Parallelization fast label multi-Bernoulli filtering method under phased array radar system

Abstract

The invention relates to a parallelization fast label multi-Bernoulli filtering method under a phased array radar system, and belongs to the field of radar target tracking. Comprising the following steps: acquiring a measurement set of a radar, and dividing the measurement set by adopting a mean shift algorithm; performing trace point condensation on the divided measurement set; carrying out parallel joint prediction and updating based on the measurement set after trace point condensation, wherein the parallel joint prediction and updating comprises LMB state transition, target and measurement grouping, parallel processing on grouping results, and merging posterior density of each group; after parallel joint prediction and updating, trimming and truncating an LMB parameter set; and estimating a target number and a state based on the trimmed and truncated LMB parameter set. According to the method, the target and the measurement are grouped, so that the parallelization processing of the FLMB filter is realized, the calculation amount can be effectively reduced under the condition that the tracking performance loss is not large, the real-time performance is improved, and the target detection speed and precision are improved.

Description

Technical Field

[0001] The invention belongs to the field of radar target tracking, and in particular relates to a parallel fast label multi-Bernoulli filtering method under a phased array radar system. Background Art

[0002] Since it avoids complex data association, the multi-target tracking method based on random finite set (RFS) has attracted widespread attention from scholars at home and abroad since it was proposed. Mahler, Vo and other scholars have successively proposed the probability hypothesis density (PHD) filter (Mahler R. Multi-target Bayes filtering via first-order multi-target moments [J]. IEEE Transactions on Aerospace and Electronic Systems, 2004, 39 (4): 1152-1178.), the potential probability hypothesis density (Cardinalized PHD, CPHD) filter (Mahler R. PHD filters of higher order in target number [J]. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43 (4): 1523-1543.) and the cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter (Vo BT, Vo BN, Cantoni A. The cardinality balanced multi-target multi-Bernoulli filter and its implementations [J]. IEEE Transactions on Signal Processing, 2009, 57(2): 409-423.) and others, and made outstanding contributions to the development of RFS theory. However, these early RFS filters are all approximations of multi-target Bayesian filters, with poor tracking performance and unable to output target tracks. To solve the above problems, scholars such as Vo proposed a generalized labeled multi-Bernoulli (GLMB) filter (Vo BT, Vo B N. Labeled random finite sets and multi-object conjugate priors [J]. IEEE Transactions on Signal Processing, 2013, 61(13): 3460-3475.).This filter is the optimal solution of the multi-target Bayesian filter. It not only has good tracking performance, but also can output the target track. However, since the filter reconsiders the complex data association, the computational complexity is very high. How to effectively reduce the computational complexity of the GLMB filter is a current research hotspot. To this end, Reuter et al. proposed the Labeled Multi-Bernoulli (LMB) filter (ReuterS, Vo BT, Vo BN, et al. The labeled multi-Bernoulli filter [J]. IEEE Transactions on Signal Processing, 2014, 62 (12): 3246-3260.). This filter is an effective approximation of the GLMB filter, which can effectively reduce the amount of computation without much loss in tracking performance. Subsequently, scholars such as Vo and Reuter proposed GLMB filters and LMB filters based on joint prediction and update and Gibbs sampling, namely, fast GLMB (Fast GLMB, FGLMB) filter (Vo BN, Vo BT, Hoang H G. An efficient implementation of the generalized labeled multi-Bernoulli filter [J]. IEEE Transactions on Signal Processing, 2017, 65 (8): 1975-1987.) and fast LMB (Fast LMB, FLMB) filter (Reuter S, Danzer A, Stübler M, et al. A fast implementation of the labeled multi-Bernoulli filter using Gibbs sampling [C] / / Proceedings of the International Conference on Intelligent Vehicles Symposium, 2017: 765-772.). These two filters are fast methods corresponding to GLMB filter and LMB filter, respectively. They have lower computational complexity without much loss in tracking performance. Among them, FLMB filter has the smallest computational complexity and has good prospects for engineering application. However, in actual engineering, when the number of targets and measurements is large, the computational complexity of the FLMB filter is still large and it is difficult to meet real-time requirements.

