Multi-target endurance tracking method under intermittent continuous loss of radar measurement data

Abstract

The invention discloses a multi-target endurance tracking method under intermittent continuous missing of radar measurement data, and belongs to the field of multi-target tracking in radar data processing. Comprising the steps that a target is predicted and updated based on a random set filter under a random set framework, specifically, the random set filter can be a GLMB filter, iteration is carried out along with time steps, the state of the target death moment is recorded, and the death target meeting the condition is stored in a'to-be-regenerated target 'pool; on the basis that multi-frame measurement meets a regeneration target activation condition, screening out a'to-be-regenerated target 'from a'to-be-regenerated target' pool and converting the'to-be-regenerated target 'into a'regeneration target'; inputting the'regeneration target 'into the GLMB filter, and re-participating in the correlation hypothesis truncation and iteration recursion process of the GLMB filter; finally, estimating the target number, the target state and the target identity based on the multi-target posterior distribution at each moment; therefore, the problem of multi-target robust tracking under the condition of intermittent continuous missing of radar measurement data is solved.

Description

Technical Field

[0001] The present invention relates to the field of multi-target tracking in radar data processing, and in particular to the field of multi-target tracking under random finite set theory. Background Art

[0002] Radar target tracking is to continuously infer and estimate the state, number and identity of the target based on the measurement time series obtained by the radar. Target tracking is one of the core links of radar data processing. However, in actual radar target detection scenarios, due to the complex characteristics of the target and the environment, the measurement data obtained by the radar may be intermittently missing. For example:

[0003] 1) Obstacle occlusion (non-line-of-sight). Due to random obstructions such as hills, islands, and trees in the radar detection environment, the target may be in the non-direct line-of-sight area of ​​the radar, resulting in target measurement loss for a certain period of time;

[0004] 2) There is strong ground clutter and sea clutter in the radar surveillance scene, which causes the measurement echo to be submerged, and the radar measurement detection probability drops sharply, resulting in measurement loss for a period of time;

[0005] 3) When the pulse Doppler radar detects a target, the following time-varying maneuvers may occur: the target may be in the radar's Doppler blind zone, causing multiple frames of radar measurement data to be missing continuously;

[0006] 4) When the radar is suppressed by intermittent electronic interference from the enemy, its detection range is reduced, making it difficult to determine the field of view information of the radar site, which will also cause intermittent target measurement.

[0007] The intermittent loss of radar measurement data will lead to discontinuous target batches, target track breaks, and even fragmentation, which seriously affects radar detection performance. In response to this problem, domestic and foreign scholars have conducted relevant research based on traditional multi-target tracking methods. In 2011, Hernandez et al. from QuinetiQ, UK, proposed a target continuous tracking method based on dynamic / static target missed detection indicators in a clutter environment. In 2019, Shuo Liu et al. from Harbin Institute of Technology in China used the traditional MHT tracking algorithm to modify the traditional MHT likelihood ratio using the target dynamic statistical characteristics and model transition probability to implement an improved multi-hypothesis "go-stop-go" target tracking method. However, on the one hand, the above methods are mainly aimed at the measurement loss problem when the target falls into the Doppler blind spot, and the solution requires prior information of the known multi-spectral blind spot; on the other hand, the above target tracking methods are mainly concentrated in the framework of traditional target tracking theory. Due to the limitations of traditional tracking modeling theory, when dealing with unknown time-varying multi-target tracking problems, it is necessary to splice the single-state filtering algorithm, data association algorithm, and track management algorithm together. However, this type of multi-process splicing-based method is not built on an optimal Bayesian framework and may have process propagation errors.

