A distributed multi-source LMB multi-target tracking method based on label matching

Abstract

A distributed multi-source LMB multi-target tracking method based on label matching belongs to the technical field of multi-target tracking and multi-sensor information fusion. The purpose of the present invention is to solve the problem that the existing target tracking method has low tracking accuracy and high computational complexity when the sensor detection probability is low. The sensor nodes of the present invention use label multi-Bernoulli filters to track multiple targets to obtain local LMB multi-target posterior probability density; the LMB multi-target posterior probability density is transmitted by using the communication link in the sensor network; each sensor node performs label matching on the local LMB multi-target posterior probability density and the LMB multi-target posterior probability density of the reference sensor node to obtain the label matching result of each sensor node and the reference sensor node; arithmetic mean fusion is performed according to the label matching result to obtain the fusion result, and the target state is obtained after the state extraction of the fusion result. The method of the present invention can be applied to multi-target tracking.

Description

Technical Field

[0001] The invention belongs to the technical field of multi-target tracking and multi-sensor information fusion, and in particular relates to a distributed multi-source LMB (Labeled Multi-Bernoulli) multi-target tracking method based on label matching. Background Art

[0002] Multi-target tracking refers to the joint estimation of the number and state of targets in a noisy and cluttered environment. Multiple Hypothesis Tracking (MHT) and Joint Probabilistic Data Association (JPDA) are two traditional multi-target tracking methods. In addition, Mahler proposed a multi-target tracking method based on random finite sets, which is unified with the Bayesian filtering method and provides a complete framework for multi-target tracking methods. Among them, multi-target Bayesian recursion is the theoretical basis of multi-target tracking methods based on random finite sets. Based on this, some multi-target filtering methods that are easy to implement in engineering, including Probabilistic Hypothesis Density (PHD) filter, Cardinalized Probabilistic Hypothesis Density (PHD, CPHD) filter, Cardinality-Balanced Multi-Target Multi-Bernoulli (CBMeMBer) filter and Poisson Multi-Bernoulli Mixture (PMBM) filter, have been proposed one after another.

[0003] Labeled random finite sets (Vo BT, Vo B N. Labeled Random Finite Sets and Multi-Object Conjugate Priors [J]. IEEE Transactions on Signal Processing, 2013, 61 (13): 3460-3475.) can output continuous multi-target trajectories based on random finite sets (RFS), thus realizing multi-target tracking in the true sense; δ-GLMB (Vo BN, Vo BT, Phung D. Labeled Random Finite Sets and the Bayes Multi-Target Tracking Filter [J]. IEEE Transactions on Signal Processing, 2014, 62 (24): 6554-6567.) and labeled multi-Bernoulli filters (Reuter, S, B.-T, et al. The Labeled Multi-Bernoulli Filter [J]. Signal Processing, 2014, 62 (12): 3246-3260.) have been proposed successively, such as Figure 1 As shown in the figure, the two filtering methods can output multi-target trajectories with label information. In addition, in order to improve robustness and scalability, some distributed label random finite set methods have been widely studied, including log-linear generalized covariance intersection (GCI) and linear arithmetic average (AA) methods. In the initial label random finite set fusion methods, it is assumed that different sensor nodes have the same label space. However, in actual tracking scenarios, due to the independence of each sensor node, it is impossible to guarantee that each sensor node has the same label space, so it is necessary to consider the label matching between each sensor node.