[0003] In addition, in actual engineering, the standard FLMB filter has the following two problems: (1) For the detection of new targets, it is often necessary to provide the initial state of each target as prior information for sampling. However, in actual engineering, the initial state of each target is difficult to obtain; (2) In the phased array radar system, in order to improve the detection performance of the target, the beam dwell between two adjacent sectors is often designed to overlap, which may result in two measurements for one target. Directly using the standard FLMB filter for filtering may estimate one target as two targets, resulting in a significant overestimation of the number of targets. Summary of the invention

[0004] The technical problems to be solved by the present invention are:

[0005] In order to avoid the shortcomings of the prior art, the present invention provides a parallel fast label multi-Bernoulli filtering method under a phased array radar system, which is used to improve the target tracking speed and accuracy.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A parallel fast label multi-Bernoulli filtering method in a phased array radar system, characterized by comprising:

[0008] Obtain the radar measurement set, and use the mean shift algorithm to divide the measurement set; perform point condensation on the divided measurement set;

[0009] Parallel joint prediction and update based on the measurement set after point trace condensation, including: LMB state transfer, target and measurement grouping, parallel processing of grouping results, and merging of posterior densities of each group;

[0010] After parallelizing joint prediction and updating, the LMB parameter set is pruned and truncated;

[0011] Estimate the number and states of targets based on the pruned and truncated LMB parameter set.

[0012] A further technical solution of the present invention: the step of performing point trace agglomeration on the divided measurement set comprises:

[0013] The divided measurement set Each measurement division unit in The measurements in the ensemble are weighted averaged according to the amplitude of each measurement to obtain the measurement set after the point traces are condensed. in, Among them, |W i | indicates W i The number of measurements, Indicates the measured amplitude, Indicates the measured location information.

[0014] A further technical solution of the present invention: the LMB state transfer comprises:

[0015] Obtain the multi-target posterior density parameter set at time k-1, which includes the existence probability and probability density of all targets;

[0016] Based on the multi-target posterior density at time k-1, the multi-target density parameter set after the state transfer of the surviving target at time k is obtained. The multi-target density parameter set after the state transfer of the surviving target includes the existence probability and probability density of all surviving targets;

[0017] The new target is detected by using the measurement driven new generation method, that is, the new target parameter set is obtained by sampling at each measurement position in the measurement set after the point traces are condensed at the previous moment. The new target parameter set includes the existence probability and probability density of all new targets.

[0018] The existence probability and probability density of all surviving targets and the existence probability and probability density of all new targets are combined into a multi-target density parameter set after state transfer.

[0019] A further technical solution of the present invention: the target and measurement grouping includes:

[0020] Treat each measurement in the measurement set after point trace condensation as a group, and add a label set to each measurement group, where the label set represents the index of the target belonging to the measurement group;

[0021] Based on the label set of each measurement group, the measurement groups are merged until the number of groups does not change;

[0022] According to the label set in each group, the corresponding target is placed in each measurement group to obtain the result after the target and measurement are grouped.

[0023] A further technical solution of the present invention: the method for obtaining the tag set comprises:

[0024] The Mahalanobis distance between each measurement in the measurement set after point condensation and all targets is calculated, and then the index numbers of all targets smaller than the preset threshold are stored as label values ​​in the label set of the measurement group.

[0025] A further technical solution of the present invention: the merging of the measurement groups comprises:

[0026] Check the label set of each measurement group in turn, and merge two measurement groups with overlapping label sets; the merging rule is as follows: merge the two measurement groups into one group, and take the union of the two measurement group label sets as the label set of the new group; starting from the first group, repeat the merging operation until the number of groups does not change.

[0027] A further technical solution of the present invention: the parallel processing of the grouping results comprises:

[0028] Calculate the joint prediction and updated multi-objective posterior density of each group respectively, wherein the multi-objective posterior density is in the form of GLMB;

[0029] The multi-objective posterior density of each group is converted from GLMB form to LMB form.

[0030] A further technical solution of the present invention: the merging of the posterior densities of the groups comprises:

[0031] The multi-objective posterior densities of each group are merged and organized into a total LMB parameter set.

[0032] A further technical solution of the present invention: the pruning and truncating of the LMB parameter set comprises:

[0033] Prune and truncate the LMB parameter set itself: compare the existence probability of the hypothesized trajectories in the LMB parameter set with the preset pruning threshold, and discard the hypothesized trajectories that are less than the pruning threshold; compare the number of hypothesized trajectories after pruning with the maximum number of trajectories. If the number of hypothesized trajectories after pruning is greater than the maximum number of trajectories, sort the hypothesized trajectories from large to small according to the existence probability, and take the hypothesized trajectories with the largest number of trajectories as the truncated LMB parameter set, otherwise no truncation is required;

[0034] The Gaussian items of each hypothesized trajectory in the LMB parameter set are pruned, fused and truncated: in each hypothesized trajectory, the weight of each Gaussian item is compared with the pruning threshold, and the Gaussian items smaller than the pruning threshold are deleted; the Mahalanobis distance between two Gaussian items is calculated, and the two Gaussian items smaller than the fusion threshold are weightedly fused according to the weight ratio, and the weight of the fused Gaussian item is the sum of the weights of the two Gaussian items; the number of Gaussian items after pruning and fusion is compared with the preset maximum number of Gaussian items. If it is greater, the Gaussian items with the largest weight are retained, otherwise no truncation is required; after pruning, fusion and truncation, the weights of the Gaussian items are normalized.