[0008] As a research hotspot in the field of multi-target tracking in recent years, random finite set theory models the measurement uncertainty and unknown time-varying characteristics of target dimensions under the framework of point process theory, providing a unified optimal Bayesian filtering framework for multi-target tracking problems. In 2019, Xie et al. from the Air Force Early Warning Academy introduced the minimum detectable velocity (MDV) model to address the problem of target tracking in the Doppler Blind Zone (DBZ) and proposed a multi-model Gaussian mixture PHD filter. In 2020, Wu et al. from the Air Force Early Warning Academy introduced MDV information into the multi-model GLMB filter, which can effectively suppress the masking effect of the Doppler blind zone. However, the above method mainly targets the "stop-go" problem caused by the Doppler blind zone, relies on the known MDV prior knowledge, and constructs a state-dependent detection probability, which is difficult to apply to the more universal "stop-go" target tracking problem, such as the temporary disappearance of the target caused by the occlusion of obstacles.

[0009] In 2022, Wang Bailu and others introduced the target regeneration process for the first time based on the framework of random finite set theory, and proposed a "go-stop-go" target tracking technology for low-altitude surveillance radar target detection. It not only solves the problem of target loss caused by drone hovering, turning around, etc. falling into the Doppler blind spot, but also solves the problem of target track interruption under the short-term occlusion of moving targets. However, this method is mainly aimed at air scenes and is difficult to apply to situations with high clutter density in radar measurements. It is prone to problems of false track regeneration and erroneous endurance. The fundamental reasons are: 1) The basic filtering framework of this method is based on the labeled multi-Bernoulli filter, which has weak suppression ability for adjacent strong clutter; 2) On the other hand, the proposed reborn target model only considers the correlation of single-frame measurements, which is difficult to apply to high-density clutter scenes. Summary of the invention

[0010] The present invention is intended to provide a multi-target endurance tracking method under intermittent and continuous loss of radar measurement data to solve the problems raised in the above background technology.

[0011] In order to achieve the above object, the present invention provides the following technical solutions:

[0012] A multi-target endurance tracking method under intermittent and continuous missing of radar measurement data is provided. The method is based on a random set filter framework, sets a reborn target model based on multi-frame measurement activation, completes the endurance of the target when the measurement is intermittently missing, and realizes robust continuous tracking of multiple targets. The specific steps include:

[0013] Step 1: Initialize system parameters including: radar scanning period T, total observation time step K; target survival probability function p S (x,l), target detection probability function p d (x, l), clutter density function κ(·);

[0014] Set the state transfer density function f according to the motion characteristics of the monitored target + (x + ,l + |x,l)=δ l (l + )(l)f + (x + |x,l) parameters, including but not limited to the target state transfer matrix F, the process noise covariance matrix Q; set the single target measurement likelihood function according to the sensor measurement type Parameters, including but not limited to the measurement matrix H and the measurement noise covariance matrix R;

[0015] Among them, x and l are the single target state and corresponding label at time k-1, respectively. + and l +are the single target state and the corresponding label at time k, respectively. k can be any time between 0 and the total observation time step K; represents the measurement z at time k j With label l + The likelihood function between the targets;

[0016] Initialize the target pool to be reborn to an empty set The size of the rebirth wave gate Γ, the maximum retention time of the "target to be reborn" t1, the minimum time threshold for the "dead target" to become the "target to be reborn" t2, and the time threshold of the "multi-frame pre-filtering" K rb , initialize the rebirth target transfer matrix F RB , GLMB component truncation threshold g1;

[0017] Step 2: Initialize time step k = 0 and initialize the GLMB multi-target distribution as follows:

[0018]

[0019] The specific implementation uses a parameter set to fully characterize;

[0020] Where h (h = 1, 2, ..., H) represents the hth GLMB component, H is the total number of GLMB components, I (h) is the target label set of the hth GLMB component, w (h) is the non-negative weight w of the hth GLMB component (h) ,satisfy X is a set of multi-target states; is the label set corresponding to the multi-target state X;

[0021] In the formula, p (h) (·,l) is the probability density function, [·] X Represents the product of the probability density functions of all elements in set X; is the Dirac function; Indicates the label inconsistency indicator, which is used to ensure that different target states have different labels;

[0022] Step 3: Let k:=k+1, the sensor receives the measurement data set Z at time k k ={z j :j=1,…,M}, determine the target pool to be reborn Is it empty?

[0023] (1) If it is not empty, execute the following steps;

[0024] Step 3.1: Update the pool of targets to be reborn, and delete the set of targets that have not been activated for t1 time.

