Parallelized fast labeled multi-bernoulli filter method under phased array radar system

Abstract

The application relates to a parallel fast label multi-Bernoulli filtering method under a phased array radar system and belongs to the field of radar target tracking. The application comprises the following steps: obtaining a measurement set of a radar, dividing the measurement set by adopting a mean shift algorithm, performing plot condensation on the divided measurement set, performing parallel joint prediction and updating based on the plot condensed measurement set, including LMB state transition, target and measurement grouping, parallel processing of the grouping results, and merging of the group posterior density, pruning and truncating the LMB parameter set after the parallel joint prediction and updating, and estimating the target number and state based on the pruned and truncated LMB parameter set. Through grouping of the target and the measurement, parallel processing of the FLMB filter is realized, the calculation amount is effectively reduced under the condition that the tracking performance loss is small, the real-time performance is improved, and the target detection speed and accuracy are improved.

Description

Technical Field

[0001] This invention belongs to the field of radar target tracking, specifically relating to a parallelized fast tag-based Bernoulli filtering method under a phased array radar system. Background Technology

[0002] Because it avoids complex data associations, the multi-target tracking method based on Random Finite Set (RFS) has attracted widespread attention from scholars at home and abroad since its proposal. Mahler and Vo et al. 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 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.) etc., made outstanding contributions to the development of RFS theory. However, these early RFS filters were all approximations of multi-object Bayesian filters, with poor tracking performance and inability to output target tracks. To solve the above problems, Vo et al. proposed the Generalized Labeled Multi-Bernoulli (GLMB) filter (Vo BT, Vo B N. Labeled randomfinite sets and multi-object conjugate priors[J].IEEE Transactions on Signal Processing, 2013, 61(13):3460-3475.).This filter is the optimal solution for the multi-target Bayesian filter, possessing not only excellent tracking performance but also the ability to output target tracks. However, due to the reconsideration of complex data associations, its computational complexity is very high. How to effectively reduce the computational complexity of the GLMB filter is currently a research hotspot. To this end, Reuter et al. proposed the Labeled Multi-Bernoulli (LMB) filter (Reuter S, 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, effectively reducing computational load with minimal loss in tracking performance. Subsequently, scholars such as Vo and Reuter proposed GLMB and LMB filters based on joint prediction and update and Gibbs sampling, namely the 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 the 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 Conferenceon Intelligent Vehicles Symposium,2017:765-772.). These two filters are fast methods corresponding to the GLMB filter and LMB filter, respectively. They have lower computational complexity with minimal loss in tracking performance. Among them, the FLMB filter has the lowest computational cost and has good prospects for engineering applications. However, in practical engineering, when the number of targets and measurements is large, the computational load of the FLMB filter is still large, making it difficult to meet real-time requirements.

[0003] In addition, in practical 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 practical engineering, it is difficult to obtain the initial state of each target; (2) In the phased array radar system, in order to improve the detection performance of targets, the beam dwell between two adjacent sectors is often designed to overlap. This may result in a target obtaining two measurements. 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 problem to be solved by this invention is:

[0005] To overcome the shortcomings of existing technologies, this invention provides a parallelized fast tag multi-Bernoulli filtering method for phased array radar systems, which can be used to improve target tracking speed and accuracy.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A parallelized fast tag-based multi-Bernoulli filtering method for phased array radar systems, characterized by comprising:

[0008] The radar measurement set is acquired, and the mean shift algorithm is used to divide the measurement set; the point clustering is then performed on the divided measurement set.

[0009] Parallel joint prediction and update based on the measurement set after point agglomeration, including: LMB state transition, target and measurement clustering, parallel processing of clustering results, and merging of posterior densities of each cluster.

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

[0011] The number and state of targets are estimated based on the trimmed and truncated LMB parameter set.

[0012] A further technical solution of the present invention: the step of performing point aggregation on the divided measurement set includes:

[0013] The divided measurement set Each measurement division unit in The measurements in the dataset are weighted and averaged according to the amplitude of each measurement to obtain the measurement set after point aggregation. in, Among them, |W i | indicates W i The number of measurements in the middle Indicates the range of measurement. This indicates the location information of the measurement.