[0035] A further technical solution of the present invention: the method of estimating the number and state of targets based on the pruned and truncated LMB parameter set comprises:

[0036] The maximum a posteriori criterion is used to estimate the number of targets, that is, Among them, ρ k(n) represents the potential distribution of the LMB parameter set;

[0037] Sort the hypothesized trajectories according to their probability of existence from large to small, and select the first Hypothesis trajectories are used for state extraction;

[0038] Get the target state estimate set Among them, the state of each hypothesized trajectory Take the item with the largest weight among the Gaussian items, and estimate the label Get the label value of the hypothesis trajectory.

[0039] The beneficial effects of the present invention are:

[0040] The invention provides a parallel fast label multi-Bernoulli filtering method in a phased array radar system, which has the following advantages over the prior art:

[0041] 1. In actual engineering, when the number of targets and measurements is large, the existing FLMB filter has a large amount of calculation and poor real-time performance. The present invention realizes parallel processing of the FLMB filter by grouping targets and measurements, which can effectively reduce the amount of calculation and improve real-time performance without much loss in tracking performance.

[0042] 2. Compared with the standard FLMB filter, the present invention has two other advantages: (1) It adopts the measurement-driven regeneration method to detect new targets and provides a specific design method for new parameters, which can realize adaptive detection of new targets; (2) It pre-processes the measurement and uses the measurement set after point condensation to participate in the filtering process, which can effectively avoid the problem of overestimation of the number of targets caused by directly using the original measurement data for filtering in the standard FLMB filter. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0044] Figure 1 It is a flow chart of the parallel fast label multi-Bernoulli filtering method under the phased array radar system of the present invention;

[0045] Figure 2 is the real motion trajectory of the target in the simulation experiment;

[0046] Figure 3 The average results of 100 Monte Carlo simulations: (a) is the estimated result of the number of targets for each method; (b) is the OSPA distance of each method. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0048] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0049] The embodiment of the present invention provides a parallel fast label multi-Bernoulli filtering method under a phased array radar system. On the basis of the standard FLMB filter, the present invention groups the targets and measurements in the joint prediction and update process, and then calculates the posterior density of a single group in each group. By parallelizing each group, the number of hypothesis components can be effectively reduced, and the amount of calculation can be reduced. In addition, in the implementation process of the PFLMB filter, a measurement-driven method is used to detect new targets, reducing the need for target prior information; at the same time, the measurements are preprocessed, and the over-estimation of the number of targets is avoided by filtering the measurement set after point trace condensation.

[0050] like Figure 1 As shown, the following steps are included:

[0051] Step 1: Initialization. The LMB parameter set is initialized according to prior information such as the target initial state. However, since the present invention uses the measurement-driven regeneration method to detect the new target, the target initial state information is no longer required. Therefore, in the specific implementation process, the initialized LMB parameter set is actually empty, and only the parameter structure of the LMB parameter set is retained. In addition, this initialization step is only performed once before the filtering process starts, and this step is no longer performed in the subsequent filtering process.

[0052] Step 2: Point trace condensation. First, divide the measurement set obtained by the radar, divide the measurements that may come from the same target into the same unit, then perform weighted average of the measurements in each unit according to the amplitude, and finally obtain the measurement set after point trace condensation. The specific steps are as follows:

[0053] The current measurement set is in, z p,i,k Indicates the measurement position information, z a,i,k Indicates the measurement amplitude information.

[0054] (1) Based on the measurement location information, the mean shift algorithm is used to divide the measurement set, and we get in, |W i | indicates W i The number of measurements,

[0055] (2) Perform point condensation on the divided measurement set and divide each measurement into units The measurements in the ensemble are weighted averaged according to the amplitude of each measurement to obtain the measurement set after the point traces are condensed. in, It should be pointed out that the measurement set after point condensation Measurement in A measurement that contains only position information.

[0056] Finally, it should be pointed out that the present invention uses the measurement-driven regeneration method to detect new targets, and needs to perform sampling based on the measurement information of the previous moment. Therefore, at the first moment, only the point trace condensation processing is performed on the measurement set, and no subsequent filtering operation is performed. The actual filtering process starts at the second moment. After the point trace condensation is performed at the first moment, the processing flow at the second moment is directly started.