[0025]

[0026] Step 3.2: Update the respawn target pool The number of frames to wait for each target to be reborn Calculate all measurements z at time k j Pseudo measurement of target l to be regenerated The Mahalanobis distance between them is:

[0027]

[0028] If a measurement falls into the σ-wave gate of the target to be regenerated, the condition is met:

[0029]

[0030] Then k rb (l):=k rb (l)+1;

[0031] If the multi-frame measurement meets the activation conditions, specifically k rb (l)>K rb , then activate the target to be reborn with label l. All activated rebirth targets constitute the set

[0032] in, Indicates the state of the target to be reborn with label l at the moment of death. The new information covariance matrix at the moment of death of the target to be reborn;

[0033] Step 3.3: Create a respawn target after activation The rebirth target distribution is specifically the LMB distribution form π RB,+ (X RB ), which is fully characterized by the following parameter set in its specific implementation:

[0034]

[0035] Among them, r RB,+ (l RB,+ ) indicates that the label is l RB,+ The target rebirth probability of π RB,+ (X RB ) corresponds to the target label set: That is, the conditions are met: Label is l RB,+ The rebirth target distribution p RB,+ (·,l) is determined by the state at the moment of death and the rebirth target transfer function F RB Joint decision

[0036] (2) If the pool of targets to be reborn is empty, the reborn target component is set to zero and the subsequent step 4 is executed;

[0037] Step 4: Based on the measurement data set Z obtained by the sensor at time k k , perform multi-target state prediction and update, specifically using joint prediction and update random set filters to calculate the updated GLMB multi-target posterior distribution π at time k k (X), its corresponding parameter set is:

[0038]

[0039] in,

[0040]

[0041] The above posterior distribution π k The calculation formula of (X) is in the form of a sum of multiple hypotheses, which includes every possible (I,ξ,I + ,θ + ), where θ + Represents the target label set I + With the generalized measurement set Some kind of association mapping θ + ;(I,ξ,I + ,θ + )Meet the conditions: is the set of all possible target labels at time k, Θ includes all possible association mappings at time k, which is called the association mapping space at time k; Ξ includes all possible association mappings at time 0:k-1, which is called the historical association mapping space at time 0:k-1. B,+ (l + ) is labeled l + The target newborn probability, P S (·,l) is the target survival probability, p B,+ (x + ,l + ) is the label for the new target distribution, p (ξ) (·,l + ) is the probability density function of the target under the k-1 time ξ association hypothesis;<f(·),g(·)> represents the inner product of functions f(·), g(·);

[0042] Considering the assumption (I,ξ,I + ,θ +) increases exponentially with the iteration time. The above method uses a sampling algorithm to filter out high-weight hypothesis components, and the sampling algorithm is specifically a Gibbs sampling algorithm;

[0043] The k-time GLMB posterior distribution is composed of all target hypotheses at the k-time. They represent the k-time measurement set, a certain survival target label set, a new target label set and a reborn target label set respectively; M is the number of measurements at time k, R is the number of targets in the survival target label set I, and P is the number of targets at time k (including survival targets, new targets and reborn targets); (R+1):(N B +R) corresponds to the new target number, N B +R+1:P indicates the rebirth target number;

[0044] The specific implementation steps include:

[0045] Step 4.1, define P-tuple vector: γ = (γ 1:P )∈{-1:M} P ;

[0046]

[0047] Step 4.2: Calculate η according to the following formula: i (j), i∈{1:P}, i∈{-1:M} represents the target index,

[0048]

[0049] η i (j) The cost matrix is ​​stored as P×(M+2P) in size, where the row number corresponds to the target index and the column number corresponds to a mapping relationship index;

[0050] Step 4.3: Based on (I,ξ,I + ,θ + ) and γ, the steady-state distribution is constructed as The Markov chain of Gibbs sampling algorithm extracts the T hypotheses with the largest weights in advance:

[0051]

[0052] The Gibbs sampling algorithm is specifically as follows:

[0053] Gibbs Sampling

[0054] γ (1) ,T,η=[η i (j)]

