A Gibbs sampling method for solving the combined measurement problem

Abstract

The present invention belongs to the field of electronic countermeasure technology, and specifically is a Gibbs sampling method for solving the problem of combined measurement. The purpose is to solve the correlation mismatch problem (called the combined measurement problem) caused by the fact that multiple targets may only produce a single measurement in a multi-target tracking application scenario, and to ensure that each target can still be tracked in this case. A traditional solution is to apply the idea of ​​grouping, and treat all targets that may produce combined measurements as a group for processing. The disadvantage of this method is that as the number of targets increases, there may be a computational explosion problem. In response to this, the present invention proposes applying the Gibbs sampling method to a labeled multi-Bernoulli (LMB) filter, and implementing it in a Gaussian mixture (GM) manner to alleviate the computational burden brought by the grouping method.

Description

Technical Field

[0001] The present invention belongs to the field of electronic countermeasure technology and aims to solve the correlation mismatch problem caused by the possibility of only generating a single measurement for multiple targets in multi-target tracking, thereby ensuring that each target can still be tracked in this case. Background Art

[0002] In typical multi-target tracking, the observation model used is a point measurement model, meaning there is a one-to-one correspondence between targets and measurements. Targets that are not associated with measurements for multiple consecutive moments are considered dead, and measurements that are not associated with targets are considered clutter / false alarms. In an ideal sensor observation environment, each target generates a corresponding measurement with a certain probability, making this observation model quite suitable. However, in real-world applications, sensor resolution is limited, and measurements generated by two or more targets are likely to fall within the same resolution bin. This results in only one measurement being generated for multiple targets. For example, in a range sensor observation scenario, if multiple intersecting targets approach each other, their spatial locations and distances to the sensor are also close. The sensor may only generate one distance information. This is due to the proximity of the targets in motion state space. Similarly, the proximity of targets in observation space can also contribute to this problem. For example, in a bearing-only sensor, if multiple targets are physically far apart (even visually distinguishable), but their angles relative to the sensor are close, only one angle information is generated. This phenomenon is called merged measurement. If a point measurement model is still used, targets may be lost, affecting tracking performance.

[0003] An intuitive solution is to group all targets close to each other in the observation space into a single group after the prediction step of the two-step tracking method. Each group generates at most one measurement. List all possible groupings, use the measurement to update the state of each group in each case, and finally fuse them to obtain the posterior state of the target. However, this method has a high computational complexity, which may increase sharply with the number of targets, making it unsuitable for large numbers of targets.

[0004] The LMB (labeled multi-Bernoulli) filter is a special case of the GLMB (generalized labeled multi-Bernoulli) filter. It approximates the multi-target probability distribution as a multi-Bernoulli distribution, with each Bernoulli component bearing a unique label to distinguish one from another. Its computational process is as follows: Given the prior LMB information, a prediction is first performed to obtain the predicted LMB information, which consists of the surviving LMB information and the newly generated LMB information. Then, based on the GLMB concept, different hypotheses are listed to obtain the predicted GLMB information. Next, using the measurement information at that moment, each prediction hypothesis is updated to obtain the updated GLMB information. Finally, the GLMB is converted back to LMB to obtain the updated LMB information, from which the state estimate can be extracted. Summary of the Invention

[0005] Aiming at the computational explosion problem caused by the grouping method, the present invention proposes applying the Gibbs sampling method to the LMB filter to reduce the computation time.

[0006] For ease of understanding, the Gibbs sampling used in the present invention is described as follows:

[0007] This is a sampling method for extracting multidimensional sample points from a complex multidimensional distribution. Due to the stationary nature of the Markov chain, when the number of samples exceeds a certain threshold, the multidimensional distribution reflected by the sample point no longer changes. Therefore, this method can be used to solve the difficulty of simultaneously selecting multidimensional sample values ​​from a complex high-dimensional distribution. For an n-dimensional probability distribution π(x1, x2, ..., x n ), the idea of ​​Gibbs sampling is to convert multi-dimensional sampling into multiple one-dimensional sampling. A common procedure is to get new samples by rotating the sampling on n coordinate axes. For any coordinate axis x rotated i The state transition probability of the Markov chain is p(x i |x1,x2,…,x i-1 ,x i+1 …,x n ), that is, fix n-1 coordinate axes and move on a certain coordinate axis. The specific implementation process is as follows:

