A Partially Discernible Group Target Tracking Method and System Based on Augmented Label RFS

Abstract

This invention relates to a method and system for tracking partially distinguishable group targets based on augmented label RFS. The method includes: acquiring a set of measurement points; judging the set of measurement points to obtain measurement points for distinguishable and indistinguishable targets; clustering the measurement points of indistinguishable targets and calculating the centroid as equivalent measurement; recursively estimating the target state using a GALMB filter to obtain a set of estimated target states; updating the target type in the augmented label using the Bernoulli elements obtained from updating the equivalent measurement in the GALMB filter update step; dividing the estimated target state set into group structures and updating the group structure part in the filter label to obtain target trajectory, state, and group structure information. This invention is applicable to complex application scenarios such as air defense early warning, air traffic control, and battlefield situational awareness.

Description

Technical Field

[0001] This invention relates to the field of group target tracking technology, and in particular to a method and system for tracking partially resolvable group targets based on augmented label RFS. Background Technology

[0002] In complex application scenarios such as modern air defense early warning, air traffic control, and battlefield situational awareness, swarm target tracking technology, as a core means of acquiring the motion state and situational information of target groups, directly determines the accuracy of situational assessment and the timeliness of decision-making response, thus attracting widespread attention from academia and industry. Swarm targets typically consist of multiple individual targets with cooperative motion characteristics or spatial correlation characteristics. Compared to single-target tracking, swarm target tracking not only requires estimating the state of each individual target but also accurately identifying the structural characteristics, evolutionary patterns, and correlations among targets within the group. With the rapid development of sensor technology, the detection range and accuracy of radar and other detection equipment are constantly improving. However, in actual tracking scenarios, the distinguishability of targets within a swarm is often dynamically changing due to factors such as target motion characteristics, detection distance, and environmental interference—a problem known as partially distinguishable swarm target tracking. This problem significantly increases the complexity of the tracking task.

[0003] To accurately describe the cooperative motion characteristics of swarm targets, existing technologies have proposed various swarm target modeling methods. Among them, the Stochastic Differential Equation (SDE) model has become an important tool for swarm target modeling because it can accurately characterize the evolution process of target states through the repulsive and restoring forces between targets within the swarm. However, this characteristic of the SDE model also brings new challenges: under the dynamic effects of repulsive forces, restoring forces, and noise in the joint process of swarm targets, the spacing between targets within the swarm will continuously change. When the spacing between multiple originally distinguishable targets shrinks to below radar resolution, the distinguishable targets will aggregate into indistinguishable targets, forming a measurement point cloud within the radar's observation range; conversely, when the spacing between individuals within the group of indistinguishable targets increases to exceed radar resolution, the indistinguishable targets will separate into distinguishable targets. This dynamic transformation process of "distinguishable-indistinguishable" leads to significant uncertainty and complexity in the measurement information acquired by the sensor. Traditional multi-target tracking methods struggle to effectively handle the dynamic switching of measurement types, easily resulting in problems such as track track breakage, target identity confusion, and swarm structure estimation bias, severely restricting the improvement of swarm target tracking performance.

[0004] To address the uncertainty issues in multi-target tracking, Random Finite Set (RFS) theory provides a rigorous mathematical framework, eliminating the need to pre-establish the correlation between targets and measurements, and effectively avoiding the computational complexity and association error risks associated with traditional data association. As a typical representative of RFS theory, the Generalized Labeled Multi-Bernoulli (GLMB) filter achieves joint estimation of target identity and state by assigning a unique label to each target, significantly improving the stability of multi-target and group target tracking. Building upon this, filters based on Argumented Labeled Random Finite Set (ALFS), such as the Generalized Augmented Labeled Multi-Bernoulli (GALMB) filter, further expand the connotation of labels, fusing target identity information and group structure information, providing a new approach to handling complex group target tracking problems. However, current GALMB filters can only be applied to fully discriminable group target tracking problems and cannot handle partially discriminable group target tracking or the conversion between discriminable and indiscriminate group targets. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention focuses on the core challenge of partially discriminable group target tracking under the SDE model, aiming to solve the measurement uncertainty caused by the dynamic transformation of target discriminability within the group. It proposes a partially discriminable group target tracking method and system based on augmented label RFS, through 3- This paper proposes a method that uses criteria and undirected graph theory to accurately distinguish between distinguishable and indistinguishable target measurements. The centroid of the indistinguishable measurement point cloud is used as an equivalent measurement to reduce measurement uncertainty. An ALRFS framework is introduced to integrate information such as group labels, group cardinality, and group target type to achieve joint estimation of group target trajectories and states. Based on this, a novel filtering algorithm is designed to achieve stable and accurate tracking of some distinguishable group targets. Finally, simulation experiments verify the effectiveness of the proposed method, providing a new technical solution and theoretical support for group target tracking in complex scenarios.

