Multi-target tracking method based on fast GM-CBMeMBer filtering

Abstract

The invention provides a multi-target tracking method based on rapid GM-CBMeMBer filtering, and the multi-target tracking is realized by constructing an F-GM-CBMeMBer filter and utilizing the constructed F-GM-CBMeMBer filter. The filter can simplify the updating step of the CBMeMBer filter, still inherits the excellent performance of the CBMeMBer filter in the aspect of state estimation, greatly improves the tracking efficiency while guaranteeing the tracking performance compared with the original CBMeMBer filter, can be considered to be the accelerated implementation of the original CBMeMBer filter, improves the operation efficiency of a multi-target tracking system, and reduces the cost of the CBMeMBer filter. And a multi-target tracking task with a relatively high real-time requirement can be better executed.

Description

Technical Field

[0001] The invention belongs to the technical field of single-sensor multi-target tracking, and relates to a fast GM-CBMeMBer filter, which can greatly simplify the calculation complexity and realize fast and effective tracking of multiple targets. Background Art

[0002] Multi-target tracking refers to estimating the number, state and other information of targets from the complex data obtained by sensors. Single-sensor multi-target tracking methods are mainly divided into two categories: ① Data Association (DA)-based methods; ② Random Finite Set (RFS)-based methods. Among them, DA-based tracking methods often have the risk of combinatorial explosion due to their complex calculations when facing many more complex target tracking problems such as sensor quality degradation and increased clutter intensity. In some complex environments, it is difficult to meet the needs of applications. In recent years, RFS-based tracking methods have attracted widespread attention, and some RFS-based filters have been proposed, such as Probability Hypothesis Density (PHD) filters, Potential PHD (CPHD) filters, Multi-target Multi-Bernoulli (MeMBer) filters, and Carinality BalancedMeMBer (CBMeMBer) filters.

[0003] The following are some representative works based on RFS tracking methods:

[0004] In 2003, R.Mahler proposed a PHD filter based on RFS, which simplified the probability space modeling of state variables into the probability hypothesis space modeling of state variables, but did not obtain a closed-form solution; subsequently, Australian scholar BNVo proposed a realizable Gaussian mixture PHD (GM-PHD) filter and a sequential Monte Carlo PHD (SMC-PHD) filter; in 2007, R.Mahler proposed a CPHD filter; in addition to the PHD filter, Mahler also proposed a multi-target multi-Bernoulli (MeMBer) filter based on multi-target density approximation under the assumption of multi-Bernoulli random finite sets. However, the MeMBer filter will have the problem of overestimation of the number of targets. In 2009, Vo made improvements on this basis and proposed a potential balanced Bernoulli filter (Carinality Balanced MeMBer, CBMeMBer). The CBMeMBer filter can not only effectively estimate the motion state of multiple targets, but also accurately estimate the number of multiple targets.

[0005] The standard GM-CBMeMBer filter approximates the multi-target density to a multi-Bernoulli form, and each Bernoulli term contains multiple Gaussian components. Therefore, before the target state is extracted, not only the Bernoulli terms need to be pruned and merged, but also the Gaussian components in each Bernoulli term need to be pruned and merged, which greatly increases the computational complexity and makes it difficult to meet the multi-target tracking task with high real-time requirements. Therefore, the present invention proposes a multi-target tracking method based on fast GM-CBMeMBer filtering (abbreviated as F-GM-CBMeMBer), which simplifies the update step: adopts the limit approximate association strategy, stipulates that a measurement can only be associated with the Gaussian term with the largest likelihood function, and after simplification, it is no longer necessary to prune and merge the Gaussian components, which reduces the computational complexity, improves the operating efficiency of the multi-target tracking system, and can better perform multi-target tracking tasks with high real-time requirements. Summary of the invention

[0006] The first object of the present invention is to propose a multi-target tracking method based on fast GM-CBMeMBer filtering (F-GM-CBMeMBer) to address the deficiencies of the prior art.

[0007] The present invention provides a multi-target tracking method based on fast GM-CBMeMBer filtering, comprising the following steps:

[0008] Step (1), constructing a single sensor multi-target tracking scenario and setting relevant parameters, including the process noise of the target motion and the observation noise of the sensor;

[0009] Step (2), modeling the states and observations of multiple targets;

[0010] Step (3), constructing the F-GM-CBMeMBer filter, specifically:

[0011] 3-1 Construct GM-CBMeMBer filter;

[0012] 3-2 Based on the GM-CBMeMBer filter, construct the F-GM-CBMeMBer filter;

[0013] Step (4), use the built F-GM-CBMeMBer filter to achieve multi-target tracking.