[0055] γ (1) ,…,γ(T)

[0056] P:size(η,1);M:=size(η,2)-2;

[0057] fort=2:T

[0058] forn=1:P

[0059]

[0060] end

[0061]

[0062] end

[0063] In the above Gibbs sampling algorithm, The calculation method is as follows:

[0064] 1) Take the nth row of data from the cost matrix and represent it with Y;

[0065] 2) Find out and The set of elements greater than 0 in Y is represented by γ0; then delete the elements with sequence numbers belonging to γ0 from Y, represented by Y';

[0066] 3) Normalize Y';

[0067] Step 5: Cut off low-weight hypothetical components and update the target pool to be regenerated

[0068] Step 5.1, split the hypothesis with weight less than the threshold g1 from the T hypotheses with the largest weights;

[0069] Step 5.2: Based on the target state and label of the target at the moment of death, a pool of dead targets is constructed, including the state space Death target state and death covariance matrix:

[0070]

[0071] Among them, the dead target refers to the target component that survived at time k-1 but has been truncated at time k, and the death time is time k-1;

[0072] Step 5.3: Filter the extracted death targets and select the historical existence frame number K d > T2 death target Merge into the target pool to be reborn, update its label space, and use express;

[0073] Step 6: Target state extraction and track reconstruction

[0074] Step 6.1: Extract the cardinality corresponding to the maximum value of the cardinality probability distribution as the target number estimate at time k And extract the N k The corresponding state of each target is taken as the target state estimation result at time k;

[0075] The cardinality distribution of the posterior distribution of GLMB is calculated according to the following formula:

[0076]

[0077] Extract the cardinality corresponding to the maximum value of the cardinality distribution of the set, that is, the target number estimate at time k as follows:

[0078]

[0079] And extract the N k The state of each target is taken as the target state estimation result at time k. The specific method can adopt the maximum a posteriori estimation method;

[0080] Step 6.2: If the target state extracted at time k includes a reborn target, the sampling interpolation method is used to complete the target track between the death time and the reborn time of the reborn target;

[0081] Step 7: Return to step 3 until the monitoring is completed and all measurement data are processed.

[0082] Compared with the prior art, the present invention has the following beneficial effects:

[0083] The present invention can realize robust multi-target tracking for continuous missing radar measurement data through the above steps. The innovation lies in proposing a fusion solution combining "GLMB filter based on Gibbs" and "go-stop-go" target tracking algorithm, and ensuring the real-time performance of the algorithm. It solves the problem of robust multi-target tracking under the condition of continuous missing radar measurement data and provides a set of fast implementation solutions.

[0084] The advantages of the present invention are that the GLMB filter tracking framework implemented based on Gibbs sampling has smaller calculation amount and faster algorithm operation speed; the algorithm has high robustness and can be applied to robust target tracking in high clutter and low detection probability scenarios; the algorithm has high accuracy and can achieve high-precision target tracking; it can effectively solve the problem of target track breakage and fragmentation caused by the loss of multiple consecutive frames of radar measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 is a flow chart of the present invention;

[0086] Figure 2 is the Gibbs sampling cost matrix. DETAILED DESCRIPTION

[0087] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments:

[0088] The specific implementation process is as follows:

[0089] according to Figure 1 As shown, this embodiment provides an application example of "a multi-target endurance tracking method under intermittent and continuous loss of radar measurement data". This method is based on the numerical implementation of a random set filter. Here, a mixed Gaussian method is used for numerical implementation, but it is not limited to other methods for numerical implementation. The implementation steps include:

[0090] Step 1: Open up CPU memory space to store initialization system parameters, which include: radar scanning period T, total observation time step K; target survival probability function p S (x,l), target detection probability function p D (x, l), clutter density function κ(·); target state transfer matrix F, process noise covariance matrix Q, observation matrix H, measurement noise covariance matrix R; rebirth gate size Γ, maximum retention time of "target to be reborn" t1, minimum time threshold for "dead target" to be "target to be reborn" t2, and time threshold K for "multi-frame pre-filtering" rb , GLMB component truncation threshold g1. The details are shown in Table 1:

[0091] Table 1: System parameter setting table

[0092]

[0093]

[0094] Step 2, initialize the data cycle pointer k = 0, receive and store the measurement data at time k, open up CPU memory space, use joint prediction and update random set filters to perform local filtering, including but not limited to GLMB filters, and dynamically store multiple hypothesis parameters of GLMB distribution in the iterative filtering process in the form of a structure. Each hypothesis includes a set of mixed Gaussian components (mapping history, target state mean, target state covariance matrix, weights, labels), a set of hypothesis weights, cardinality distribution, the number of Gaussian components, and other information. The mathematical expression of the GLMB posterior distribution is as follows:

[0095]

[0096] Since the GLMB posterior density at time k is composed of multiple target hypotheses (ξ, I) at time k, the specific data format is shown in Table 2.

[0097] At the same time, initialize the target pool to be reborn (the state of the target to be reborn in the pool, the information covariance matrix and the label); the reborn target pool (the state of the activated reborn target in the pool, the information covariance matrix and the label); open the dead target pool (the pool stores the target GLMB posterior distribution), and the specific component settings are shown in Table 2-5:

[0098] Table 2: GLMB Goal Subscale

[0099]

[0100] Table 3: Target of rebirth subscale

[0101]

[0102] Table 4: Rebirth Goal Subscale

[0103]

[0104]

[0105] Table 5: Death Goal Subscale

[0106]

[0107] Step 3: Let k:=k+1, the sensor receives the measurement data set Z at time k k ={z j :j=1,…,M}, determine the target pool to be reborn Is it empty?

[0108] (1) If it is not empty, execute the following steps;

[0109] Step 3.1: Update the pool of targets to be reborn, and delete the set of targets that have not been activated for t1 time.

[0110]

[0111] Step 3.2: Update the respawn target pool The number of frames to wait for each target to be reborn Calculate all measurements z at time k j Pseudo measurement of target l to be regenerated The Mahalanobis distance between them is:

[0112]

[0113] If a measurement falls into the σ-wave gate of the target to be regenerated, the condition is met:

[0114]

[0115] Then k rb (l):=k rb (l)+1;

[0116] If the multi-frame measurement meets the activation conditions, specifically k rb (l)>K rb , then activate the target to be reborn with label l. All activated rebirth targets constitute the set

[0117] in, Indicates the state of the target to be reborn with label l at the moment of death. The new information covariance matrix at the moment of death of the target to be reborn;

[0118] Step 3.3: Create a respawn target after activation The rebirth target distribution is specifically the LMB distribution form π RB,+ (X RB ), which is fully characterized by the following parameter set in its specific implementation:

[0119]

[0120] Among them, r RB,+ (l RB,+ ) indicates that the label is l RB,+ The target rebirth probability of π RB,+ (X RB ) corresponds to the target label set: That is, the conditions are met: Label is l RB,+ The rebirth target distribution p RB,+ (·,l) is determined by the state at the moment of death and the rebirth target transfer function F RB Joint decision.

[0121] (2) If the pool of targets to be reborn is empty, the reborn target component is set to zero and the subsequent step 4 is executed;

[0122] Step 4: Based on the measurement data set Z obtained by the sensor at time k k , perform multi-target state prediction and update, specifically using joint prediction and update random set filters to calculate the updated GLMB multi-target posterior distribution π at time k k (X), its corresponding parameter set is:

[0123]

[0124] in,

[0125]

[0126] The above posterior distribution π k The calculation formula of (X) is in the form of a sum of multiple hypotheses, which includes every possible (I,ξ,I + ,θ + ), where θ + Represents the target label set I + With the generalized measurement set Some kind of association mapping θ + ;(I,ξ,I + ,θ + )Meet the conditions: is the set of all possible target labels at time k, Θ includes all possible association mappings at time k, which is called the association mapping space at time k; Ξ includes all possible association mappings at time 0:k-1, which is called the historical association mapping space at time 0:k-1. B,+ (l + ) is labeled l + The target newborn probability, P S (·,l) is the target survival probability, p B,+ (x + ,l + ) is the label for the new target distribution, p (ξ) (·,l + ) is the probability density function of the target under the k-1 time ξ association hypothesis;<f(·),g(·)> represents the inner product of the functions f(·) and g(·).