[0006] To achieve the above objectives, the present invention provides the following solution: A partially resolvable group target tracking method based on augmented label RFS includes: Obtain a set of measurement points, and determine the measurement points of distinguishable and indistinguishable targets. Cluster the measurement points of the indistinguishable targets and calculate the centroid as the equivalent measurement; The target state is recursively estimated using a GALMB filter to obtain a set of estimated target states; in the update step of the GALMB filter, the target type in the augmented label is updated by the Bernoulli element obtained from the update of the equivalent measurement. The target estimated state set is divided into groups, and the group structure of the filter labels is updated to obtain target trajectory, state and group structure information.

[0007] Optionally, obtaining the measurement points for the distinguishable and indistinguishable targets includes: Using the set of measurement points, a first distance matrix is ​​constructed, and based on 3- The distance rule is used to calculate the standard deviation of the measurement noise in the radar field of view corresponding to each measurement point, and a 3- matrix; Through the first distance matrix and the 3- Construct a first adjacency matrix. If a group of measurement points located in the same connected component appears in the first adjacency matrix, then the group of measurement points is regarded as an indistinguishable target. If an independent measurement point appears in the first adjacency matrix, then the measurement point is regarded as a distinguishable target.

[0008] Optionally, calculating the centroid includes: ; in, For equivalent measurement of indistinguishable targets, The quantity measured for this indistinguishable target. For measurement index, For the measurement of this indistinguishable target.

[0009] Optionally, the target state includes: The state transitions of the group of targets are determined by using the stochastic differential module of single-target motion and the joint stochastic differential model of group targets: ; in, For the Markov transition density of the group's objective state, The repulsive force control matrix, for The set of states of the target within the subgroup at time step. for The set of states of the target within the subgroup at time step. Let be the subgroup state transition matrix. Let the vector be the joint repulsive force vector of the subgroups. This refers to the noise in the joint process of subgroup objectives.

[0010] Optionally, the prediction step of the GALMB filter includes: ; ; ; ; in, For multi-objective prior probability density functions, for The parameter set of the target still exists at all times. For survival target tags The prior existence probability of the corresponding target. Let this be the prior probability density of the target. Let be the parameter set of the probability density function of the newborn target. Tags for freshmen goals The prior existence probability of the corresponding target. Let this be the prior probability density of the target. Predictive step augmentation tags The probability of the existence of the corresponding Bernoulli component. To broaden labels after prediction steps The state probability density corresponding to the Bernoulli component. The prior probability density normalization factor, for Moment Tags The corresponding target is The probability density of time that still exists. For tags The Markov transition density corresponding to the target state, For tags The corresponding target is The posterior probability density at time t; The update steps include: ; ; ; ; ; ; ; in, Let be the posterior probability density function. For measurement set, Let be the parameter set of the posterior probability density function. For target tags, For the target label space after the prediction step, for A family of sets consisting of all subsets of . For mapping The set, For indicator functions, when The value is 1 if it is true, and 0 otherwise. For the tag The state probability density of the Bernoulli component, For a subset of tags and measurement allocation The combined weights, To measure the normalization factor of the likelihood, For tags Corresponding target in measurement allocation The conditional probability density under the following conditions The state of an individual's goals. For prediction step label The prior state probability density corresponding to the target. To measure the likelihood function, The target is in a state The probability of being detected by the sensor at any time. This represents the state probability density when the target is not detected. For space Towards space The mapping, For the tag The corresponding target was observed and measured by the sensor. The probability density, Assign function to measurement label Assigned to measurement set In Measurement The intensity of Poisson clutter. Assign instructions for measurement. Indicates label Assigned to the Individual measurements; This indicates that no measurement has been assigned.