[0014] A second object of the present invention is to provide a fast GM-CBMeMBer multi-target tracking device, comprising:

[0015] The data acquisition module is responsible for obtaining the status and observation of multiple targets;

[0016] The multi-target tracking module is responsible for realizing multi-target tracking using the F-GM-CBMeMBer filter.

[0017] A third object of the present invention is to provide a computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method described above.

[0018] A fourth object of the present invention is to provide a computing device, comprising a memory and a processor, wherein the memory stores executable code, and when the processor executes the executable code, the method described is implemented.

[0019] The beneficial effects of the present invention are:

[0020] The present invention proposes a complete multi-target tracking solution, and adopts the extreme approximate association strategy to simplify the update steps of the GM-CBMeMBer filter respectively. The tracking efficiency is greatly improved compared with the original GM-CBMeMBer filter, and the multi-target tracking efficiency can be effectively improved under the premise of ensuring tracking accuracy and robustness; not only that, compared with the GM-PHD filter in which the time-varying multi-target posterior density is approximated as a multi-target Poisson process, the GM-CBMeMBer filter approximates the multi-target posterior density as a multi-target multi-Bernoulli. This approximation method is closer to the actual scene and has better robustness, which has broader practical significance for the rapid implementation of GM-CBMeMBer. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a flowchart of the specific implementation of the core part of the F-GM-CBMeMBer method of the present invention;

[0022] Figure 2 is a multi-target motion trajectory diagram;

[0023] Figure 3 It is a comparison chart of the average values ​​of the target estimation numbers obtained by the method of the present invention and the common GM-CBMeMBer filter under 100 Monte Carlo;

[0024] Figure 4 It is a comparison chart of the OSPA average values ​​obtained by the method of the present invention and the common GM-CBMeMBer filter under 100 Monte Carlo. DETAILED DESCRIPTION

[0025] The present invention is further analyzed below in conjunction with specific implementation methods;

[0026] The multi-target tracking method of F-GM-CBMeMBer, such as Figure 1 The following steps are involved:

[0027] Step (1) constructs a single sensor multi-target tracking scenario and sets relevant parameters, including the process noise of the target motion and the observation noise of the sensor, specifically:

[0028] The target moves in a two-dimensional plane, and its state is represented by x = [p x , v x , p y , v y ] T , where p x , p y are the positions of the target in the x and y directions, respectively, and v x 、v y are the speeds of the target in the x and y directions, respectively, and T represents transposition;

[0029] The process noise covariance of the target motion is set to σ x (k) 2 represents the noise variance of the environment at time k on the target at x speed, σ y (k) 2 represents the noise variance of the environment on the target's y velocity at time k;

[0030] Set the sensor's observation noise covariance to where δ x 2 ,δ y 2 Respectively represent the noise variance of the sensor to the target x position and y position;

[0031] Step (2) is to model the states and observations of multiple targets, specifically:

[0032] 2-1 Target State Modeling

[0033] Let the number of targets at time k be N k , the target states are The target state at time k can be represented by a random finite set (RFS) X k Indicates that

[0034]

[0035] where χ is the state space, is the set of all finite subsets of χ;

[0036] The target is a state x at time k-1. k-1 Transfer to a state x at time k k It is called state transfer. Assume that the probability density of each target state transfer is f k|k-1 (x k |x k-1) conforms to the linear Gaussian model and is expressed as:

[0037] f k|k-1 (x k |x k-1 )=N(x k ; F k-1 x k-1 , Q k-1 ) (2)

[0038] Where N(x k ; F k-1 x k-1 , Q k-1 ) represents the target state x k The spatial distribution of its obedience state is F k-1 x k-1 , with covariance Q k-1 Gaussian distribution, F k-1 is the state transfer matrix, Q k-1 is the process noise covariance matrix;

[0039] 2-2 Target kinematic observation modeling

[0040] Assume that the number of target measurements received at time k is M k , the target measurements are The sensor measurement vector at time k is expressed as z k,α =[z x,α ,z y,α ] T , α=1,2,…,M k , the target measurement at time k can be obtained from a finite set Z k Indicates that

[0041]

[0042] Among them, z k,α ,z y,α are the positions of the αth target measured by the sensor in the x and y directions, respectively, T represents transposition, is the observation space, yes The set of all finite subsets of ;

[0043] Assume that the sensor measurement model g at time k k|k (z k |x k ) conforms to the linear Gaussian model and is expressed as:

[0044] g k|k (z k |x k )=N(z k ;H k xk ,R k ) (4)