[0008] (1) Given a prior distribution π(x1,x2,…,x n ), set the required number of samples N;

[0009] (2) Randomly initialize a set of initial values

[0010] (3) for t = 0: N - 2

[0011] 1) From the conditional probability distribution Samples are obtained by sampling

[0012] 2) From the conditional probability distribution Samples are obtained by sampling

[0013] …

[0014] i) From the conditional probability distribution Samples are obtained by sampling

[0015] …

[0016] n) From the conditional probability distribution Samples are obtained by sampling

[0017] Sample Set That is, in order to reflect the final stable distribution of samples, one or more groups of values ​​can be directly selected from the samples according to the probability distribution.

[0018] The technical solution adopted in the present invention is:

[0019] A Gibbs sampling method for solving the problem of combined observations is proposed by approximating the multi-target probability density function to a multi-Bernoulli distribution, that is, in is the label set of all trajectories, L is the label set of the selected trajectory, so the multi-target state can be expressed as Simplified representation: The Gaussian mixture method is used to implement the LMB filter using the Gibbs sampling method, that is, the weighted sum of multiple Gaussian distributions is used to approximate the probability distribution of the target, which is suitable for tracking under the linear Gaussian motion / observation model. For each specific probability distribution s(x), the following approximation is obtained: where w c are the Gaussian component weights, The expectation is m c , the covariance matrix is ​​P c The multidimensional Gaussian distribution of v is the number of Gaussian components. Therefore, the probability distribution s(x) can be expressed as Instead, there is Therefore, the multi-objective state can be expressed as:

[0020]

[0021] The general process of this program is as follows:

[0022]

[0023] Where k≥1 indicates different measurements with different arrival times. k-1(k=1), after the above steps, the multi-target state information at the first moment is obtained, which is expressed in LMB form as LMB k (k=1), from which the multi-target state estimation information EST at the first moment is extracted k (k=1). The subsequent process repeats this process and the estimated information EST of each moment k is k Used in practical applications.

[0024] The specific steps are as follows:

[0025] S1. Get predicted LMB information (input LMB k-1 、B k , output LMB k|k-1 ):

[0026] Known LMB information at time k-1 in is the label of trajectory i at time k-1, and the labels of different trajectories are different; is the probability of existence of trajectory i at time k-1, and are the weight, expectation and covariance matrices of the cth Gaussian component of trajectory i at time k-1 respectively; is the number of Gaussian components of trajectory i at time k-1, n k-1 is the number of trajectories at time k-1; the specific sub-steps are as follows:

[0027] S11. A trajectory that exists at time k-1 and still exists at time k is called a survival trajectory; for a survival trajectory i=1,…,n k-1 , the prediction information needed is:

[0028]

[0029] The subscript k|k-1 indicates that the information at time k is predicted based on the information at time k-1.

[0030] The Kalman motion model is used for prediction. The model is as follows:

[0031] x k|k-1 =F k-1 x k-1 +ε k-1

[0032] where x k|k-1 and x k-1 They represent the predicted motion state of a single trajectory at time k and the motion state of a single trajectory at time k-1 respectively; F k-1is the motion state transfer matrix at time k-1, which maps the initial motion state to the predicted motion state; ε k-1 is the process noise at time k-1, with an expectation of 0 and a covariance matrix of Q k-1 Gaussian distribution;

[0033] The specific prediction equation is as follows:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] in is the survival probability of trajectory i at time k-1 to time k; (·) T is the matrix transpose operation;

[0040] It can be seen that in the prediction of surviving trajectories, the labels remain unchanged, the number of trajectories, and the number of Gaussian components under each trajectory remain unchanged;

[0041] S12. The trajectory that enters the observation range at time k is called a new trajectory; for the new trajectory i b =1,…,b k , the following prior information is known:

[0042]

[0043] The subscript b represents the newborn trajectory to distinguish it from the survival trajectory; For freshman trajectory i b The label of the new trajectory must be different from each other and cannot be the same as the label of the existing trajectory. For freshman trajectory i b The survival probability is generally set to a smaller value; and They are the newborn trajectories i at time k b c b The weights, expectations, and covariance matrices of the Gaussian components are is the new trajectory i at time k b The number of Gaussian components, b k is the total number of new trajectories at time k;