[0011] Optionally, the augmentation tag includes: ; in, For the moment of the target's birth, For the index of the target at the current time, For the centroid of the group target, For the index of group targets, It is a marker used to indicate the type of group objective. For the group target index space, For the target type space, To broaden the label, To broaden the individual identity attributes of the target in the tag, To broaden the group identity attributes of the target in the tag.

[0012] Optionally, partitioning the target estimated state set into a group structure includes: Based on the target estimated state set, construct the second distance matrix and the second adjacency matrix; Set a target threshold. When the Mahalanobis distance between targets in the second distance matrix is ​​less than the target threshold, it proves that there is an edge between the targets. Then, the second adjacency matrix is ​​used to partition the group structure.

[0013] Optionally, constructing the second distance matrix includes: ; ; in, This is the second distance matrix. For the target posterior state and Mahalanobis distance, It is the identity matrix. Here is the posterior covariance matrix of the state estimate. Estimate the quantity for the target.

[0014] To achieve the above objectives, the present invention also provides a partially resolvable group target tracking system based on augmented label RFS, comprising: The sensor module is used to acquire a set of measurement points; The measurement processing module is used to judge the set of measurement points, obtain the measurement points of distinguishable and indistinguishable targets, cluster the measurement points of indistinguishable targets, and calculate the centroid as an equivalent measurement. The state estimation module is used to recursively estimate the target state using a GALMB filter to obtain a set of estimated target states; in the update step of the GALMB filter, the target type in the augmented label is updated using the equivalent measurement; The group structure analysis module is used to divide the target estimated state set into group structures and update the group structure of the filter labels to obtain target trajectory, state and group structure information.

[0015] The beneficial effects of this invention are as follows: This invention proposes ALRFS and GALMB filters for partially resolvable group target tracking under a stochastic differential equation model. The structure and type of the group target are incorporated into the label of the Bernoulli RFS. After the radar obtains measurements of the group target, it uses a 3- Criteria and undirected graph theory are used to distinguish between the measurement points, distinguishing between the measurements of distinguishable and indistinguishable targets. The centroid of the indistinguishable target measurement is calculated as the equivalent measurement. In the filter update step, the target type part of the label is updated for the Bernoulli element associated with the equivalent measurement. After filtering, undirected graph theory is used to partition the group structure and update the group target structure part of the label.

[0016] Finally, simulation experiments demonstrate that the algorithm proposed in this invention achieves good tracking results in some distinguishable group target tracking scenarios, and also achieves good results when group targets split, merge, or their distinguishability changes. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a partially resolvable group target tracking method based on augmented label RFS according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the actual motion trajectory of a group of targets according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the tracking trajectory according to an embodiment of the present invention; Figure 4 This is a schematic diagram of potential estimation according to an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the estimation of the number of group targets according to an embodiment of the present invention; Figure 6 This is a schematic diagram illustrating the estimation of the number of distinguishable and indistinguishable group targets according to an embodiment of the present invention. Figure 7 This is a schematic diagram of OSPA error according to an embodiment of the present invention; Figure 8 The target process noise standard deviation in this embodiment of the invention. exist A schematic diagram comparing the OSPA error of the traditional method with the OSPA error of the traditional method under the same conditions; Figure 9 The target process noise standard deviation in this embodiment of the invention. exist A schematic diagram comparing the OSPA error of the traditional method with the OSPA error of the traditional method under the same conditions; Figure 10The target process noise standard deviation in this embodiment of the invention. exist A schematic diagram comparing the OSPA error of the traditional method with the OSPA error of the traditional method under the same conditions. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] like Figure 1 As shown, this embodiment discloses a method for tracking partially distinguishable group targets based on augmented label RFS, including: acquiring a set of measurement points; judging the set of measurement points to obtain measurement points of distinguishable and indistinguishable targets; clustering the measurement points of indistinguishable targets and calculating the centroid as equivalent measurement; using a GALMB filter to recursively estimate the target state to obtain a set of estimated target states; updating the target type in the augmented label using the equivalent measurement in the GALMB filter update step; dividing the target estimated state set into group structures and updating the group structure of the filter label to obtain target trajectory, state, and group structure information.