[0045] Where N(z k ;H k x k ,R k ) represents a measurement z at time k k The spatial distribution of k x k , the covariance is R k Gaussian distribution, H k is the observation matrix, R k is the measurement noise covariance matrix;

[0046] 2-3 Clutter kinematic observation modeling

[0047] Assume that the number of clutter received at time k follows a Poisson distribution with parameter λ, and the position distribution of clutter in the measurement space follows a uniform distribution, that is,

[0048]

[0049] Among them, n c represents the expected number of clutter at time k, ρ(n c ) represents the probability function of the Poisson distribution with parameter λ, The observed value of clutter j is The probability density of , V represents the volume of the observation space;

[0050] Then, the intensity of clutter at time k is expressed as:

[0051]

[0052] Step (3), constructing the F-GM-CBMeMBer filter, specifically:

[0053] 3-1GM-CBMeMBer filter

[0054] Prediction step:

[0055] At time k-1, the posterior multi-target density can be expressed in multi-Bernoulli form:

[0056]

[0057] in, represents the probability of existence of the i-th posterior Bernoulli term at time k-1, represents the probability density of the i-th posterior Bernoulli term at time k-1, V k-1 represents the number of posterior Bernoulli terms at time k-1, It is a Gaussian mixture form:

[0058]

[0059] in, and They represent the weight, mean, and covariance matrix of the jth Gaussian term in the i-th posterior Bernoulli term at time k-1, respectively. represents the number of Gaussian terms in the i-th posterior Bernoulli.

[0060] The multi-target density predicted at time k can be expressed as a multi-Bernoulli form of the combination of survival targets and new targets:

[0061]

[0062] in, represents the existence probability of the i-th survival target Bernoulli term at time k, represents the probability density of the Bernoulli term of the ith survival target at time k, V k-1 represents the number of Bernoulli items of the posterior target at time k-1, represents the survival probability of the i-th new target Bernoulli item at time k, represents the probability density of the i-th new target Bernoulli term at time k, V Γ,k Represents the number of new target Bernoulli items at time k.

[0063]

[0064] in, represents the number of Gaussian components in the Bernoulli term of the i-th new target at time k, They represent the weight, mean and covariance of the j-th Gaussian component of the i-th new target Bernoulli term, respectively.

[0065] The multi-Bernoulli component of survival target prediction can be calculated by the following formula:

[0066]

[0067] Write the predicted multi-target density in a multi-Bernoulli form:

[0068]

[0069] in, represents the survival probability of the i-th predicted target Bernoulli item, represents the probability density of the i-th predicted target Bernoulli term, It is a Gaussian mixture form:

[0070]

[0071] in, represents the number of Gaussian terms in the Bernoulli term of the i-th predicted target at time k, Represents the weight, mean, and covariance of the jth Gaussian component of the i-th predicted target Bernoulli term.

[0072] renew:

[0073] The updated multi-target density can be approximated as a multi-Bernoulli form:

[0074]

[0075] in, represents the probability of missing the Bernoulli term at time k-1, represents the probability density of missing Bernoulli items at time k-1, represents the survival probability of the updated Bernoulli term, represents the probability density of the updated Bernoulli term.

[0076]

[0077] Among them, p D,k represents the detection probability, c k (z) represents the clutter intensity at time k.

[0078]

[0079] Prune and merge:

[0080] As time goes by, the Gaussian items in each Bernoulli are increasing. Therefore, after the update at time k, pruning and merging operations are required to reduce the number of Gaussian items propagated to the next moment. The specific process is as follows:

[0081] Assume that the Gaussian term of the i-th updated Bernoulli term at time k is expressed as:

[0082]

[0083] in, and They represent the weight, mean, and covariance matrix of the jth Gaussian term in the i-th updated Bernoulli term at time k, respectively. represents the number of Gaussian terms in the i-th posterior Bernoulli.

[0084] First, perform pruning operations to satisfy The Gaussian particles are deleted, and the Gaussian particle set after deletion is expressed as:

[0085]

[0086] in, and They represent the weight, mean, and covariance matrix of the jth Gaussian term in the i-th posterior Bernoulli term after pruning, respectively. Represents the number of Gaussian terms in the i-th posterior Bernoulli after pruning.

[0087] After pruning, the merging operation is performed. Assume that the weight of the lth Gaussian particle is the largest. If the following conditions are met, fusion is performed:

[0088]

[0089] Among them, U represents the fusion threshold, and the Gaussian component after fusion is:

[0090]

[0091] After the first fusion, the remaining components are fused for the second time, and so on, until the fusion is complete.