[0127] Considering the assumption (I,ξ,I + ,θ + ) increases exponentially with the iteration time. The above method uses a sampling algorithm to screen out high-weight hypothesis components. The sampling algorithm is specifically a Gibbs sampling algorithm. The specific implementation steps include:

[0128] The k-time GLMB posterior distribution is composed of all target hypotheses at the k-time. They represent the k-time measurement set, a certain survival target label set, a new target label set and a reborn target label set respectively; M is the number of measurements at time k, R is the number of targets in the survival target label set I, and P is the number of targets at time k (including survival targets, new targets and reborn targets); (R+1):(N B +R) corresponds to the new target number, N B +R+1:P indicates the rebirth target number;

[0129] Step 4.1, define P-tuple vector: γ = (γ 1:P )∈{-1:M} P ;

[0130]

[0131] Step 4.2: Calculate η according to the following formula: i (j), i∈{1:P}, i∈{-1:M} represents the target index,

[0132]

[0133] η i (j) The cost matrix is ​​stored as P×(M+2P) in size, where the row number corresponds to the target index and the column number corresponds to a mapping relationship index, such as Figure 2 shown.

[0134] Step 4.3: Based on (I,ξ,I + ,θ + ) and γ, the steady-state distribution is constructed as The Markov chain of Gibbs sampling algorithm extracts the T hypotheses with the largest weights in advance:

[0135]

[0136] The Gibbs sampling algorithm is specifically as follows:

[0137] Gibbs Sampling

[0138] γ (1) ,T,η=[η i (j)]

[0139] γ (1) ,...,γ (T)

[0140] P:size(η,1);M:=size(η,2)-2;

[0141] fort=2:T

[0142] forn=1:P

[0143]

[0144] end

[0145]

[0146] end

[0147] In the above Gibbs sampling algorithm, The calculation method is as follows:

[0148] 1) Take the nth row of data from the cost matrix and represent it with Y;

[0149] 2) Find out and The set of elements greater than 0 in Y is represented by γ0; then delete the elements with sequence numbers belonging to γ0 from Y, represented by Y';

[0150] 3) Normalize Y';

[0151] Step 5: Truncate low-weight assumptions and update the death target pool

[0152] Step 5.1: Split the T hypotheses with the largest weights into the hypothesis with weight less than the threshold g1.

[0153] Step 5.2: Based on the target state and label of the target at the moment of death, a pool of dead targets is constructed, including the state space Death target state and death covariance matrix:

[0154]

[0155] The death target refers to the target component that survived at time k-1 but has been truncated at time k, and the death time is time k-1.

[0156] Step 5.3: Filter the extracted death targets and select the historical existence frame number K d > T2 death target Merge into the target pool to be reborn, and update its label space, which is expressed as

[0157] Step 6: Target state extraction and track reconstruction.

[0158] Step 6.1: Extract the cardinality corresponding to the maximum value of the cardinality probability distribution as the target number estimate at time k And extract the N k The corresponding state of each target is taken as the target state estimation result at time k;

[0159] The cardinality distribution of the posterior distribution of GLMB is calculated according to the following formula:

[0160]

[0161] Extract the cardinality corresponding to the maximum value of the cardinality distribution of the set, that is, the target number estimate at time k as follows:

[0162]

[0163] And extract the N k The state of each target is taken as the target state estimation result at time k. The specific method can adopt the maximum a posteriori estimation method.

[0164] Step 6.2: If the target state extracted at time k includes a reborn target, the sampling interpolation method is used to complete the target track between the death time and the reborn time of the reborn target.

[0165] The CPU memory space is opened up to dynamically store the extracted output target information in the form of real-time storage (as shown in Table 6), including the historical target status information (as shown in Table 7), and output it to the display control interface in real time.