[0014] A further technical solution of the present invention: the LMB state transition includes:

[0015] Obtain the multi-target posterior density parameter set at time k-1. The multi-target posterior density parameter set 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 transition of the surviving target at time k is obtained. The multi-target density parameter set after the state transition of the surviving target includes the existence probability and probability density of all surviving targets.

[0017] The measurement-driven nascent method is used to detect new targets. That is, the parameter set of new targets is obtained by sampling at each measurement position in the measurement set after the point trace is aggregated at the previous time step. The parameter set of new targets includes the existence probability and probability density of all new targets.

[0018] The existence probabilities and probability densities of all surviving targets and all newly generated targets are merged into a multi-target density parameter set after state transition.

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

[0020] Each measurement in the aggregated measurement set is considered as a group, and a label set is added to each measurement group, where the label set represents the index of the target belonging to that measurement group;

[0021] Based on the label set of each measurement group, the measurement groups are merged until the number of groups no longer changes.

[0022] Based on the label set in each group, the corresponding target is placed into each measurement group, and the results of target and measurement grouping are obtained.

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

[0024] The Mahalanobis distance between each measurement in the aggregated measurement set and all targets is calculated, and then the index numbers of all targets less than a 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 measurement groups includes:

[0026] The label set of each measurement group is checked sequentially, and two measurement groups with overlapping label sets are merged. The merging rules are as follows: two measurement groups are merged into one group, and the union of the label sets of the two measurement groups is taken as the label set of the new group. Starting from the first group, the merging operation is performed in a loop until the number of groups does not change.

[0027] A further technical solution of the present invention: the parallel processing of the clustering results includes:

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

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

[0030] A further technical solution of the present invention: the merging of the posterior densities of each group includes:

[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 trimming and truncation of the LMB parameter set includes:

[0033] The LMB parameter set itself is pruned and truncated: the existence probability of the hypothetical trajectory in the LMB parameter set is compared with the preset pruning threshold, and hypothetical trajectories with a probability less than the pruning threshold are discarded; the number of pruned hypothetical trajectories is compared with the maximum number of trajectories. If the number of pruned hypothetical trajectories is greater than the maximum number of trajectories, the hypothetical trajectories are sorted from largest to smallest according to their existence probability, and the top few hypothetical trajectories are taken as the truncated LMB parameter set; otherwise, no truncation is required.

[0034] For each hypothetical trajectory in the LMB parameter set, Gaussian terms are pruned, merged, and truncated: In each hypothetical trajectory, the weight of each Gaussian term is compared with the pruning threshold, and Gaussian terms smaller than the pruning threshold are deleted; the Mahalanobis distance between two Gaussian terms is calculated, and two Gaussian terms smaller than the fusion threshold are merged according to their weight ratios, and the weight of the merged Gaussian term is the sum of the weights of the two Gaussian terms; the number of Gaussian terms after pruning and fusion is compared with the preset maximum number of Gaussian terms, and if it is greater, the maximum number of Gaussian terms with the largest weights are retained, otherwise no truncation is required; after pruning, fusion, and truncating, the weights of the Gaussian terms are normalized.

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

[0036] The target number is estimated using the maximum a posteriori criterion, i.e. Where, ρ k(n) represents the potential distribution of the LMB parameter set;

[0037] The hypothetical trajectories are sorted from highest to lowest probability of existence, and the top ones are selected. State extraction is performed on the hypothetical trajectory;

[0038] Obtain the target state estimation set Among them, the state of each hypothetical trajectory Label estimation is performed by selecting the term with the largest weight from the Gaussian terms. Take the label value of the hypothetical trajectory.

[0039] The beneficial effects of this invention are as follows:

[0040] The parallelized fast tag-based multi-Bernoulli filtering method provided by this invention for phased array radar systems has the following advantages compared to existing technologies:

[0041] 1. In practical engineering, when the number of targets and measurements is large, existing FLMB filters suffer from high computational complexity and poor real-time performance. This invention achieves parallel processing of the FLMB filter by grouping the targets and measurements, effectively reducing computational complexity and improving real-time performance with minimal 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 newborn method to detect newborn targets and provides a specific design method for the newborn parameters, which can realize adaptive detection of newborn targets; (2) The measurement is preprocessed and the measurement set after point aggregation is used to participate in the filtering process, which can effectively avoid the problem of target overestimation caused by directly using the original measurement data for filtering in the standard FLMB filter. Attached Figure Description

[0043] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0044] Figure 1 This is a flowchart of the parallelized fast tag multi-Bernoulli filtering method under the phased array radar system of the present invention;

[0045] Figure 2 This represents the actual trajectory of the target in the simulation experiment.