[0004] To this end, the literature (Li S, Battistelli G, Chisci L, et al. Computationally Efficient Multi-Agent Multi-Object Tracking With Labeled Random Finite Sets [J]. IEEE Transactions on Signal Processing, 2019, 67 (1): 260-275.) proposed a label matching GCI (Label Matching-GCI, LM-GCI) method, which can minimize the label inconsistency index derived from the GCI fusion criterion. The literature (Shen K, Dong P, Jing Z, et al. Consensus-Based Labeled Multi-Bernoulli Filter for Multitarget Tracking in Distributed Sensor Network [J]. IEEE Transactions on Cybernetics, 2021, PP (99)) assigns labels from different sensor nodes by constructing a lookup table. It has been proved that LRFS density fusion can be decomposed into two sub-problems: label matching and posterior probability density fusion (Gao L, Battistelli G, Chisci L. Fusion of Labeled RFS Densities With Minimum Information Loss [J]. IEEE Transactions on Signal Processing, 2020, 68: 5855-5868). Based on LM-GCI, in order to adapt to low detection probability scenarios, some studies have proposed an improved method using Jensen-Shannon Divergence (JSD). However, the above label matching methods all rely on the matching cost function derived from the GCI fusion criterion. Considering the inherent multiplication property of GCI fusion, it is necessary to calculate the fractional exponential power of the probability density of multiple targets, so the computational complexity is higher. In addition, like GCI fusion, when the detection capability of the sensor node is poor, the accuracy of this label matching method will be significantly reduced, resulting in lower tracking accuracy of the tracking results.Although the literature (Gao L, Battistelli G, Chisci L. Fusion of Labeled RFSDensities With Minimum Information Loss [J]. IEEE Transactions on Signal Processing, 2020, 68: 5855-5868) proposed an improvement strategy for this, the proposed method still requires additional computing resources.

[0005] In summary, it is necessary to propose a new method to solve the problems of low tracking accuracy and high computational complexity of existing target tracking methods. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that the existing target tracking methods have low tracking accuracy and high computational complexity when the sensor detection probability is low, and to propose a distributed multi-source LMB multi-target tracking method based on label matching.

[0007] The technical solution adopted by the present invention to solve the above technical problems is:

[0008] A distributed multi-source LMB multi-target tracking method based on label matching, the method specifically comprises the following steps:

[0009] Step 1: Each sensor node uses label multi-Bernoulli filter to track multiple targets, and obtains the local LMB multi-target posterior probability density of each sensor node;

[0010] Step 2: Construct a sensor network based on the communication relationship between sensor nodes. The constructed sensor network is represented as is the set of nodes in the sensor network, It is the edge set in the sensor network. When sensor node i and sensor node j communicate with each other, there is an edge between sensor node i and sensor node j.

[0011] Each sensor node uses the communication link in the sensor network to transmit the LMB multi-target posterior probability density;

[0012] Step 3: Select a reference sensor node, and each sensor node performs label matching on the local LMB multi-target posterior probability density and the LMB multi-target posterior probability density of the reference sensor node to obtain the label matching result between each sensor node and the reference sensor node;

[0013] Step 4: Perform arithmetic mean fusion based on the label matching results to obtain the fusion result. After state extraction of the fusion result, the target state is obtained.

[0014] The beneficial effects of the present invention are:

[0015] The present invention proposes a distributed LMB multi-sensor multi-target tracking method based on efficient label matching. First, label matching is performed based on the label random finite set theory, and then fusion is performed based on the arithmetic mean. Compared with the existing label random finite set multi-sensor multi-target tracking method, the present invention overcomes the condition limitation that the label space of the local posterior distribution of each sensor must be the same, and improves the tracking accuracy and robustness of the multi-target tracking system under low detection probability, and speeds up the calculation speed by reducing the calculation complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic diagram of label assignment of three trajectories;

[0017] Figure 2 It is a diagram of the sensor network structure;

[0018] Figure 3 is a flowchart of two local multi-target posterior LMB density label matching algorithms. DETAILED DESCRIPTION

[0019] Specific implementation method 1: This implementation method is a distributed multi-source LMB multi-target tracking method based on label matching. Multi-source means that the number of sensors used is greater than or equal to 2, and multi-target means that the number of targets is greater than or equal to 2. The method specifically includes the following steps:

[0020] Step 1: Each sensor node uses label multi-Bernoulli filter to track multiple targets, and obtains the local LMB multi-target posterior probability density of each sensor node;

[0021] Step 2: Construct a sensor network based on the communication relationship between sensor nodes. The constructed sensor network is represented as is the set of nodes in the sensor network, It is the edge set in the sensor network. When sensor node i and sensor node j communicate with each other, there is an edge between sensor node i and sensor node j.

