi-Bernoulli random set. max After merging, the existence probability of the target is reset between (0,1).

[0086] Using the pruned and merged target label multi-Bernoulli random set, count the number of all targets with an existence probability greater than 0.5, and use the statistical result as the estimated number of targets at this moment; extract the mean of the target state of all targets with an existence probability greater than 0.5, use the extracted result as the estimated value of the target state at this moment, and generate the target track according to the label in the target label multi-Bernoulli random set.

Claims

1. A multi-radar tag multi-Bernoulli multi-target tracking method under low detection probability, comprising the following steps: S1: Initialize target state: Use label multi-Bernoulli distribution to describe multiple target states; S2: Target state prediction: The multi-Bernoulli distribution of labels for multi-target state prediction is obtained based on the multi-Bernoulli posterior distribution of labels for multi-target states at the previous moment; S3: Measurement partitioning: A two-step greedy measurement partitioning mechanism is used to perform measurement partitioning based on the label Bernoulli distribution of the predicted multi-target states; The two-step greedy measurement partitioning includes: Assume that at time K, there are M labeled multi-Bernoulli items and the measurement set generated by V radars is Then the mapping relationship between the label multi-Bernoulli term and the measurement partition result can be written as: where θ (m,s) Represents the index of the measurement of radar s that is assigned to the mth label multi-Bernoulli term in all measurements of radar s. The weight of the measurement partition hypothesis θ is calculated as follows: in Represents the measurement of θ (l,s) The cost allocated to target x; The first step is to obtain a measurement set with a larger weight for each label multi-Bernoulli term; first, find the local optimal solution for each label Bernoulli term, that is, to obtain a measurement set with a larger weight; the solution process is carried out in sequence according to the radar order; when obtaining a measurement set with a larger weight in sequence according to the radar order, retain W max -1 measurement set with the largest weight excluding missed items and the measurement set including missed items; The second step is to convert the W of each label Bernoulli item max The final measurement partitioning result is obtained by combining the measurement sets with larger weights, and using Indicates that the label Bernoulli term is not associated with a measurement; a single measurement can only be assigned to a single target. When combining measurement sets with different label Bernoulli terms, avoid repeatedly assigning a measurement to different targets. S4: Target state update: Update the multi-target state label multi-Bernoulli density function according to the measurement division result to obtain the multi-target state label multi-Bernoulli posterior distribution at the current moment; S5: Generate track: Prune and merge all label Bernoulli items representing multi-target states, extract multi-target states according to the label multi-Bernoulli posterior distribution, and generate multi-target tracks.

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