[0046] Figure 3 The average results of 100 Monte Carlo simulations are as follows: (a) the estimated number of objectives for each method; (b) the OSPA distance for each method. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this 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, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such terms can be used interchangeably where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0049] This invention provides a parallelized fast tag-based multi-Bernoulli filtering method for phased array radar systems. Based on the standard FLMB filter, this invention groups targets and measurements during the joint prediction and update process, then calculates the posterior density of each group. By parallelizing the processing of each group, the number of hypothetical components is effectively reduced, lowering the computational load. Furthermore, in the implementation of the PFLMB filter, a measurement-driven method is used to detect emerging targets, reducing the need for prior target information. Simultaneously, measurements are preprocessed, and filtering is performed using a measurement set agglomerated with point traces, avoiding overestimation of the number of targets.

[0050] like Figure 1 As shown, it includes the following steps:

[0051] Step 1: Initialization. The LMB parameter set is initialized based on prior information such as the target's initial state. However, since this invention uses a measurement-driven nascent detection method, the target's initial state information is no longer needed. Therefore, in practice, the initialized LMB parameter set is actually empty; only the parameter structure of the LMB parameter set is retained. Furthermore, this initialization step is only executed once before the filtering process begins; it is not executed again in subsequent filtering processes.

[0052] Step 2: Point Clustering. First, the radar-acquired measurement set is divided, grouping measurements potentially originating from the same target into the same cell. Then, the measurements within each cell are weighted and averaged by amplitude. Finally, the point clustered measurement set is obtained. The specific steps are as follows:

[0053] Let the measurement set at the current time be denoted as in, z p,i,k Indicates measurement location information, z a,i,k This indicates the measurement amplitude information.

[0054] (1) Based on the measurement location information, the measurement set is divided using the mean shift algorithm to obtain... in, |W i | indicates W i The number of measurements in the middle

[0055] (2) Perform point aggregation on the divided measurement set, dividing each measurement into units. The measurements in the dataset are weighted and averaged according to the amplitude of each measurement to obtain the measurement set after point aggregation. in, It should be noted that the measurement set after point agglomeration Measurement in Measurements that only contain location information.

[0056] Finally, it should be noted that this invention employs a measurement-driven neoplasm detection method, which requires sampling based on measurement information from the previous moment. Therefore, in the first moment, only point aggregation processing is performed on the measurement set, without subsequent filtering operations. The actual filtering process begins in the second moment. After point aggregation is completed in the first moment, the processing flow in the second moment begins directly.

[0057] Step 3: Parallel Joint Prediction and Update. This step includes four steps: first, LMB state transition; second, target and measurement clustering; third, parallel processing of the clustering results; and fourth, merging the posterior densities of each cluster. The specific steps are as follows:

[0058] (1) LMB state transition

[0059] ① Survival target state transition

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

[0061]

[0062] In the formula, J k-1 (l k-1 ) represents the number of terms in the Gaussian mixture, w j,k-1 (l k-1 ) represents the weight of the j-th Gaussian mixture term. The mean is m j,k-1 (l k-1 ), covariance is P j,k-1 (l k-1 The Gaussian probability density function is given. Then, the multi-target density after the state transition 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 Let and represent the probability of existence and probability density of the surviving target, respectively, 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 F represents the probability of the target surviving. k-1 Let Q represent the state transition matrix. k-1 This represents the process noise covariance matrix.

[0071] ② Measurement-driven regeneration

[0072] This invention employs a measurement-driven nascent detection method, specifically by using the measurement set generated after the aggregation of traces at the previous time step. Each measurement in Newborn parameters are obtained by sampling at the location. Modeling the newborn target as an LMB RFS, the newborn target model can be expressed as: Where, r B,k (l k ) and p B,k (x k ,l k ) represent the probability of the existence of a new target and its probability density, respectively. Let represent the label space of the newly generated target at time k. Then, the generation parameters using the measurement-driven 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 Indicates the probability of a target newborn. P0 represents the initial covariance matrix.