[0022] Each sensor node uses the communication link in the sensor network to transmit the LMB multi-target posterior probability density;

[0023] Step 3: Select a reference sensor node, and each sensor node performs label matching on the local LMB multi-target posterior probability density and the LMB multi-target posterior probability density of the reference sensor node to obtain the label matching result between each sensor node and the reference sensor node;

[0024] Step 4: Perform arithmetic mean fusion based on the label matching results to obtain the fusion result. After state extraction of the fusion result, the target state is obtained. The three continuous trajectory tracking results are as follows: Figure 1 shown.

[0025] Distributed sensor networks such as Figure 2 As shown in the figure, each sensor node in the network has detection, computing and communication capabilities. The sensor node uses the detection function to collect target information and obtain measurement information. The computing function means that the sensor node can run the LMB multi-target tracking method locally to obtain the local posterior probability density, and can also run the fusion algorithm to obtain the global posterior probability density. The communication function means that the sensor node can transmit local information to other nodes through the network. With the help of the mathematical description method in graph theory, the sensor network can be expressed as in is a set of sensor nodes, yes A subset of It represents the sensor communication link. The number of sensor nodes is represented by Represents all communication nodes connected to sensor node i (including node i itself).

[0026] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that: based on the multi-objective Bayesian recursive theory, the label space of the sensor node at time k is:

[0027]

[0028] in, is the label space at time k, is the label space at time k-1, is the new target space at time k; and space and are mutually exclusive.

[0029] The other steps and parameters are the same as those in the first embodiment.

[0030] Specific implementation method three: This implementation method is different from specific implementation method one or two in that: the LMB multi-target posterior probability density of the sensor node at time k is:

[0031] For any sensor node:

[0032] Step 1: Prediction step: The Chapman-Kolmogorov equation is used to describe the dynamic characteristics of the target, the new target and the target disappearance. A multi-Bernoulli random finite set is used to represent the new target at time k. The LMB posterior probability density of the new target at time k is:

[0033]

[0034] in, yes The probability of the existence of the Bernoulli component corresponding to the trajectory l is, yes The probability density of the Bernoulli component corresponding to the trajectory l;

[0035] The LMB posterior probability density at time k-1 is:

[0036]

[0037] in, yes The probability of the existence of the Bernoulli component corresponding to the trajectory l is, yes The probability density of the Bernoulli component corresponding to the trajectory l;

[0038] Then the LMB posterior probability density of multi-target prediction at time k is:

[0039]

[0040] in, is the probability of existence of the Bernoulli component corresponding to the predicted k-time trajectory l, is the probability density of the Bernoulli component corresponding to the predicted trajectory l at time k;

[0041]

[0042]

[0043] Among them, h S (l) is the intermediate variable, p S (·, l) is the survival probability of trajectory l, f(x|·, l) is the state transition density of trajectory l, and <·,·> represents the inner product operation;

[0044] Step 1 and 2: The LMB posterior probability density of multiple targets at time k is:

[0045]

[0046] in: is the probability of existence of the Bernoulli component corresponding to the trajectory l at time k, is the probability density of the Bernoulli component corresponding to the trajectory l at time k, Represented by space , Θ represents the space composed of all the mappings between sensor measurements and trajectories, θ is an element in the mapping space Θ, θ(l) represents the sensor measurement value mapped by the trajectory l. When θ(l)=θ(l′)>0, it means l=l′, ω (I,θ) (Z) represents the corresponding probability when mapped to θ, p (θ) (x,l) represents the posterior probability density of trajectory l when the trajectory is mapped to θ, 1 I (l) is the inclusion function, which is used to confirm whether the current trajectory l exists in the set I;

[0047]

[0048]

[0049] in, Definition The calculation method is as follows: x represents the kinematic state of the target, x and label l together form the augmented state (x, l), p D (x,l) is the probability of detection of state (x,l), g(z θ(l) |x,l) means when the state is (x,l), measure z θ(l) The corresponding likelihood function, k(z θ(l) ) is the clutter density of the Poisson distribution,

[0050] The other steps and parameters are the same as those in the first or second embodiment.