[0044] Combine the prediction information of the survival trajectory and the newborn trajectory to obtain the prediction information:

[0045]

[0046] Among them, n k|k-1 =n k-1 +b k is the number of predicted trajectories at time k, that is, the number of surviving trajectories plus the number of new trajectories;

[0047] S2. Convert LMB information to GLMB information (input LMB k|k-1 、W τ , output GLMB k|k-1 ):

[0048] Now we know the predicted LMB information LMB at time k k|k-1 , need to be in n k|k-1 Select different combinations of trajectories from the prediction trajectories as different hypotheses to form the prediction GLMB information; in theory, it is necessary to select hypothesis; the predicted GLMB information is expressed as follows using the hypothesis label set, hypothesis weight and corresponding Gaussian component parameters:

[0049]

[0050] The specific acquisition method is as follows:

[0051]

[0052]

[0053]

[0054] Where I(h) is the set of label superscripts of the h-th hypothesis; is the set of labels of all selected prediction targets in the h-th hypothesis; is the weight of the h-th hypothesis, which is equal to the product of the existence probabilities of all selected trajectories and the non-existence probabilities of all unselected trajectories; is the relevant Gaussian component information of the h-th hypothesis, which is composed of the Gaussian component information of all selected prediction targets;

[0055] In actual processing, in order to improve computational efficiency, only some hypotheses with larger weights need to be retained; only those with weights exceeding the threshold W are retained. τ The weights of , reindex these assumptions as:

[0056]

[0057] Among them H k|k-1is the number of prediction hypotheses that exceed the weight threshold, satisfying

[0058] The weights of the prediction hypotheses are finally normalized, so that the complete predicted GLMB information is obtained;

[0059] S3. Get updated GLMB information (input LMB k|k-1 GLMB k|k-1 、 H k , output GLMB k ):

[0060] The predicted LMB information LMB at time k is known k|k-1 and forecast GLMB information GLMB k|k-1 ; This step requires using the observation information to associate the predicted trajectory with the observation information, and then update the corresponding prediction information; the updated GLMB information to be obtained is Among them H k Update the number of hypotheses at time k; association is achieved through Gibbs sampling, and the update of prediction information is achieved through the Kalman observation model; the specific sub-steps are as follows:

[0061] S31. Update using the Kalman observation model, the model is as follows:

[0062] x k =ψ k (x k|k-1 )+η k

[0063] where x k represents the motion state of a single trajectory at time k; ψ k (·) is the observation function at time k, which maps the predicted motion state to the updated motion state; η k is the observation noise at time k, with an expectation of 0 and a covariance matrix of R k Gaussian distribution;

[0064] Compute the cost matrix C, whose element values ​​reflect the relative likelihood of associating a predicted trajectory with an observed value; it is an n k|k-1 ×(M k +1), the value of the element at position (i, j) in the matrix is:

[0065]

[0066] in, is the detection probability of trajectory i being detected by the sensor at time k; det(·) is the determinant operation of the matrix; the matrix hk The Jacobian matrix of (·), is the partial derivative of the function f(x) at x0; is the observation set Z at time k k The jth single observation in M ​​may be generated by one or more trajectories or by clutter in the case of combined measurement; k is the number of observations at time k; κ(·) is the intensity function of the clutter in the observation space;

[0067] S32. For each prediction hypothesis, Gibbs sampling, producing update hypothesis; round(·) is a rounding operation; Gibbs sampling for each prediction hypothesis is performed independently and the process is consistent, so only the sampling process of one prediction hypothesis is given, and the sampling of the remaining prediction hypotheses can traverse this step. The specific process is as follows:

[0068] S321. According to the idea of ​​Gibbs sampling, no sampling is required for the first time, and the initial sample value can be directly specified arbitrarily; the initial value is that all the prediction trajectories in the prediction hypothesis are equal to j=M k +1 association, that is, all the predicted trajectories in the prediction hypothesis are missed; the label set and the corresponding Gaussian component information of the first updated hypothesis generated by the prediction hypothesis remain unchanged, that is, Assumption weight in Represents the multi-target index; the acquisition of the updated weight can be understood as multiplying the original prediction hypothesis weight by the probability of missing all trajectories in the prediction hypothesis; since all predicted trajectories are missed, all observations are generated by clutter, so it is multiplied by the intensity function of all observations being clutter; in this way, the first updated hypothesis is obtained

[0069] S322. From the second to the Starting from the updated hypothesis, each Gibbs sampling is performed according to the cost matrix C. Taking the second updated hypothesis as an example, the remaining hypotheses can be traversed through step S322: First, only the rows corresponding to I(h) in C are retained. The sampling of each row represents the association process between a predicted target and an observation in the prediction hypothesis; since multiple targets may correspond to the same observation in the combined measurement, the sampling method for each row is the same. Here, only the operation method for one row is given: for any row in C, find all elements greater than or equal to 1, list their element values, normalize them, and sample according to probability. The number of columns corresponding to the sampled elements is the association value θ of trajectory i. i ; If all elements are less than 1, the column number corresponding to the largest element is selected as θ i; After processing all the rows corresponding to the prediction trajectories under the prediction hypothesis in the above manner, the update of the prediction hypothesis is completed; the label set of the second updated hypothesis generated by the prediction hypothesis remains unchanged, that is, Assumption weight The updated weight is obtained by adding Replace with The Gaussian component information is updated through the Kalman filter as follows:

[0070]

[0071]

[0072]

[0073] in is the Kalman gain matrix, and E is the identity matrix. Then, all Gaussian components of the predicted trajectory i are normalized to obtain the updated Gaussian component information:

[0074]

[0075] For all predicted trajectories i under this prediction hypothesis, there are That is, the number of Gaussian components remains unchanged;

[0076] S323.Complete After updating the hypothesis, if there are repeated association results, the duplicates are removed and the result is Update the hypothesis that the associated results are not repeated; if there are no duplicates, let Reindex as

[0077] S33. Process all prediction hypotheses according to step S32, and then normalize all update hypothesis weights to obtain the complete updated GLMB information

[0078] S4. Convert GLMB information back to LMB information (input GLMB k , output LMB k ):

[0079] This step requires updated LMB information The specific acquisition method is as follows:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] Update the label of trajectory i Select from the label set of all update hypotheses; update the probability of existence of trajectory i is the sum of the weights of all updated hypotheses containing the trajectory; Gaussian component information is the set of Gaussian component information with the same label in the updated GLMB information; To update the number of Gaussian components of trajectory i, it depends on how many observations the trajectory is associated with; n k =n k|k-1 is the number of updated trajectories;

[0086] S5. Track trimming (input LMB k , output LMB' k ):

[0087] First, only keep the probability threshold r th Update trajectory of

[0088] Then, for the remaining trajectories, we need to continue to clean up their respective Gaussian components, which is divided into three steps: Gaussian pruning, Gaussian merging, and Gaussian limiting. Pruning is similar to removing trajectories, and only those above the threshold w are retained. th Gaussian components; Gaussian merging is to merge all Gaussian components close to each other in the state space into one Gaussian component; Gaussian limit means that if the number of Gaussian components of a trajectory exceeds the upper limit v up , then retain v up Finally, normalize the weights of these Gaussian components and obtain the pruned LMB information as LMB' k ;

[0089] S6. State estimation (input LMB k , output EST k ):

[0090] First estimate the number of targets at time k: where |·| represents the operation of taking the number of elements in a set; that is, the probability of existence exceeds the threshold r ex The trajectory of is considered as the target, and the estimated number of targets at this moment is equal to the sum of the number of trajectories exceeding the threshold;

[0091] Let's estimate the motion state of each target: in That is, for each trajectory judged as a target, the expectation-maximization (EAP) estimation method is used, and the weighted sum of Gaussian components is used as the estimate of the target state;

[0092] Finally, the state extraction information at time k is obtained

[0093] After completing the tracking at the first moment, the subsequent steps are iterated continuously to obtain the complete tracking trajectory.