[0080] (2) Target and Measurement Clustering

[0081] The multi-objective density after the state transition can be organized into a parameter set as follows: The LMB RFS. The measurement set after point agglomeration is This step involves grouping the measurements of the target and the aggregated points for subsequent parallel processing.

[0082] ① Grouping targets based on measurements after point clustering

[0083] Each measurement is treated as a group, and then the target is grouped according to the measurement groups.

[0084] A label set is added to each measurement group, where the label values ​​represent the indices of the targets belonging to that measurement group. Measurement groups with empty label sets are considered clutter and are removed. Specifically, the method involves using the measurement set... 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 no longer changes.

[0087] The label set of each measurement group is checked sequentially, and two measurement groups with overlapping label sets are merged. The merging rule is as follows: two measurement groups are merged into one group, and the union of the label sets of the two measurement groups is taken as the label set of the new group. Starting from the first group, the merging operation is performed repeatedly until the number of groups does not change.

[0088] ③ Integrate the final target with the measurement clustering results

[0089] According to step ②, the measurements were grouped into different clusters, each with a different set of labels. Then, the corresponding targets were placed into each cluster based on their respective label sets. For targets not assigned to any cluster, each target formed a separate cluster. Within these clusters, the measurement set was empty.

[0090] The final clustering result is represented as in, and Let 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 This represents the set of all measurements whose label set is empty when individual measurements are grouped together. Furthermore,

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

[0092]

[0093] (3) Parallelize the clustering results

[0094] ① Calculate the posterior density for each group.

[0095] ● Posterior density expression for each group

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

[0097]

[0098]

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

[0100]

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

[0102]

[0103] Furthermore, in the above formula, [·] denotes a multi-objective exponential function, defined as:

[0104]

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

[0106] ● Expanded cost matrix for each group

[0107] In the process of calculating the posterior density expression for each group, to calculate the expression with larger weights... The assumed components require the calculation of an extended cost matrix that comprehensively considers target survival, extinction, rebirth, detection and missed detection, etc. The specific calculation method is as follows.

[0108] The nth group is represented as in, express The number of measurements. The goal of this step is to calculate the group. It has a large weight Pairing The set. For each pair definition

[0109]

[0110] γ (n) Inherited A positive 1-1 property, therefore, when When, i,i′∈{1:P (n) They are equal. (Use) express Given the set of all positive 1-1 elements in the set, then, Tag set and association mapping It can be restored in the following ways:

[0111]

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

[0113]

[0114] In the formula, 1≤i≤R (n) For the survival target in the nth group, R (n) +1≤i≤P (n) This corresponds to the newly emerging target in the nth group. This indicates the trajectory assigned in the nth group. The index of the measurement, j = -1 indicates the trajectory. Extinction, j=0 represents the trajectory Missed detection. Thus, formula (18) can be written as:

[0115]

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

[0117]

[0118]

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

[0120] ● Gibbs sampling for each group

[0121] See each γ (n) In group n The above follows the probability distribution π (n) An implementation of a random variable. Then, by using π... (n) Sampling can generate candidate γ (n) Constructing π (n) as follows:

[0122]

[0123] Direct sampling from the above distribution is difficult; therefore, this invention uses a Gibbs sampler for sampling. From an initial solution... Let's begin with the next solution. It can be obtained from a series of conditional distributions Obtained by sampling, where (γ′) 1:s-1 ) (n) and Let represent the associations of the newly sampled components and the associations derived from previous solutions, respectively. The Gibbs sampler is computationally efficient, but it requires that the conditional distributions be easily computed and sampled. Therefore, a closed-form expression is provided here for each conditional distribution so that they can be computed or sampled at a lower cost. For each s∈{1:P} (n)}:

[0124]

[0125] In the formula, Then, for a non-positive j, for Thus, sampling from the conditional distribution is easier and less costly, with only linear complexity in terms of the number of measurements. Finally, since Gibbs sampling may return the same assumptions, duplicates must also be removed.