[0051] By adopting the method of this embodiment, the LMB multi-target posterior probability density of each sensor node is obtained respectively.

[0052] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that: the intermediate variable h S (l) is:

[0053]

[0054] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0055] Label matching can be considered as an independent sub-problem in the AA fusion process and can be expressed as an optimization problem for the AA fusion divergence.

[0056]

[0057] Among them, τ * It is the optimal solution for label matching.

[0058] The label matching process of the present invention is performed based on the above label matching concept.

[0059] Specific implementation method five: Combination Figure 3 The present embodiment is described as follows. The present embodiment is different from any one of the specific embodiments 1 to 4 in that: the sensor node a is used as the reference sensor node, and the tag matching process of the sensor node b and the sensor node a is:

[0060] Step 3.1: Record the label space of sensor node a as The label space of sensor node b is recorded as Using π a represents the LMB multi-target posterior probability density of sensor node a, Using π b represents the LMB multi-target posterior probability density of sensor node b,

[0061] The LMB multi-target posterior probability density and fusion weight of sensor node a are combined into (ω a ,π a ),ω a is the fusion weight of sensor node a, and the LMB multi-target posterior probability density and fusion weight of sensor node b are combined into (ω b ,π b ),ω b is the fusion weight of sensor node b;

[0062] Step 32: Define the cost matrix is the label space The number of trajectories in is the label space The number of trajectories in the

[0063] Step 33, initialize i=1;

[0064] Step 34, initialize j=1;

[0065] Step 35: Calculate label space The i-th trajectory and label space in The fusion probability distribution p of the j-th trajectory in , and then calculate the element of the i-th row and j-th column in the cost matrix according to the fusion probability distribution p;

[0066] Step 36: Determine whether it is satisfied

[0067] like Then let j=j+1, and return to step 35;

[0068] like Then execute step 37;

[0069] Step 37: Determine whether it is satisfied

[0070] like Then let i=i+1, and return to execute steps 3 and 4;

[0071] like Then execute step 38;

[0072] Step 38: Design a cost function, and obtain the label matching result of sensor node b and sensor node a according to the designed cost function and cost matrix.

[0073] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0074] At any time, the matching method of this embodiment is used to perform label matching.

[0075] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that: the calculation label space The i-th trajectory and label space in The fusion probability distribution p of the j-th trajectory in is specifically:

[0076] Step 1. Calculate the probability r:

[0077]

[0078] in, is the label space The i-th trajectory in is the label space The probability of the existence of the Bernoulli component corresponding to the i-th trajectory in is, is the label space The jth trajectory in is the label space The existence probability of the Bernoulli component corresponding to the j-th trajectory in ;

[0079] Step 2: Calculate weights and

[0080]

[0081] Step 3: According to weight and Calculate the fusion probability distribution p:

[0082]

[0083] in, is the label space The probability density of the Bernoulli component corresponding to the i-th trajectory in is, is the label space The probability density of the Bernoulli component corresponding to the j-th trajectory in .

[0084] The other steps and parameters are the same as those in Specific Implementations 1 to 5.

[0085] Specific implementation method 7: This implementation method is different from any one of specific implementation methods 1 to 6 in that: the element of the i-th row and j-th column in the cost matrix is ​​calculated according to the fusion probability distribution p, specifically:

[0086]

[0087] in, is the element in the i-th row and j-th column of the cost matrix, D KL (·||·) means calculating KL divergence.

[0088] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0089] Specific implementation eight: This implementation differs from any one of the specific implementations one to seven in that: the fusion weight ∑ n＝a,b ω n =1.