[0092] 3-2F-GM-CBMeMBer filter

[0093] Compared with the standard algorithm, the fast GM-CBMeMBer algorithm uses the extreme approximate association strategy to simplify the update step. The principle of approximation is to stipulate that a measurement can only be associated with the Gaussian term with the largest likelihood function. After simplification, it is no longer necessary to trim and merge the Gaussian components, which can greatly simplify the computational complexity and improve the operation speed.

[0094] predict:

[0095] Assume that at time k-1, the posterior multi-target density is is a Gaussian mixture form. After adopting the limit approximate association strategy in the update step, there is only one Gaussian term in each Bernoulli term of the posterior multi-target at time k-1, and its weight is set to 1, so the posterior multi-target density can be expressed as:

[0096]

[0097] The predicted multi-target density can be expressed in multi-Bernoulli form:

[0098]

[0099] in, Derived from equations (10) and (11), and the others from (41) to (44):

[0100]

[0101]

[0102] The predicted multi-target density can be written in a multi-Bernoulli form:

[0103]

[0104] It is a Gaussian mixture form, which omits the weight term compared with (17):

[0105]

[0106] V k|k-1 =V k-1 +V Γ,k (47)

[0107]

[0108] renew:

[0109] The updated multi-target density can be approximated as a multi-Bernoulli form:

[0110]

[0111] in

[0112]

[0113] The probability of existence in formula (52) Extraction of the largest Bernoulli term:

[0114]

[0115] Transform equation (23) into equation (54):

[0116]

[0117] Transform equation (24) into equation (55):

[0118]

[0119] After simplification, the Gaussian term pruning and merging operation is no longer performed, so the updated multi-objective density is the posterior multi-objective density.

[0120] Step (4): Use the built F-GM-CBMeMBer filter to achieve multi-target tracking;

[0121] The target tracking effect of the present invention is as follows Figure 2 , Figure 3 , Figure 4 As shown; Figure 2 For the tracking scene, the scene contains the true trajectories and filtered trajectories of three targets; Figure 3 , Figure 4 This is a comparison chart of the average target estimation number and the OSPA average value obtained after 100 Monte Carlo simulations. Figure 3 It can be seen that the number of target estimates of the method of the present invention is close to that of the ordinary GM-CBMeMBer filter; Figure 4 It can be seen that the OSPA average value of the method of the present invention is slightly higher than that of the ordinary GM-CBMeMBer filter; however, it can be seen from Table 1 that the running time of the ordinary GM-CBMeMBer filter is more than 1.87 times that of the method of the present invention. Therefore, the method of the present invention can effectively improve the tracking efficiency of multiple targets while ensuring tracking accuracy and robustness.

[0122] Table 1 Comparison of running time under 100 Monte Carlo experiments

[0123]

[0124] An embodiment of the present invention provides an electronic device. Specifically, the electronic device includes a memory and a processor. The memory stores executable code. When the processor executes the executable code, the method described in any one of the implementation modes is implemented.

[0125] The memory may include high-speed random access memory (RAM), and may also include non-volatile memory (Non-volatile Memory), such as at least one disk memory. The communication connection between the system network element and at least one other network element is realized through at least one communication interface (which may be wired or wireless), and the Internet, wide area network, local area network, metropolitan area network, etc. may be used.

[0126] The bus may be an ISA bus, a PCI bus or an EISA bus, etc. The bus may be divided into an address bus, a data bus, a control bus, etc.

[0127] Among them, the memory is used to store the program, and the processor executes the program after receiving the execution instruction. The method executed by the device for flow process definition disclosed in any embodiment of the above-mentioned embodiment of the present invention can be applied to the processor or implemented by the processor.

[0128] The processor may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in the processor or an instruction in the form of software. The above processor may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it may also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The methods, steps and logic block diagrams disclosed in the embodiments of the present invention can be implemented or executed. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in conjunction with the embodiments of the present invention can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in a decoding processor. The software module may be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware.

[0129] The computer program product of the readable storage medium provided in the embodiment of the present invention includes a computer-readable storage medium storing program code, and the instructions included in the program code can be used to execute the methods described in the previous method embodiments. The specific implementation can be referred to the previous method embodiments, which will not be repeated here.