[0057] Step 3: Parallel joint prediction and update. This step includes four steps: LMB state transfer, target and measurement grouping, parallel processing of grouping results, and merging of posterior densities of each group. The specific steps are as follows:

[0058] (1)LMB state transition

[0059] ① Survival target state transfer

[0060] Assume that the multi-target posterior density at time k-1 can be expressed as the parameter set is LMB RFS, where π k-1 (X k-1 ) represents the multi-target posterior density at time k-1, X k-1 represents the set of target states, r k-1 (l k-1 ) and p k-1 (x k-1 ,l k-1 ) represent the target lk-1 The existence probability and probability density of represents the label space at time k-1, and p k-1 (x k-1 ,l k-1 ) can be expressed as a Gaussian mixture form:

[0061]

[0062] In the formula, J k-1 (l k-1 ) represents the number of Gaussian mixture terms, w j,k-1 (l k-1 ) represents the weight of the j-th Gaussian mixture term, Indicates that the mean is m j,k-1 (l k-1 ), the covariance is P j,k-1 (l k-1 ). Then, the multi-target density after the state transfer of the surviving target at time k can be expressed as the parameter set is LMB RFS, where r S,k|k-1 (l k ) and p S,k|k-1 (x k ,l k ) represent the existence probability and probability density of the surviving target, respectively, and are calculated as follows:

[0063] r S,k|k-1 (l k )=p S,k r k-1 (l k-1 ) (2)

[0064]

[0065] J S,k|k-1 (l k )=J k-1 (l k-1 ) (4)

[0066] w S,j,k|k-1 (l k )=w j,k-1 (l k-1 ) (5)

[0067] m S,j,k|k-1 (l k )=F k-1 m j,k-1 (l k-1 ) (6)

[0068]

[0069] l k = l k-1 (8)

[0070] In the formula, p S,k represents the target survival probability, F k-1 represents the state transfer matrix, Q k-1 represents the process noise covariance matrix.

[0071] ② Measurement drives rebirth

[0072] The present invention adopts the measurement driven regeneration method to detect the new target, that is, the measurement set after the point trace of the previous moment is condensed Each measurement in The new target is modeled as LMB RFS, and the new target model can be expressed as Among them, r B,k (l k ) and p B,k (x k ,l k ) represent the existence probability and probability density of the new target, represents the label space of the new target at time k. Then, the new parameters of the measurement-driven new generation method can be calculated as follows:

[0073] r B,k (l k )=p b,k (9)

[0074]

[0075] J B,k (l k )=1 (11)

[0076]

[0077] P B,j,k (l k )=P0 (14)

[0078]

[0079] In the formula, p b,k represents the target newborn probability, P0 represents the initial covariance matrix.

[0080] (2) Target and measurement grouping

[0081] The multi-target density after state transfer can be organized into a parameter set as The LMB RFS of the point traces is This step groups the targets and the measurements after point condensation for subsequent parallel processing.

[0082] ① Group the targets based on the measurement after point condensation

[0083] Treat each measurement as a group, and then group the targets according to the measurement group.

[0084] Add a label set to each measurement group, where the label value represents the index of the target belonging to the measurement group, and the measurement group with an empty label set is considered as clutter removal. Each measurement The Mahalanobis distance between the center and all targets is calculated, and then the index numbers of all targets smaller than the preset threshold are stored as label values ​​in the label set of the measurement.

[0085] ②Merge measurement groups

[0086] Based on the label set of each measurement group, the measurement groups are merged until the number of groups does not change.

[0087] Check the label set of each measurement group in turn, and merge two measurement groups with overlapping label sets. The merging rule is as follows: merge two measurement groups into one group, and take the union of the two measurement group label sets as the label set of the new group. Starting from the first group, perform the merging operation repeatedly until the number of groups does not change.

[0088] ③Integrate the final goal and measurement grouping results

[0089] According to ②, the measurements are divided into different groups, each with a different label set. Then, the corresponding targets are placed in each group according to the label set in each group. For targets that are not classified into any group, each target forms a separate group. In these groups, the measurement set is an empty set.