[0090] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0091] Specific implementation method 9: This implementation method is different from the specific implementation methods 1 to 8 in that the specific process of step 38 is:

[0092] The design cost function J(τ) is:

[0093]

[0094] By minimizing the cost function value, we get the label matching function τ b , That is, through the label matching function τ b What you get exist The matching results in the label space Each trajectory i in the label space Find the corresponding trajectory in And it is the label space The set of matching results found by each trajectory in should satisfy: the sum of the corresponding elements in the cost matrix of the matching results is the smallest.

[0095] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0096] For the local multi-target density π i (X), i = 1, ..., s, the result of arithmetic mean fusion can be obtained by Kullback-Leibler mean, expressed as:

[0097]

[0098] Further, the fusion results shown below can be obtained:

[0099]

[0100] in, Represents the sum of fusion weights.

[0101] Based on the above fusion concept, the present invention performs the following fusion process.

[0102] Specific implementation method 10: This implementation method is different from the specific implementation methods 1 to 9 in that the specific process of step 4 is:

[0103] The LMB multi-target posterior probability density of sensor node b is expressed as τ b (l) is the trajectory that matches trajectory l in the label space of sensor node b at time k, b = 1, 2, ..., N, then the fused LMB posterior probability density is:

[0104]

[0105] in, is the trajectory τ of sensor node b in the label space at time k b (l) The probability of the existence of the corresponding Bernoulli component, is the trajectory τ of sensor node b in the label space at time k b (l) The probability density of the corresponding Bernoulli component;

[0106]

[0107] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0108] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A distributed multi-source LMB target tracking method based on label matching, characterized in that: The method specifically comprises the following steps: Step 1: Each sensor node uses a label multi-Bernoulli filter to track multiple targets, and obtains the local LMB multi-target posterior probability density of each sensor node; The LMB multi-target posterior probability density of the sensor node at time k is: For any sensor node: Step 1. The LMB posterior probability density of the new target at time k is: in, yes The probability of the existence of the Bernoulli component corresponding to the trajectory l is, yes The probability density of the Bernoulli component corresponding to the trajectory l in is, is the new target space at time k; The LMB posterior probability density at time k-1 is: in, yes The probability of the existence of the Bernoulli component corresponding to the trajectory l is, yes The probability density of the Bernoulli component corresponding to the trajectory l in is, is the label space at time k-1; Then the LMB posterior probability density of multi-target prediction at time k is: in, is the probability of existence of the Bernoulli component corresponding to the predicted k-time trajectory l, is the probability density of the Bernoulli component corresponding to the predicted k-time trajectory l, is the label space at time k; Among them, h S (l) is the intermediate variable, p S (·, l) is the survival probability of trajectory l, f(x|·, l) is the state transition density of trajectory l, and <·,·> represents the inner product operation; Step 1 and 2: The LMB posterior probability density of multiple targets at time k is: in: is the probability of existence of the Bernoulli component corresponding to the trajectory l at time k, is the probability density of the Bernoulli component corresponding to the trajectory l at time k, Represented by space , Θ represents the space composed of all the mappings between sensor measurements and trajectories, θ is an element in the mapping space Θ, θ(l) represents the sensor measurement value mapped by trajectory l, ω (I,θ) (Z) represents the corresponding probability when mapped to θ, p (θ) (x,l) represents the posterior probability density of trajectory l when the trajectory is mapped to θ, 1 I (l) is the inclusion function; in, Definition The calculation method is as follows: x represents the kinematic state of the target, x and label l together form the augmented state (x, l), p D (x,l) is the probability of detection of state (x,l), g(z θ(l) |x,l) means when the state is (x,l), measure z θ(l) The corresponding likelihood function, k(z θ(l) ) is the clutter density of the Poisson distribution, Step 2: Construct a sensor network based on the communication relationship between sensor nodes. The constructed sensor network is represented as is the set of nodes in the sensor network, It is the edge set in the sensor network. When sensor node i and sensor node j communicate with each other, there is an edge between sensor node i and sensor node j. Each sensor node uses the communication link in the sensor network to transmit the LMB multi-target posterior probability density; Step 3: Select a reference sensor node, and each sensor node performs label matching on the local LMB multi-target posterior probability density and the LMB multi-target posterior probability density of the reference sensor node to obtain the label matching result between each sensor node and the reference sensor node; Step 4: Perform arithmetic mean fusion based on the label matching results to obtain the fusion result. After state extraction of the fusion result, the target state is obtained.