[0166] Table 6: Extraction target status list

[0167]

[0168] Table 7: List of historical extraction target states

[0169]

[0170]

[0171] Among them, N is the total number of extracted targets, and T is the total number of frames of the monitoring scene.

[0172] Step 7: Return to step 3 and continue until the scene ends.

[0173] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical solutions and / or characteristics in the solution is not described in detail here. It should be pointed out that for those skilled in the art, without departing from the technical solution of the present invention, several modifications and improvements can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A multi-target endurance tracking method under intermittent and continuous loss of radar measurement data, characterized in that: The method is based on a random set filter framework, sets a reborn target model based on multi-frame measurement activation, completes the target endurance when measurement is intermittently missing, and realizes robust continuous tracking of multiple targets. The specific steps include: Step 1: Initialize system parameters including: radar scanning period T, total observation time step K; target survival probability function p S (x,l), target detection probability function p d (x, l), clutter density function κ(·); Set the state transfer density function f according to the motion characteristics of the monitored target + (x + ,l + |x,l)=δ(l + )(l)f + (x + |x,l) parameters, including the target state transfer matrix F and the process noise covariance matrix Q; set the single target measurement likelihood function according to the sensor measurement type Parameters, including the observation matrix H and the measurement noise covariance matrix R; Among them, x and l are the single target state and corresponding label at time k-1, respectively. + and l + are the single target state and the corresponding label at time k, respectively. k can be any time between 0 and the total observation time step K; represents the measurement z at time k j With label l + The likelihood function between the targets; Initialize the target pool to be reborn to an empty set The rebirth wave gate size Γ, the maximum retention time of "target to be reborn" t1, the minimum time threshold t2 for "dead target" to be "target to be reborn", and the time threshold K for "multi-frame pre-filtering" rb , initialize the rebirth target transfer matrix F RB , GLMB component truncation threshold g1; Step 2: Initialize time step k = 0 and initialize the GLMB multi-target distribution as follows: The specific implementation uses a parameter set to fully characterize; Where h (h = 1, 2, ..., H) represents the hth GLMB component, H is the total number of GLMB components, I (h) is the target label set of the hth GLMB component, w (h) is the non-negative weight w of the hth GLMB component (h) ,satisfy X is a set of multi-target states; is the label set corresponding to the multi-target state X; In the formula, p (h) (·,l) is the probability density function, [·] X Represents the product of the probability density functions of all elements in set X; is the Dirac function; Indicates the label inconsistency indicator, which is used to ensure that different target states have different labels; Step 3: Let k:=k+1, the sensor receives the measurement data set Z at time k k ={z j :j=1,…,M}, determine the target pool to be reborn Is it empty? (1) If it is not empty, execute the following steps; Step 3.1: Update the pool of targets to be reborn, and delete the set of targets that have not been activated for t1 time. Step 3.2: Update the respawn target pool The number of frames to wait for each target to be reborn Calculate all measurements z at time k j Pseudo measurement of target l to be regenerated The Mahalanobis distance between them is: If a measurement falls into the σ-wave gate of the target to be regenerated, the condition is met: Then k rb (l):=k rb (l)+1; If the multi-frame measurement meets the activation conditions, specifically k rb (l)>K rb , then activate the target to be reborn with label l. All activated rebirth targets constitute the set in, Indicates the state of the target to be reborn with label l at the moment of death. The new information covariance matrix at the moment of death of the target to be reborn; Step 3.3: Create a respawn target after activation The rebirth target distribution is specifically the LMB distribution form π RB,+ (X RB ), which is fully characterized by the following parameter set in its specific implementation: Among them, r RB,+ (l RB,+ ) indicates that the label is l RB,+ The target rebirth probability of π RB,+ (X RB ) corresponds to the target label set: That is, the conditions are met: Label is l RB,+ The rebirth target distribution p RB,+ (·,l) is determined by the state at the moment of death and the rebirth target transfer function F RB Joint decision (2) If the pool of targets to be reborn is empty, the reborn target component is set to zero and