[0126] ② Convert GLMB in each group to LMB

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

[0128]

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

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

[0131]

[0132] Will Further organize into a parameter set

[0133] Step 4: Pruning and Truncation. After parallelizing joint prediction and updating, the parameter set needs to be pruned and truncated. Pruning and truncation are performed. This mainly includes two aspects: first, pruning and truncation of the LMB parameter set itself; and second, pruning, merging, and truncation of the Gaussian terms of each hypothetical 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, determine the probability of existence for each hypothetical trajectory. The hypothetical trajectories are compared with a preset trimming threshold, and those smaller than the threshold are discarded. Then, the number of trimmed hypothetical trajectories is compared with the maximum number of trajectories T. max Compare them. If it is greater than T. max Then, based on the probability of existence Sort the hypothetical trajectories from largest to smallest, and take the top T. max One hypothetical trajectory is used as the truncated LMB parameter set; otherwise, truncation is not required.

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

[0137] Pruning: In each hypothetical trajectory, the weight of each Gaussian term is compared with a pruning threshold, and Gaussian terms with weights less than the threshold are deleted. Fusion: In each hypothetical trajectory, the Mahalanobis distance between two Gaussian terms is calculated. Two Gaussian terms with weights less than the fusion threshold are fused according to their weight ratios. The weight of the fused Gaussian term is the sum of the weights of the two Gaussian terms. Truncation: In each hypothetical trajectory, the number of pruned and fused Gaussian terms is compared with the preset maximum number of Gaussian terms J. max Compare the results; if the weight is greater than the given weight, retain the J with the largest weight. max If there are no Gaussian terms, then no truncation is needed. Finally, after pruning, merging, and truncation, the weights of the Gaussian terms in each hypothetical 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 this parameter set. The specific steps are as follows:

[0139] First, the maximum a posteriori criterion is used to estimate the target number, i.e. Where, ρ k (n) represents the potential distribution of the LMB parameter set. Then, the hypothetical trajectories are sorted from largest to smallest according to the probability of their existence, and the top ones are selected. The state is extracted using the assumed trajectory. Finally, the target state estimation set can be obtained. It should be noted that, when extracting the target state, the state of each hypothetical trajectory... Label estimation is performed by selecting the term with the largest weight from the Gaussian terms. Simply take the label value of the hypothetical trajectory.

[0140] Step 6: Determine if the process has ended. Check if the observation has ended. If so, end the filtering process; otherwise, proceed to Step 3 to begin the filtering process at the next time step. It should be noted that in practice, the timing of the point aggregation in Step 2 is flexible; it only needs to be executed before the target and measurement clustering operation in Step 3. Therefore, it can be executed before or after Step 3. In this embodiment, it is executed before Step 3.

[0141] The technical effects of the present invention will be further described below in conjunction with simulation experiments:

[0142] 1. Simulation conditions

[0143] In the simulation experiment, the monitoring area was [-1000, 1000]m × [-1000, 1000]m, and a total of 8 targets appeared in the monitoring area. The actual movement trajectories of the targets are as follows. Figure 2As shown. Target 1's survival time is 1-60s, Target 2's survival time is 5-70s, Target 3's survival time is 10-80s, Target 4's survival time is 15-90s, Target 5's survival time is 20-100s, Target 6's survival time is 25-100s, Target 7's survival time is 30-100s, and Target 8's survival time is 35-100s. The target motion model is a constant velocity (CV) model, with a sampling interval of 1s and a process noise standard deviation of 5m / s². 2 The observation duration for the entire monitoring area was 100 seconds. Clutter was uniformly distributed throughout the monitoring area, with an average value of 10. The target survival probability was set to 0.99, the detection probability to 0.98, and the measurement noise standard deviation to 10 m. To simulate the measurement situation under a phased array radar system, the measurement generated by the first detected target in the target state set was set as two measurements. The generation processes of these two measurements were independent of each other, both randomly generated, and followed the same Gaussian distribution. In addition, the two measurements had different amplitudes, with the measurement closer to the actual position having a larger amplitude. The tracking results were evaluated using Optimal Sub-Pattern Assignment (OSPA) distance, with the cutoff distance and sensitivity parameters set to c = 100 and p = 1, respectively. The hardware platform for the simulation experiment was an Intel(R) Core(TM) i5-8250U CPU @ 1.60GHz / 1.80GHz processor and 16.0GB RAM, and the software platform was Matlab R2018b.