[0094] The beneficial effects of the present invention are: in a relatively dense target tracking scenario, compared with the traditional grouping method, the calculation efficiency is greatly improved, while the tracking effect is maintained well, and it can be used in actual engineering design. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 Observed values ​​at each moment.

[0096] Figure 2 Actual motion trajectories of the target and sensor.

[0097] Figure 3 Actual tracking performance of the Gibbs sampling method (100 Monte Carlo runs).

[0098] Figure 4 Actual tracking effect of the grouping method (100 Monte Carlo runs).

[0099] Figure 5 Comparison of OSPA distance between the two methods (100 Monte Carlo runs).

[0100] Figure 6 Comparison of target number estimation between the two methods (100 Monte Carlo runs). DETAILED DESCRIPTION

[0101] The present invention will be described in detail below with reference to the embodiments:

[0102] Example

[0103] This example uses MATLAB to verify the proposed method based on Gibbs sampling to solve the problem of merging observations:

[0104] Consider a scenario with four targets moving in an area [0, 10000] × [0, 10000] with time intervals of k = 1:80, k = 16:90, k = 11:80, and k = 6:85. The motion state is four-dimensional (position and velocity), and the motion model is as follows:

[0105]

[0106] The state transfer matrix T is the sampling interval, represents the motion state of target i at time k-1, and Represent the position and velocity in the x-axis direction, is the predicted motion state of target i at time k, ε k is a four-dimensional Gaussian process noise with zero mean, and the covariance matrix is

[0107] The observation model is:

[0108]

[0109] The observation function is the position of the sensor at time k, is the observation angle information of target i at time k, η k is a one-dimensional Gaussian observation noise with zero mean and variance

[0110] Set the initial states of the four targets to [1000, 110, 4000, 70] T 、[1010,110,5000,30] T 、[1780,110,7000,-50] T and [1130,100,9000,-60] T , the initial position of the sensor is [8000,2000] T Some parameters are set as follows: the target survival probability is 0.95, the detection probability is 0.9. The average number of clutter is 2, and it is uniformly distributed between 0 and π. The upper limit of the number of Gaussian components of each trajectory (survival and new) is set to 3, the initial existence probability of the new trajectory is 0.1, the number of survival hypotheses is 1500, the number of new hypotheses is 10, the number of update hypotheses is 50, the upper limit of the number of LMB filter trajectories is 7, and the resolution of the sensor is The sampling interval is 1 and the number of Monte Carlo is 100. Compared with the grouping method, the simulation results are as follows Figure 1 、 Figure 2 、 Figure 3 、 Figure 4 、 Figure 5 and Figure 6 As shown. (The above parameters are all in international units)

[0111] Figure 1 The figure shows how the observed angle values ​​change over time. It can be seen that in some time periods (such as around 30 seconds), the number of observations generated by the target is less than the number of actual targets, which means that merged measurements have occurred.

[0112] Figure 2 The actual motion trajectories of the four targets and the sensor's motion trajectory are shown. It can be seen that there are multiple motion intersections between the targets.

[0113] Figure 3 and Figure 4 The results show that the two methods are used for tracking LMB filters. From a qualitative point of view, the grouping method is still slightly better than the Gibbs sampling method, especially in the period before the second target, the estimation deviation of the Gibbs sampling method is significantly greater than that of the grouping method.

[0114] Figure 5 The OSPA distances of the two methods are shown, with a correlation cutoff radius of c = 200 and an order of p = 1. Quantitatively, the error of the grouping method is smaller than that of the Gibbs sampling method during the time period when the combined measurements occur, while the difference between the two methods is not significant during the rest of the time period.

[0115] Figure 6 The two methods estimate the number of targets. It can be seen that the Gibbs sampling method is slightly biased downward, while the grouping method is closer to the true value.

[0116] Overall, the grouping method performs slightly better than the Gibbs sampling method, but Gibbs sampling is significantly more efficient, with the former taking 551 seconds compared to the latter's 143 seconds, a difference of nearly four times. As the number of targets increases, the grouping method struggles to cope. Gibbs sampling, however, significantly reduces computation time while maintaining a certain level of tracking effectiveness, making it suitable for scenarios where multiple targets within a scene may require combined measurements.