[0090] The final clustering result is expressed as in, and Represent the label space and measurement set in the nth group respectively. and The constraints are as follows: For n≠m, we have For n≠m, we have represents the set of all measurements whose label set is empty when a single measurement is grouped. In addition,

[0091] After grouping the targets and measurements, the multi-target density parameter set of state transition can be expressed as:

[0092]

[0093] (3) Parallel processing of clustering results

[0094] ① Calculate the posterior density of each group

[0095] ●The posterior density expression for each group

[0096] For each group, the joint prediction and updated multi-objective posterior density can be expressed in GLMB form, and its related parameters are calculated as follows:

[0097]

[0098]

[0099] In the formula, Represents the mapping in the nth group space, express The number of measurements, Indicated by The set consists of a finite subset of . If but p D,k represents the target detection probability, κ(·) represents the clutter intensity, H k represents the measurement matrix, R k represents the measurement noise covariance matrix. represents the generalized Kronecker delta function and is calculated as follows:

[0100]

[0101] In the formula, express A collection of labels. represents the generalized inclusion function, which is calculated as follows:

[0102]

[0103] In addition, in the above formula, [·] represents a multi-objective exponential function, which is defined as:

[0104]

[0105] In the formula, h(x) represents a real-valued function, X represents a set, Represents the empty set.

[0106] ●The expanded cost matrix for each group

[0107] In the above process of calculating the posterior density expression of each group, in order to calculate the It is necessary to calculate an extended cost matrix that comprehensively considers the target survival, extinction, birth, detection and missed detection. The specific calculation method is as follows.

[0108] The nth group is represented by in, express The goal of this step is to calculate the number of measurements in the group Has a greater weight Pairing For each pair definition

[0109]

[0110] γ (n) Inherited Positive 1-1 property, so when When, i,i′∈{1:P (n)} are equal. Use express The set of all positive 1-1 elements in , then, Label Set and association mapping You can restore it by:

[0111]

[0112] For all i∈{1:P (n)},definition:

[0113]

[0114] Where 1≤i≤R (n) Corresponding to the survival target in the nth group, R (n) +1≤i≤P (n) Corresponding to the new target in the nth group. Indicates the number of trajectories assigned to the nth group The index of the measurement, j = -1 represents the trajectory extinction, j = 0 means the trajectory Missed detection. In this way, formula (18) can be written as:

[0115]

[0116] In the formula, Therefore, search has a greater weight Pairing Equivalent to searching A positive 1-1 vector with a large value γ (n) This can be achieved by solving the following permutation assignment problem:

[0117]

[0118]

[0119] In the formula, represents the assignment matrix of the nth group, represents the expanded cost matrix of the nth group. Each γ (n) Corresponding to an S (n) , tr((S (n) ) T C (n) ) is S (n) The price, Here, Gibbs sampling is used to solve the permutation assignment problem.

[0120] ● Gibbs sampling for each group

[0121] Each γ (n) For group n The probability distribution π (n) is a realization of a random variable of . Then, by (n) Sampling can generate candidate γ (n) . Construct π (n) as follows:

[0122]

[0123] It is difficult to directly sample from the above distribution, so the present invention uses a Gibbs sampler for sampling. Let’s start with the next solution. can be obtained by selecting from a series of conditional distributions Sampling is obtained, where (γ′ 1:s-1 ) (n) and denote the association of the new sample and the association derived from the previous solution, respectively. The Gibbs sampler is computationally efficient, but it requires that the conditional distributions are easy to compute and sample. Therefore, a closed-form expression is provided here for each conditional distribution so that they can be computed or sampled at a low cost. For each s∈{1:P (n)}:

[0124]

[0125] In the formula, Then, for a non-positive j, for This makes sampling from the conditional distribution easier and cheaper, with complexity only linear in the number of measurements. Finally, since Gibbs sampling can return the same hypothesis, duplicates must also be removed.

[0126] ②Convert GLMB in each group into LMB

[0127] The multi-objective posterior density in the nth group is in GLMB form. To achieve closed recursion, it needs to be converted into LMB form. Through first-order moment matching, formula (17) can be converted into the following LMB form:

[0128]

[0129] (4) Merge the posterior densities of each group

[0130] The total multi-objective posterior density is calculated as follows:

[0131]

[0132] Will Further organized into parameter sets

[0133] Step 4: Pruning and truncation. After parallelizing joint prediction and updating, the parameter set Prune and truncate. This mainly includes two aspects: one is the pruning and truncation of the LMB parameter set itself, and the other is the pruning, fusion and truncation of the Gaussian terms of each hypothesized trajectory in the LMB parameter set. The specific steps are as follows:

[0134] (1) Pruning and truncation of the LMB parameter set itself

[0135] First, the existence probability of each hypothesized trajectory Compare it with the preset pruning threshold and discard the hypothesized trajectories that are smaller than the pruning threshold. Then, the number of hypothesized trajectories after pruning is compared with the maximum number of trajectories T max Compare. If it is greater than T max , then according to the existence probability Sort the hypothesis trajectories from large to small and take the top T max The hypothesized trajectory is used as the truncated LMB parameter set; otherwise, no truncation is required.