2. A distributed multi-source LMB target tracking method based on label matching according to claim 1, characterized in that: The label space of the sensor node at time k is: in, is the label space at time k, is the label space at time k-1, is the new target space at time k.

3. A distributed multi-source LMB target tracking method based on label matching according to claim 2, characterized in that: The intermediate variable h S (l) is:

4. The distributed multi-source LMB target tracking method based on label matching according to claim 1 is characterized in that: Taking sensor node a as the reference sensor node, the tag matching process of sensor node b and sensor node a is as follows: Step 3.1: Record the label space of sensor node a as The label space of sensor node b is recorded as Using π a represents the LMB multi-target posterior probability density of sensor node a, Using π b represents the LMB multi-target posterior probability density of sensor node b, The LMB multi-target posterior probability density and fusion weight of sensor node a are combined into (ω a ,π a ),ω a is the fusion weight of sensor node a, and the LMB multi-target posterior probability density and fusion weight of sensor node b are combined into (ω b ,π b ),ω b is the fusion weight of sensor node b; Step 32: Define the cost matrix is the label space The number of trajectories in is the label space The number of trajectories in the Step 33, initialize i=1; Step 34, initialize j=1; Step 35: Calculate label space The i-th trajectory and label space in The fusion probability distribution p of the j-th trajectory in , and then calculate the element of the i-th row and j-th column in the cost matrix according to the fusion probability distribution p; Step 36: Determine whether it is satisfied like Then let j=j+1, and return to step 35; like Then execute step 37; Step 37: Determine whether it is satisfied like Then let i=i+1, and return to execute steps 3 and 4; like Then execute step 38; Step 38: Design a cost function, and obtain the label matching result of sensor node b and sensor node a according to the designed cost function and cost matrix.

5. A distributed multi-source LMB target tracking method based on label matching according to claim 4, characterized in that: The computation label space The i-th trajectory and label space in The fusion probability distribution p of the j-th trajectory in is specifically: Step 1. Calculate the probability r: in, is the label space The i-th trajectory in is the label space The probability of the existence of the Bernoulli component corresponding to the i-th trajectory in is, is the label space The jth trajectory in is the label space The existence probability of the Bernoulli component corresponding to the j-th trajectory in ; Step 2: Calculate weights and Step 3: According to weight and Calculate the fusion probability distribution p: in, is the label space The probability density of the Bernoulli component corresponding to the i-th trajectory in is, is the label space The probability density of the Bernoulli component corresponding to the j-th trajectory in .

6. A distributed multi-source LMB target tracking method based on label matching according to claim 5, characterized in that: The element of the i-th row and j-th column in the cost matrix is ​​calculated according to the fusion probability distribution p, specifically: in, is the element in the i-th row and j-th column of the cost matrix, D KL (·||·) means calculating KL divergence.

7. A distributed multi-source LMB target tracking method based on label matching according to claim 6, characterized in that: The fusion weight ∑ n＝a,b ω n =1.

8. The distributed multi-source LMB target tracking method based on label matching according to claim 7 is characterized in that: The specific process of step thirty-eight is: The design cost function J(τ) is: By minimizing the cost function value, we get the label matching function τ b , That is, through the label matching function τ b What you get exist The matching results in .

9. A distributed multi-source LMB target tracking method based on label matching according to claim 8, characterized in that: The specific process of step 4 is as follows: The LMB multi-target posterior probability density of sensor node b is expressed as τ b (l) is the trajectory that matches trajectory l in the label space of sensor node b at time k, b = 1, 2, ..., N, then the fused LMB posterior probability density is: in, is the trajectory τ of sensor node b in the label space at time k b (l) The probability of the existence of the corresponding Bernoulli component, is the trajectory τ of sensor node b in the label space at time k b (l) The probability density of the corresponding Bernoulli component;

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