the subsequent step 4 is executed; Step 4: Based on the measurement data set Z obtained by the sensor at time k k , perform multi-target state prediction and update, specifically using joint prediction and update random set filters to calculate the updated GLMB multi-target posterior distribution π at time k k (X), its corresponding parameter set is: in, The above posterior distribution π k The calculation formula of (X) is in the form of a sum of multiple hypotheses, which includes every possible (I,ξ,I + ,θ + ), where θ + Represents the target label set I + With the generalized measurement set Some kind of association mapping θ + ;(I,ξ,I + ,θ + )Meet the conditions: ξ∈Ξ, ξ∈Θ; is the set of all possible target labels at time k, Θ includes all possible association mappings at time k, which is called the association mapping space at time k; Ξ includes all possible association mappings at time 0:k-1, which is called the historical association mapping space at time 0:k-1. B,+ (l + ) is labeled l + The target newborn probability, P S (·,l) is the target survival probability, p B,+ (x + ,l + ) is the label for the new target distribution, p (ξ) (·,l + ) is the probability density function of the target under the k-1 time ξ association hypothesis;<f(·),g(·)> represents the inner product of functions f(·), g(·); Considering the assumption (I,ξ,I + ,θ + ) increases exponentially with the iteration time. The above method uses a sampling algorithm to filter out high-weight hypothesis components, and the sampling algorithm is specifically a Gibbs sampling algorithm; The k-time GLMB posterior distribution is composed of all target hypotheses at the k-time. Let Z k ={z 1:M },I={l 1:R }, They represent the k-time measurement set, a certain survival target label set, a new target label set and a reborn target label set respectively; M is the number of measurements at time k, R is the number of targets in the survival target label set I, and P is the number of targets at time k (including survival targets, new targets and reborn targets); (R+1):(N B +R) corresponds to the new target number, N B +R+1:P indicates the rebirth target number; The specific implementation steps include: Step 4.1, define P-tuple vector: γ = (γ 1:P )∈{-1:M} P ; Step 4.2: Calculate η according to the following formula: i (j), i∈{1:P}, i∈{-1:M} represents the target index, η i (j) The cost matrix is ​​stored as P×(M+2P) in size, where the row number corresponds to the target index and the column number corresponds to a mapping relationship index; Step 4.3: Based on (I,ξ,I + ,θ + ) and γ, the steady-state distribution is constructed as The Markov chain of Gibbs sampling algorithm extracts the T hypotheses with the largest weights in advance: The Gibbs sampling algorithm is specifically as follows: Gibbs Sampling In the above Gibbs sampling algorithm, The calculation method is as follows: 1) Take the nth row of data from the cost matrix and represent it with Y; 2) Find out and The set of elements greater than 0 in Y is represented by γ0; then delete the elements with sequence numbers belonging to γ0 from Y, represented by Y'; 3) Normalize Y'; Step 5: Cut off low-weight hypothetical components and update the target pool to be regenerated Step 5.1, split the hypothesis with weight less than the threshold g1 from the T hypotheses with the largest weights; Step 5.2: Based on the target state and label of the target at the moment of death, a pool of dead targets is constructed, including the state space Death target state and death covariance matrix: Among them, the dead target refers to the target component that survived at time k-1 but has been truncated at time k, and the death time is time k-1; Step 5.3: Filter the extracted death targets and select the historical existence frame number K d > T2 death target Merge into the target pool to be reborn, update its label space, and use express; Step 6: Target state extraction and track reconstruction; Step 6.1: Extract the cardinality corresponding to the maximum value of the cardinality probability distribution as the target number estimate at time k And extract the N k The corresponding state of each target is taken as the target state estimation result at time k; The cardinality distribution of the posterior distribution of GLMB is calculated according to the following formula: Extract the cardinality corresponding to the maximum value of the cardinality distribution of the set, that is, the target number estimate at time k as follows: And extract the N k The state of each target is taken as the target state estimation result at time k. The specific method can adopt the maximum a posteriori estimation method; Step 6.2: If the target state extracted at time k includes a reborn target, the sampling interpolation method is used to complete the target track between the death time and the reborn time of the reborn target; Step 7: Return to step 3 until the monitoring is completed and all measurement data are processed.

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