[0136] (2) Pruning, fusion, and truncation of Gaussian terms for each hypothesis trajectory in the LMB parameter set

[0137] Pruning: In each hypothetical trajectory, the weight of each Gaussian item is compared with the pruning threshold, and the Gaussian items smaller than the pruning threshold are deleted. Fusion: In each hypothetical trajectory, the Mahalanobis distance between two Gaussian items is calculated, and the two Gaussian items smaller than the fusion threshold are weighted and fused according to the weight ratio. The weight of the fused Gaussian item is the sum of the weights of the two Gaussian items. Truncation: In each hypothetical trajectory, the number of Gaussian items after pruning and fusion is compared with the preset maximum number of Gaussian items J. max Compare, if it is greater than, retain the J with the largest weight max Gaussian terms, otherwise no truncation is required. Finally, after pruning, fusion and truncation, the weights of the Gaussian terms in each hypothesis trajectory are normalized.

[0138] Step 5: State estimation. The pruned and truncated LMB parameter set is denoted as The number and state of targets are estimated based on the parameter set. The specific steps are as follows:

[0139] First, the maximum a posteriori criterion is used to estimate the number of targets, that is, Among them, ρ k (n) represents the potential distribution of the LMB parameter set. Then, the hypothesized trajectories are sorted from large to small according to the probability of existence of each hypothesized trajectory, and the top Finally, the target state estimation set can be obtained. It should be noted that when extracting the target state, the state of each hypothesized trajectory Take the item with the largest weight among the Gaussian items, and estimate the label Just take the label value of the hypothesized trajectory.

[0140] Step 6: Determine whether it is finished. Check whether the observation is finished. If so, end the filtering process. Otherwise, jump to step 3 to start the filtering process at the next moment. It should be pointed out that in the specific implementation process, the execution time of the point trace aggregation in step 2 is relatively flexible. It only needs to be executed before the target and measurement grouping operation in step 3 is executed. Therefore, it can be executed before the start of step 3 or after the start of step 3. This embodiment executes it before the start of step 3.

[0141] The following is a further description of the technical effects of the present invention in combination with simulation experiments:

[0142] 1. Simulation conditions

[0143] In the simulation experiment, the size of the monitoring area is [-1000, 1000] m × [-1000, 1000] m. A total of 8 targets appear in the monitoring area. The actual movement trajectory of the target is as follows: Figure 2As shown. The survival time of target 1 is 1-60s, the survival time of target 2 is 5-70s, the survival time of target 3 is 10-80s, the survival time of target 4 is 15-90s, the survival time of target 5 is 20-100s, the survival time of target 6 is 25-100s, the survival time of target 7 is 30-100s, and the survival time of target 8 is 35-100s. The target motion model is a constant velocity (CV) model, the sampling interval is set to 1s, and the process noise standard deviation is set to 5m / s 2 . The observation time of the entire monitoring area is 100s. The clutter is evenly distributed in the monitoring area, and its average is set to 10. The target survival probability is set to 0.99, the detection probability is set to 0.98, and the standard deviation of the measurement noise is set to 10m. In order to simulate the measurement situation under the phased array radar system, the measurement generated by the first detected target in the target state set is set as two measurements. The two measurement generation processes are independent of each other, both randomly generated, and obey the same Gaussian distribution. In addition, the two measurements have different amplitudes, and the amplitude of the measurement closer to the true position is set larger. The tracking results are evaluated using the optimal sub-pattern assignment (OSPA) distance, and its cutoff distance and sensitivity parameters are set to c=100 and p=1 respectively. The hardware platform of the simulation experiment is Intel(R) Core(TM) i5-8250U CPU@1.60GHz1.80GHz processor and 16.0GB RAM, and the software platform is Matlab R2018b.