Claims

1. A Gibbs sampling method for solving the combined measurement problem, characterized in that: The following steps are involved: S1. Get predicted LMB information: Known LMB information at the moment ,in yes Time Track The labels of different trajectories are different; yes Time Track The probability of existence, 、 and They are Time Track No. The weights, expectations, and covariance matrices of the Gaussian components; yes Time Track The number of Gaussian components of yes The number of time trajectories; the specific method is as follows: S11. For Always present, The trajectory that still exists at any time is called a survival trajectory; , the prediction information needed is: ， The subscript Indicates known Under the premise of the information at the moment, the prediction is Information at the moment; The Kalman motion model is used for prediction. The model is as follows: ， in and Respectively The predicted motion state of a single trajectory at time The motion state of a single trajectory at a given moment; yes The motion state transfer matrix at the moment maps the initial motion state to the predicted motion state; yes The process noise at the moment is subject to expectation of 0, and the covariance matrix is Gaussian distribution; The specific prediction equation is as follows: ， ， ， ， ， in for Time Track Survive to The probability of survival at the moment; is the matrix transpose operation; It can be seen that in the prediction of surviving trajectories, the labels remain unchanged, the number of trajectories, and the number of Gaussian components under each trajectory remain unchanged; S12. For The trajectory that enters the observation range at any moment is called a new trajectory; for the new trajectory , the following prior information is known: ， The subscript represents the nascent trajectory, as distinguished from the survival trajectory; For the new trajectory The label of the new trajectory must be different from each other and cannot be the same as the label of the existing trajectory. For the new trajectory The probability of survival; 、 and They are The trajectory of constant renewal No. The weights, expectations, and covariance matrices of the Gaussian components are ; yes The trajectory of constant renewal The number of Gaussian components of for The total number of new trajectories at a given moment; Combine the prediction information of the survival trajectory and the newborn trajectory to obtain the prediction information: ， in, for The number of predicted trajectories at the moment is the sum of the number of surviving trajectories and the number of new trajectories; S2. Convert LMB information to GLMB information: Now known Predicted LMB information at the moment , need to Different combinations of trajectories are selected from the predicted trajectories as different hypotheses to form the predicted GLMB information; the predicted GLMB information is expressed by the hypothesis label set, hypothesis weight and corresponding Gaussian component parameters as follows: ， The specific acquisition method is as follows: ， ， ， in, It is a set of hypothetical label superscripts; It is The set of labels of all selected prediction targets in the hypothesis; It is The weight of a hypothesis is equal to the product of the existence probability of all selected trajectories and the non-existence probability of all unselected trajectories; It is The relevant Gaussian component information of each hypothesis is composed of the Gaussian component information of all selected prediction targets; Only keep those that exceed the weight threshold The weights of , reindex these assumptions as: ， in is the number of prediction hypotheses that exceed the weight threshold, satisfying ; The weights of the prediction hypotheses are finally normalized to obtain complete predicted GLMB information; S3. Get updated GLMB information: Known Predicted LMB information at the moment and predicting GLMB information ; Use the observation information to associate the predicted trajectory with the observation information, and then update the corresponding prediction information; the updated GLMB information to be obtained is ,in for The number of hypotheses is updated at all times; association is achieved through Gibbs sampling, and the update of prediction information is achieved through the Kalman observation model; the specific methods are as follows: S31. Update using the Kalman observation model. The model is as follows: ， in express The motion state of a single trajectory at a given moment; yes The observation function at the moment maps the predicted motion state to the updated motion state; yes The observation noise at the moment is subject to expectation of 0, and the covariance matrix is Gaussian distribution; Calculate the cost matrix , whose element values ​​reflect the relative likelihood of associating a predicted trajectory with an observed value. It is a The matrix, the position in the matrix The element value at: ,in, for Moment-by-moment prediction trajectory the detection probability of being detected by the sensor; To find the determinant of a matrix; , for The Jacobian matrix of For function exist The partial derivative at ; yes Observation set at time Middle A single observation, in the case of combined measurements, is generated by one or more trajectories, or by clutter; yes The number of observations at a time; is the intensity function of clutter in the observation space; S32. For each prediction hypothesis, Gibbs sampling, producing update hypothesis; This is a rounding operation; the Gibbs