[0022] Specifically, this embodiment discloses a partially resolvable group target tracking method based on augmented label RFS, including: firstly, using SDE to model the group targets; after the sensor acquires the measurement set, preprocessing the measurements; and then using graph theory and 3- The criteria perform target distinguishability analysis, differentiating between distinguishable and indistinguishable target measurements. The centroid of the indistinguishable group target measurement is calculated as the equivalent measurement and labeled. Furthermore, labels for the RFS (Representational Statistical Set) are constructed using individual target identity information, group target structure, and group target type, forming an ALRFS (Aggregate Statistical Set) with the group target type added to the original ALRFS labels. A GALMB filter is built on this ALRFS, and the preprocessed measurements are fed into the GALMB filter for filtering. In the filter update step, the augmented labels representing target types for elements associated with the equivalent measurement are updated, ensuring that the target type indicated by the label is an indistinguishable group target. After filtering, graph theory is used to partition the posterior state set into group structures, and the augmented labels representing the group structure are updated. More specifically: S1: Use stochastic differential equation models to model the motion state of a group of targets, describing the repulsive and restoring forces between targets within the group; S2: Receives the set of measurement points collected by the sensor, based on 3- Criteria and undirected graph theory for distinguishing between discriminable and indiscriminate targets in measurement points; S3: Cluster the measurement points of indistinguishable targets and calculate their centroids as equivalent measurements; S4: Based on the ALRFS framework, construct an augmented state representation that includes target label, group label, group cardinality, and target type; S5: Use GALMB to recursively estimate the target state, and update the target type label based on the equivalent measurement in the update step; S6: Based on graph theory, partition the estimated target state set into a group structure and update the group structure label; S7: Outputs target trajectory, status, and group structure information.

[0023] In one embodiment, Bayesian recursive filtering is used: The set of states of the target at any given time is The number of targets is Then the set of states of the target is represented as The set of measurements at time is The number of measurements is Then the measurement set is represented as . The multi-objective posterior probability density function at time step is ,but The prior probability density function at time t is: ; The posterior probability density function at time t is: ; in, for Time's up Markov transition density at time t, for The sensor likelihood function at time t. Let be the Dirac measure, representing the integration over a finite set of variables.

[0024] ALRFS: RFS and Labeled Random Finite Set (LRFS). RFS is a set-valued random variable. The elements of the set are unordered and random, and the cardinality of the set is also random. In multi-target tracking, the elements of the set are used to represent the state of a single target, and the cardinality of the set is used to represent the number of targets. In the standard RFS model, the filter output is a multi-target state estimate set without labels, such as the Probability Hypothesis Density (PHD) filter and the Cardinalized Probability Hypothesis Density (CPHD) filter. LRFS adds a label to each element of the set, building upon RFS. In multi-target tracking, the label is used to indicate the identity information of the target state, thereby obtaining the target's trajectory. Building upon LRFS, ALRFS also incorporates group target structure information into the label to expand the target's identity information. However, it currently can only handle the tracking of distinguishable group targets.

[0025] This invention, based on LRFS, adds group target structure and group target type to the tags to form augmented tags. That is, group target type is added to the original ALRFS tags. Such augmented tags are represented as follows: ; in, For the moment of the target's birth, For the index of the target at the current time, For the centroid of the group target, For the index of group targets, It is a marker used to indicate the type of group target.

[0026] If using express Each belongs to its own space. (Note) , indicating the first in the tag The element and the first The space shared by all elements is the tag space. , , , .set up ,but , ,in, This represents the number of elements in RFS.

[0027] Indicates space Towards space The mapping, that is, ; Indicates space Towards space The mapping, for example, ; Indicates space Towards space The mapping, for example, ; Indicates space Towards space The mapping, that is, ; Indicates space Towards space The mapping, that is, In the case of ALRFS, The GALMB filter density at time t is: ; in, for The set of historical correlation mappings before a certain time, i.e. ,and Each Labels representing a set of targets, weights sum function for -GALMB's weight, Since the mapping does not change the number of elements in the RFS, the ALRFS has the same potential distribution as its corresponding LRFS.