[0144] The methods involved in the comparison include LMB-MD filter, LMB-MD-DC filter, FLMB-MD filter, FLMB-MD-DC filter, PFLMB-MD filter and PFLMB-MD-DC filter. Among them, LMB-MD filter and FLMB-MD filter are respectively improved versions of standard LMB filter and standard FLMB filter using the measurement drive regeneration method proposed in the scheme of the present invention, and LMB-MD-DC filter and FLMB-MD-DC filter are respectively versions of LMB-MD filter and FLMB-MD filter after adding the point trace condensation method proposed in the scheme of the present invention. PFLMB-MD filter is a version of the technical scheme proposed in the present invention that does not consider point trace condensation, and PFLMB-MD-DC filter is the technical scheme proposed in the present invention. It should be pointed out that since it is difficult to obtain the initial state information of each target in actual engineering, this simulation experiment does not provide the initial state information of the target, which will cause the standard LMB filter and standard FLMB filter to be unable to be used directly. Therefore, all the methods involved in the comparison in this simulation are improved using the measurement drive regeneration method proposed in the scheme of the present invention.

[0145] 2. Simulation results and analysis

[0146] The average results of 100 Monte Carlo simulations are as follows: Figure 3 shown. Figure 3 (a) shows the estimated result of the target number. Figure 3 (b) shows the OSPA distance of each method. The average running time of 100 Monte Carlo simulations of each method is shown in Table 1.

[0147] analyze:

[0148] (1) From Figure 3 It can be seen that each method can adaptively detect new targets. However, when a new target appears, the target number estimation will be delayed, and the OSPA distance will have a peak at the corresponding moment. This is because each method uses the measurement-driven new method proposed in the solution of the present invention to detect new targets, which needs to use the measurement information of the previous moment for sampling. Therefore, when a new target appears, the target number estimation will be delayed, and the corresponding OSPA distance will have a peak.

[0149] (2) From Figure 3 It can also be seen that the number of targets for LMB-MD filter, FLMB-MD filter and PFLMB-MD filter is obviously over-estimated, and the OSPA distance is also high, while the number of targets for LMB-MD-DC filter, FLMB-MD-DC filter and PFLMB-MD-DC filter is estimated very accurately, and the OSPA distance is also low. This is because the first three filters directly use the original measurement information for filtering without point condensation, which easily estimates a single target with two measurement points as two targets, while the latter three filters pre-process the measurement and use the measurement set after point condensation for filtering, so a more accurate target number estimation and a lower OSPA distance can be obtained.

[0150] (3) It can be seen from Table 1 that: ① The running time of the LMB-MD-DC filter, the FLMB-MD-DC filter and the PFLMB-MD-DC filter is shorter than that of the LMB-MD filter, the FLMB-MD filter and the PFLMB-MD filter, mainly because the first three filters have been subjected to point condensation and the number of measurements has been reduced. ② From the LMB-MD-DC filter to the FLMB-MD-DC filter and then to the PFLMB-MD-DC filter, the running time is gradually reduced. The LMB-MD-DC filter takes 33.1824s, the FLMB-MD-DC filter takes 12.3695s, and the running time is reduced to 37.28% of the LMB-MD-DC filter. This is because the FLMB-MD-DC filter is based on joint prediction and update and Gibbs sampling, and fewer components are assumed in the filtering process, so the computational complexity is lower. The PFLMB-MD-DC filter of the technical solution proposed in the present invention takes 3.1908s, and the running time is further reduced to 25.80% of the FLMB-MD-DC filter, and the computational efficiency is significantly improved. This is because the PFLMB-MD-DC filter is parallelized based on the FLMB-MD-DC filter, which can further reduce the amount of calculation.

[0151] (4) General Figure 3 It can be seen from Table 1 that the PFLMB-MD-DC filter of the technical solution proposed in the present invention not only has good tracking performance, but also has good real-time performance, and thus has good engineering application prospects.

[0152] Table 1

[0153]

[0154] The above is only an embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims

1. A parallel fast label multi-Bernoulli filtering method in a phased array radar system, characterized in that: include: Obtain the radar measurement set and use the mean shift algorithm to divide the measurement set; Perform point condensation on the divided measurement set; Parallel joint prediction and update based on the measurement set after point trace condensation, including: LMB state transfer, target and measurement grouping, parallel processing of grouping results, and merging of posterior densities of each group; After parallelizing joint prediction and updating, the LMB parameter set is pruned and truncated; Estimate the number and states of targets based on the pruned and truncated LMB parameter set.

2. According to claim 1, a parallel fast label multi-Bernoulli filtering method in a phased array radar system is characterized in that: The step of performing point agglomeration on the divided measurement set includes: The divided measurement set Each measurement division unit in The measurements in the ensemble are weighted averaged according to the amplitude of each measurement to obtain the measurement set after the point traces are condensed. in, Among them, |W i | indicates W i The number of measurements, Indicates the measured amplitude, Indicates the measured location information.