sampling of each prediction hypothesis is performed independently and the process is consistent. Therefore, only one prediction hypothesis sampling process is given, and the sampling of the remaining prediction hypotheses can traverse this step. The specific process is as follows: S321. According to the idea of ​​Gibbs sampling, there is no need to sample for the first time, and the initial sample value can be directly specified; the initial value is that all the prediction trajectories in the prediction hypothesis are equal. Association, that is, all the predicted trajectories in the prediction hypothesis are missed; the label set and the corresponding Gaussian component information of the first updated hypothesis generated by the prediction hypothesis remain unchanged, that is , ; Assume weight ,in Represents the multi-target index; the acquisition of the updated weight can be understood as multiplying the original prediction hypothesis weight by the probability of missing all trajectories in the prediction hypothesis; since all predicted trajectories are missed, all observations are generated by clutter, so it is multiplied by the intensity function of all observations being clutter; in this way, the first updated hypothesis is obtained ; S322. From the second to the Starting from the updated hypothesis, each Gibbs sampling is performed according to the cost matrix To proceed, the second update assumption is: first, only keep Corresponding to The sampling of each row represents the association process between a prediction target and an observation in the prediction hypothesis; since multiple targets may correspond to the same observation in the combined measurement, the sampling method of each row is the same: In any row, find all elements greater than or equal to 1, list their element values, normalize them, and sample them according to the probability. The number of columns corresponding to the sampled elements is the trajectory The associated value ; If all elements are less than 1, the column number corresponding to the largest element is selected as ; After processing all the rows corresponding to the prediction trajectories under the prediction hypothesis, the update of the prediction hypothesis is completed; the label set of the second update hypothesis generated by the prediction hypothesis remains unchanged, that is, ; Assume weight The updated weight is obtained by replacing the weight in step S321 with Replace with ; The Gaussian component information is updated through the Kalman filter, as follows, ， ， ， in is the Kalman gain matrix, is the identity matrix; then the predicted trajectory Normalizing all Gaussian components of , we can get the updated Gaussian component information as follows: ， For all the prediction trajectories under this prediction hypothesis , both , that is, the number of Gaussian components remains unchanged; For the rest of the assumptions, just traverse S322; S323. Completed After updating the hypothesis, if there are repeated association results, remove the duplicates and get Update the hypothesis that the associated results are not repeated; if there are no duplicates, let ; Reindex to ; S33. Process all prediction hypotheses according to step S32, and then normalize all update hypothesis weights to obtain the complete updated GLMB information ; S4. Convert GLMB information back to LMB information: Get updated LMB information The specific acquisition method is as follows: ， ， ， ， ， Update track Tags Select from the set of labels of all update hypotheses; update trajectory The probability of existence is the sum of the weights of all updated hypotheses containing the trajectory; Gaussian component information is the set of Gaussian component information with the same label in the updated GLMB information; To update the trajectory The number of Gaussian components depends on how many observations the trajectory is associated with; is the number of updated trajectories; S5. Track Pruning: First, only keep the probability threshold greater than or equal to Update trajectory of Then, for the remaining trajectories, we need to continue to clean up their respective Gaussian components, which is divided into three steps: Gaussian pruning, Gaussian merging, and Gaussian limiting. The same is true for Gaussian pruning and removal of trajectories, and only those above the threshold are retained. Gaussian components; Gaussian merging is to merge all Gaussian components close to each other in the state space into one Gaussian component; Gaussian limit means that if the number of Gaussian components of a trajectory exceeds the upper limit , then retain components with larger weights; finally, normalize the weights of these Gaussian components to obtain the pruned LMB information as ; S6. State Estimation: First estimate Time target number: ,in Indicates the operation of taking the number of elements in a set; that is, the probability of existence exceeds the threshold The trajectory of is considered as the target, and the estimated number of targets at this moment is equal to the sum of the number of trajectories exceeding the threshold; Let's estimate the motion state of each target: ,in ; That is, for each trajectory judged as a target, the expected maximum expectation estimation method is used, and the weighted sum of Gaussian components is used as the estimate of the target state; Finally, we get Status extraction information at the moment ; After completing the tracking at the first moment, the subsequent steps are iterated continuously to obtain the complete tracking trajectory.

Images