[0130] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0131] Finally, it should be noted that the above-described embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The protection scope of the present invention is not limited thereto. Although the present invention is described in detail with reference to the above-described embodiments, ordinary technicians in the field should understand that any technician familiar with the technical field can still modify the technical solutions recorded in the above-described embodiments within the technical scope disclosed by the present invention, or can easily think of changes, or make equivalent replacements for some of the technical features therein; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A multi-target tracking method based on fast GM-CBMeMBer filtering, characterized by The following steps are involved: Step (1), constructing a single sensor multi-target tracking scenario and setting relevant parameters, including the process noise of the target motion and the observation noise of the sensor; Step (2), modeling the states and observations of multiple targets; Step (3), constructing the F-GM-CBMeMBer filter, specifically: 3-1 Construct GM-CBMeMBer filter; 3-2 Based on the GM-CBMeMBer filter, construct the F-GM-CBMeMBer filter; Step (4), use the built F-GM-CBMeMBer filter to achieve multi-target tracking.

2. The method according to claim 1, characterized in that Step 3-2 is specifically: 3-2-1 Prediction: Assume that at time k-1, the posterior multi-target density is in They represent the existence probability and probability density of the i-th posterior Bernoulli term at time k-1, respectively, and V k-1 represents the number of posterior Bernoulli items at time k-1; after adopting the limit approximate association strategy in the update step, there is only one Gaussian item in each Bernoulli item of the posterior multi-target at time k-1, and its weight is set to 1, so It is a Gaussian mixture form; Predicted multi-target density π k|k-1 Expressed in multi-Bernoulli form: in They represent the existence probability and probability density of the Bernoulli term of the i-th survival target at time k respectively; Respectively represent the existence probability and probability density of the i-th new target Bernoulli term at time k; V Γ,k represents the number of new target Bernoulli items at time k; The predicted multi-target density π k|k-1 Written in a multi-Bernoulli form: V k|k-1 =V k-1 +V Γ,k (3) Where V k|k-1 Indicates the number of predicted target Bernoulli items; They represent the existence probability and probability density of the i-th prediction target Bernoulli item respectively; It is a Gaussian mixture form; 3-2-2 Update: Update multi-target density π k Approximately in multi-Bernoulli form: in They represent the existence probability and probability density of the missed Bernoulli item at time k-1 respectively. Respectively represent the survival probability and probability density of the updated Bernoulli term, Z k represents a finite set of sensor measurement vectors at time k, and z represents a sensor measurement vector at time k; where p D,k represents the detection probability, represents the product of detection probability and likelihood function, κ k (z) represents the clutter intensity, represents the probability of existence of the updated Bernoulli term; The probability of existence in formula (7) Extraction of the largest Bernoulli term: therefore, in Respectively represent the mean and covariance of the Gaussian component in the index-th updated Bernoulli term, represents the likelihood function, H k represents the observation matrix, R k represents the observation error covariance matrix, Represents the mean of the Gaussian component in the index-th Bernoulli term of the predicted target, represents the Kalman gain, Represents the covariance of the Gaussian component in the index-th predicted Bernoulli term; After the above updating steps, no Gaussian term pruning and merging operations are performed, so the updated multi-objective density is the posterior multi-objective density.

3. The method according to claim 2, characterized in that In step 3-2-1 It is a Gaussian mixture form, expressed as: in represents the spatial distribution of the target state x at time k-1, which obeys the mean of the Gaussian term in the i-th posterior Bernoulli term Covariance Gaussian distribution.

4. The method according to claim 2, characterized in that The existence probability and probability density of the Bernoulli term of the i-th survival target at time k in step 3-2-1 Specifically: where p S,k represents the target survival probability, Respectively represent the mean and covariance of the jth Gaussian component of the i-th predicted target Bernoulli term; F k-1 represents the state transfer matrix, Q k-1 represents the process noise covariance matrix, They represent the weight, mean and covariance of the jth Gaussian component of the i-th new target Bernoulli term respectively; Represents the number of Gaussian components in the Bernoulli term of the i-th new target at time k.

5. The method according to claim 2, characterized in that In step 3-2-1 It is a Gaussian mixture form, expressed as: in Respectively represent the mean and covariance of the Gaussian component in the Bernoulli term of the i-th prediction target; Respectively represent the first (iJ γ,k ) The mean and covariance of the Gaussian components in the Bernoulli terms of the survival targets; V Γ,k represents the number of new target Bernoulli terms, V k|k-1 Represents the number of predicted target Bernoulli items.

6. A multi-target tracking device based on the method according to any one of claims 1 to 5, characterized in that include: The data acquisition module is responsible for obtaining the status and observation of multiple targets; The multi-target tracking module is responsible for realizing multi-target tracking using the F-GM-CBMeMBer filter.

7. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method according to any one of claims 1 to 6.

8. A computing device, comprising a memory and a processor, wherein the memory stores executable code, and when the processor executes the executable code, the method according to any one of claims 1 to 6 is implemented.

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