[0144] The methods used for comparison include the LMB-MD filter, LMB-MD-DC filter, FLMB-MD filter, FLMB-MD-DC filter, PFLMB-MD filter, and PFLMB-MD-DC filter. Specifically, the LMB-MD filter and FLMB-MD filter are improved versions of the standard LMB filter and standard FLMB filter, respectively, using the measurement-driven generation method proposed in this invention. The LMB-MD-DC filter and FLMB-MD-DC filter are versions of the LMB-MD filter and FLMB-MD filter, respectively, after adding the point aggregation method proposed in this invention. The PFLMB-MD filter is the version of the technical solution proposed in this invention that does not consider point aggregation, and the PFLMB-MD-DC filter is the technical solution proposed in this invention. It should be noted 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 targets, which will prevent the standard LMB filter and standard FLMB filter from being used directly. Therefore, all methods used for comparison in this simulation have been improved using the measurement-driven generation method proposed in this invention.

[0145] 2. Simulation Results and Analysis

[0146] The average result of 100 Monte Carlo simulations is as follows Figure 3 As shown. Figure 3 (a) presents the estimated number of targets. Figure 3 (b) shows the OSPA distance for each method. The average runtime of 100 Monte Carlo simulations for each method is shown in Table 1.

[0147] analyze:

[0148] (1) From Figure 3 As can be seen, all methods can adaptively detect newly emerging targets. However, when a new target appears, the target count estimation is delayed, and the OSPA distance spikes accordingly. This is because all methods use the measurement-driven new target detection method proposed in this invention, which requires sampling using measurement information from the previous moment. Therefore, when a new target appears, the target count estimation is delayed, and the corresponding OSPA distance spikes.

[0149] (2) From Figure 3 It can also be seen that the LMB-MD, FLMB-MD, and PFLMB-MD filters showed significant overestimation of the target number and high OSPA distances, while the LMB-MD-DC, FLMB-MD-DC, and PFLMB-MD-DC filters provided accurate target number estimations and lower OSPA distances. This is because the first three filters directly use the raw measurement information for filtering without point clustering, which easily leads to the estimation of a single target with two measurement points as two targets. The latter three filters preprocess the measurements and use the measured set after point clustering for filtering, thus obtaining more accurate target number estimations and lower OSPA distances.

[0150] (3) As can be seen from Table 1: ① The running time of the LMB-MD-DC filter, FLMB-MD-DC filter, and PFLMB-MD-DC filter is shorter than that of the LMB-MD filter, FLMB-MD filter, and PFLMB-MD filter, mainly because the first three filters incorporate point clustering, reducing the number of measurements. ② The running time gradually decreases from the LMB-MD-DC filter to the FLMB-MD-DC filter and then to the PFLMB-MD-DC filter. The LMB-MD-DC filter takes 33.1824s, and the FLMB-MD-DC filter takes 12.3695s, with the running time decreasing to 37.28% of that 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 assumes fewer components during the filtering process, thus resulting in lower computational complexity. The PFLMB-MD-DC filter proposed in this invention takes 3.1908s, further reducing the running time to 25.80% of that of the FLMB-MD-DC filter, significantly improving computational efficiency. This is because the PFLMB-MD-DC filter is parallelized based on the FLMB-MD-DC filter, which can further reduce the amount of computation.

[0151] (4) Comprehensive Figure 3 As can be seen from Table 1, the PFLMB-MD-DC filter proposed in this invention not only has good tracking performance but also good real-time performance, thus showing good prospects for engineering applications.

[0152] Table 1

[0153]

[0154] The above description is merely an embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of this application should be included within the scope of the claims of this application.