[0028] GALMB filter: (Set) The target state space at time t is The tag space is Then the parameter set of the multi-objective posterior probability density function is: ; The label space of the newborn target model at time step is Then the parameter set of the probability density function of the new target model is: ; but The parameter set of the time-prior PHD is: ; ; It is a mapping The set, The time tag space is , Let be the Poisson intensity of the clutter, then the parameter set of the posterior PHD is: ; ; ; ; ; ; ; in, Let be the posterior probability density function. For measurement set, Let be the parameter set of the posterior probability density function. For target tags, For the target label space after the prediction step, for A family of sets consisting of all subsets of . For mapping The set, For indicator functions (when) The value is 1 if it is true, and 0 otherwise. For the tag The state probability density of the Bernoulli component, For a subset of tags and measurement allocation The combined weights, To measure the normalization factor of the likelihood, For tags Corresponding target in measurement allocation The conditional probability density under the following conditions The state of an individual's goals. For prediction step label The prior state probability density corresponding to the target. To measure the likelihood function, The target is in a state The probability of being detected by the sensor at any time. This represents the state probability density when the target is not detected. For space Towards space The mapping, For the tag The corresponding target was observed and measured by the sensor. The probability density, Assign function to measurement label Assigned to measurement set In Measurement The intensity of Poisson clutter. Assign instructions for measurement. Indicates label Assigned to the Individual measurements; This indicates that no measurement has been assigned.

[0029] Group structure estimation and augmented label updating: Group structure estimation is implemented using methods for undirected graphs. Undirected graphs are the most fundamental and intuitive class of graphs in graph theory. An undirected graph... It consists of two sets, namely the non-empty vertex set. and edge set , recorded as .in, A non-empty finite set, denoted as: , represents all vertices of an undirected graph; It is an unordered set of vertices, denoted as: , representing all vertex pairs with an edge. In group target tracking, the vertex set... To represent targets, if the Mahalanobis distance between two targets is short, then an edge is considered to exist between them. All targets within the same graph are considered to form a group of targets. Meanwhile, Used to represent group structure, denoted as ,in, Indicates the first The target is located at the... Within the group objectives.

[0030] set up The target posterior state estimate set output by the time-time filter is: Based on this, a distance matrix is ​​constructed. and adjacency matrix : ; ; ; in, For a given threshold, if the Mahalanobis distance between targets is less than this threshold, then an edge is considered to exist between them. This is based on the adjacency matrix. The group structure can then be obtained. Then update the group structure part of the filter label.

[0031] Target distinguishability analysis: Definitions of distinguishable group targets, indistinguishable group targets, and partially distinguishable group targets. Under the assumption that an individual target generates at most one measurement point, when the distance between the target and the radar is relatively short, or the spatial distribution of targets is relatively sparse, the measurement point generated by each individual target within a group can be detected by one resolution cell of the radar. Such a group of targets is called a distinguishable group target. Conversely, when the distance between the target and the sensor is relatively long, or the spatial distribution of targets is relatively dense, the measurement points generated by multiple individual targets will fall within the same resolution cell of the radar. Such a densely distributed group of targets is called an indistinguishable group target. When distinguishable and indistinguishable group targets coexist or alternate, it is called a partially distinguishable group target.

[0032] When analyzing the distinguishability of a group of targets, the distance to the targets can be used. With radar resolution ratio Perform a judgment. When the ratio is greater than or equal to 1, that is... When the ratio is less than 1, the target is a distinguishable target; when the ratio is less than 1, that is... At that time, the target was indistinguishable. Among them, and They are represented as follows: ; ; In the formula, Indicates the radar's detection range. Indicates beamwidth (where This is the radar antenna aperture value. The wavelength of the electromagnetic waves radiated by the radar antenna. (where the constant is) This represents the standard deviation of the measurement noise in the area where the target is located. Equation (21) is also called the standard distance of a group of targets, or 3- Distance rule: When the distance between two targets is less than... If the value is greater than 0, it is an indistinguishable group target; otherwise, it is greater than 0. The target is a distinguishable group of targets.

[0033] As the relative position between the target and the radar changes, the measurement noise covariance matrix also changes. Let the radar's inherent measurement noise covariance matrix be... , Momentary Goal The covariance matrix of the measurement noise at the measurement location is: ,but: ; ; ; ; ; in, and The target and radar exist direction and directional deviation, It is a constant matrix. , It is a constant. For the goal exist The position of direction, For the goal exist velocity in direction, For the goal exist The position of direction, For the goal exist velocity in direction, It is the transpose symbol. For radar exist The position of direction, For radar exist velocity in direction, For radar exist The position of direction, For radar exist velocity in direction, , If it is a constant, then the target The measurement corresponding for: ; This invention is achieved through 3- A method combining criteria and graph theory is used to determine the discriminability of a target. If... The measurement set obtained by the time sensor is First, construct a distance matrix for the measurement points: ; Next, use 3- The distance rule calculates the corresponding distance for each measurement point. and construct 3- matrix: ; in, ; Then, through the distance matrix and 3- Matrix construction of adjacency matrix ,like Representation matrix No. Line 1 The elements of the column, then: ; In an adjacency matrix, measurement points located within the same connected component can be considered as measurements of indistinguishable targets; independent measurement points are considered as measurements of distinguishable targets. For measurements of indistinguishable targets, the centroid of the measurement needs to be calculated as the equivalent measurement. If the measurement of an indistinguishable target is: The method for calculating the centroid is as follows: ; in, For equivalent measurement of indistinguishable targets, The quantity measured for this indistinguishable target. For measurement index, For the measurement of this indistinguishable target.