3. According to claim 1, the method for parallel fast label multi-Bernoulli filtering in a phased array radar system is characterized in that: The LMB state transfer includes: Obtain the multi-target posterior density parameter set at time k-1, which includes the existence probability and probability density of all targets; Based on the multi-target posterior density at time k-1, the multi-target density parameter set after the state transfer of the surviving target at time k is obtained. The multi-target density parameter set after the state transfer of the surviving target includes the existence probability and probability density of all surviving targets; The new target is detected by using the measurement driven new generation method, that is, the new target parameter set is obtained by sampling at each measurement position in the measurement set after the point traces are condensed at the previous moment. The new target parameter set includes the existence probability and probability density of all new targets. The existence probability and probability density of all surviving targets and the existence probability and probability density of all new targets are combined into a multi-target density parameter set after state transfer.

4. According to claim 1, the method for parallel fast label multi-Bernoulli filtering in a phased array radar system is characterized in that: The target and measurement grouping includes: Treat each measurement in the measurement set after point trace condensation as a group, and add a label set to each measurement group, where the label set represents the index of the target belonging to the measurement group; Based on the label set of each measurement group, the measurement groups are merged until the number of groups does not change; According to the label set in each group, the corresponding target is placed in each measurement group to obtain the result after the target and measurement are grouped.

5. According to claim 4, a parallel fast label multi-Bernoulli filtering method in a phased array radar system is characterized in that: The method for obtaining the tag set includes: The Mahalanobis distance between each measurement in the measurement set after point condensation and all targets is calculated, and then the index numbers of all targets smaller than the preset threshold are stored as label values ​​in the label set of the measurement group.

6. According to claim 4, a parallel fast label multi-Bernoulli filtering method in a phased array radar system is characterized in that: The merging of the measurement groups includes: Check the label set of each measurement group in turn, and merge two measurement groups with overlapping label sets; the merging rule is as follows: merge the two measurement groups into one group, and take the union of the two measurement group label sets as the label set of the new group; starting from the first group, repeat the merging operation until the number of groups does not change.

7. The method for parallel fast label multi-Bernoulli filtering in a phased array radar system according to claim 1, characterized in that: The parallel processing of the grouping results includes: Calculate the joint prediction and updated multi-objective posterior density of each group respectively, wherein the multi-objective posterior density is in the form of GLMB; The multi-objective posterior density of each group is converted from GLMB form to LMB form.

8. The method for parallel fast label multi-Bernoulli filtering in a phased array radar system according to claim 1, characterized in that: The merging of the posterior densities of the groups includes: The multi-objective posterior densities of each group are merged and organized into a total LMB parameter set.

9. The method for parallel fast label multi-Bernoulli filtering in a phased array radar system according to claim 1, characterized in that: The pruning and truncating of the LMB parameter set includes: Prune and truncate the LMB parameter set itself: compare the existence probability of the hypothesized trajectories in the LMB parameter set with the preset pruning threshold, and discard the hypothesized trajectories that are less than the pruning threshold; compare the number of hypothesized trajectories after pruning with the maximum number of trajectories. If the number of hypothesized trajectories after pruning is greater than the maximum number of trajectories, sort the hypothesized trajectories from large to small according to the existence probability, and take the hypothesized trajectories with the largest number of trajectories as the truncated LMB parameter set, otherwise no truncation is required; The Gaussian items of each hypothesized trajectory in the LMB parameter set are pruned, fused and truncated: in each hypothesized trajectory, the weight of each Gaussian item is compared with the pruning threshold, and the Gaussian items smaller than the pruning threshold are deleted; the Mahalanobis distance between two Gaussian items is calculated, and the two Gaussian items smaller than the fusion threshold are weightedly fused according to the weight ratio, and the weight of the fused Gaussian item is the sum of the weights of the two Gaussian items; the number of Gaussian items after pruning and fusion is compared with the preset maximum number of Gaussian items. If it is greater, the Gaussian items with the largest weight are retained, otherwise no truncation is required; after pruning, fusion and truncation, the weights of the Gaussian items are normalized.

10. The parallel fast label multi-Bernoulli filtering method in a phased array radar system according to claim 1, characterized in that: The method of estimating the number and state of targets based on the pruned and truncated LMB parameter set includes: The maximum a posteriori criterion is used to estimate the number of targets, that is, Among them, ρ k (n) represents the potential distribution of the LMB parameter set; Sort the hypothesized trajectories according to their probability of existence from large to small, and select the first Hypothesis trajectories are used for state extraction; Get the target state estimate set Among them, the state of each hypothesized trajectory Take the item with the largest weight among the Gaussian items, and estimate the label Get the label value of the hypothesis trajectory.

Images