Claims

1. A parallelized fast tag-based multi-Bernoulli filtering method for phased array radar systems, characterized in that, include: The radar measurement set is acquired, and the mean shift algorithm is used to partition the measurement set. Point aggregation is performed on the divided measurement set; Parallel joint prediction and update based on the measurement set after point agglomeration, including: LMB state transition, target and measurement clustering, parallel processing of clustering results, and merging of posterior densities of each cluster. The LMB state transition includes: Get k The multi-target posterior density parameter set at time -1 includes the existence probability and probability density of all targets. based on k Multi-objective posterior density acquisition at time -1 k The set of multi-target density parameters after the state transition of the surviving target at any time includes the existence probability and probability density of all surviving targets. The measurement-driven nascent method is used to detect new targets. That is, the parameter set of new targets is obtained by sampling at each measurement position in the measurement set after the point trace is aggregated at the previous time step. The parameter set of new targets includes the existence probability and probability density of all new targets. The existence probabilities and probability densities of all surviving targets and the existence probabilities and probability densities of all newly generated targets are merged into a multi-target density parameter set after state transition; The target and measurement clusters include: Each measurement in the aggregated measurement set is considered as a group, and a label set is added to each measurement group, where the label set represents the index of the target belonging to that measurement group; Based on the label set of each measurement group, the measurement groups are merged until the number of groups no longer changes. Based on the tag set in each group, the corresponding target is placed into each measurement group, and the results of grouping the target and measurement are obtained. The merging of measurement groups includes: The label set of each measurement group is checked sequentially, and two measurement groups with overlapping label sets are merged. The merging rules are as follows: two measurement groups are merged into one group, and the union of the label sets of the two measurement groups is taken as the label set of the new group. Starting from the first group, the merging operation is performed in a loop until the number of groups does not change. The parallel processing of the clustering results includes: Calculate the joint prediction and updated multi-objective posterior density for each group, wherein the multi-objective posterior density is in GLMB form; Transform the multi-objective posterior density of each group from GLMB form to LMB form; After parallelizing joint prediction and updating, the LMB parameter set is pruned and truncated. The number and state of targets are estimated based on the trimmed and truncated LMB parameter set.

2. The parallelized fast tag-based multi-Bernoulli filtering method under phased array radar system according to claim 1, characterized in that, The step of aggregating the points in the divided measurement set includes: The divided measurement set Each measurement division unit in The measurements in the dataset are weighted and averaged according to the amplitude of each measurement to obtain the measurement set after point aggregation. ,in, , ;in, express The number of measurements in the middle Indicates the range of measurement. This indicates the location information of the measurement.

3. The parallelized fast tag-based multi-Bernoulli filtering method under phased array radar system according to claim 1, characterized in that, The method for obtaining the tag set includes: The Mahalanobis distance between each measurement in the aggregated measurement set and all targets is calculated, and then the index numbers of all targets less than a preset threshold are stored as label values ​​in the label set of the measurement group.

4. The parallelized fast tag-based multi-Bernoulli filtering method under phased array radar system according to claim 1, characterized in that, The merged posterior density of each group includes: The multi-objective posterior densities of each group are merged and organized into a total LMB parameter set.

5. The parallelized fast tag-based multi-Bernoulli filtering method for phased array radar according to claim 1, characterized in that, The trimming and truncation of the LMB parameter set includes: The LMB parameter set itself is pruned and truncated: the existence probability of the hypothetical trajectory in the LMB parameter set is compared with the preset pruning threshold, and hypothetical trajectories with a probability less than the pruning threshold are discarded; the number of pruned hypothetical trajectories is compared with the maximum number of trajectories. If the number of pruned hypothetical trajectories is greater than the maximum number of trajectories, the hypothetical trajectories are sorted from largest to smallest according to their existence probability, and the top few hypothetical trajectories are taken as the truncated LMB parameter set; otherwise, no truncation is required. For each hypothetical trajectory in the LMB parameter set, Gaussian terms are pruned, merged, and truncated: In each hypothetical trajectory, the weight of each Gaussian term is compared with the pruning threshold, and Gaussian terms smaller than the pruning threshold are deleted; the Mahalanobis distance between two Gaussian terms is calculated, and two Gaussian terms smaller than the fusion threshold are merged according to their weight ratios, and the weight of the merged Gaussian term is the sum of the weights of the two Gaussian terms; the number of Gaussian terms after pruning and fusion is compared with the preset maximum number of Gaussian terms, and if it is greater, the maximum number of Gaussian terms with the largest weights are retained, otherwise no truncation is required; after pruning, fusion, and truncating, the weights of the Gaussian terms are normalized.

6. The parallelized fast tag-based multi-Bernoulli filtering method under phased array radar system according to claim 1, characterized in that, The estimation of the number of targets and states based on the pruned and truncated LMB parameter set includes: The target number is estimated using the maximum a posteriori criterion, i.e. ,in, This represents the potential distribution of the LMB parameter set; The hypothetical trajectories are sorted from highest to lowest probability of existence, and the top ones are selected. State extraction is performed on the hypothetical trajectory; Obtain the target state estimation set ; where the state of each hypothetical trajectory Label estimation is performed by selecting the term with the largest weight from the Gaussian terms. Take the label value of the hypothetical trajectory.

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