[0034] A measurement label is set for the equivalent measurement. In the filter update step, the posterior state updated by the equivalent measurement is regarded as the state of the indistinguishable target, and the target type part in the label is updated at the same time.

[0035] Stochastic differential equation modeling: When modeling the motion of a group of targets, it is necessary to consider the motion coupling between individual targets within the group. Stochastic differential equations use the repulsive and restoring forces between individual targets and the centroid of the group to describe the interactions between targets. When a target is far from the centroid, the restoring force it experiences is greater than the repulsive force, causing its trajectory to move closer to the centroid; conversely, the trajectory moves away from the centroid.

[0036] The stochastic differential equation model for single-objective motion is: ; in, The location of the centroid of the group target. The velocity of the centroid of the group of targets, parameters , , Indicates the strength of the restoring force. It represents the repulsive force experienced by an individual.

[0037] The joint stochastic differential equation for the group objective is expressed as: ; The joint state vector of the group objectives is: ; in, for Momentary Goal exist The position of direction, for Momentary Goal exist velocity in direction, for Momentary Goal exist The position of direction, for Momentary Goal exist Velocity in a certain direction.

[0038] The joint repulsive force vector is: ; in, For constants It is a process variable.

[0039] The joint vector of Brownian motion of individual targets in a group of targets is: ; in, for Momentary Goal exist Brownian motion in direction for Momentary Goal exist Brownian motion in a certain direction.

[0040] The Brownian motion covariance matrix of the individual target is: ; in, , for direction and Variance of direction.

[0041] The joint vector of the Brownian motion of the group of targets is: ; in, , For the group target in and The joint vector of Brownian motion in the direction.

[0042] The Brownian motion covariance matrix of the group of targets is: ; in, Let V be the variance of Brownian motion.

[0043] The following describes how to model a swarm objective using stochastic differential equations. Based on the stochastic differential equation model, the state transition equation for the swarm objective is: ; in, For the Markov transition density of the group's objective state, It is a Gaussian function. For process variables, For process variables, For the measurement matrix, Let be the covariance matrix.

[0044] Here is the state transition matrix: ; in, ; ; ; ; in, It is a constant matrix. For the filter period, , , , It is a constant. The target number in the subgroup.

[0045] The repulsive force control matrix is: ; in, The lower limit of integration, For time, The filter period is 1.

[0046] The process noise covariance matrix is: ; in, , It is a process variable.

[0047] Under the motion coupling among group members, the individual target state prediction equation and covariance prediction equation are: ; ; in, For the goal The centroid of the group to which one belongs The covariance matrix of the centroid is calculated as follows: ; ; The matrices in formulas (45) and (46) and The matrix in formula (38) can be used to solve the problem. The calculation shows that: ; The matrices in formulas (45) and (46) , The calculation method is as follows: ; ; in, For the first Individual group goals For the goal The prior state, For the goal The prior covariance matrix, for The partial derivatives, for The first derivative, for The partial derivatives, for The partial derivatives of .

[0048] This embodiment also discloses a partially resolvable group target tracking system based on augmented label RFS, including: The sensor module is used to acquire a set of measurement points; The measurement processing module is used to judge the set of measurement points, obtain the measurement points of distinguishable and indistinguishable targets, cluster the measurement points of indistinguishable targets, and calculate the centroid as the equivalent measurement. The state estimation module is used to recursively estimate the target state using a GALMB filter to obtain a set of estimated target states; in the update step of the GALMB filter, the target type in the augmented label is updated using equivalent measurements. The group structure analysis module is used to divide the target estimated state set into group structures and update the group structure of the filter labels to obtain target trajectory, state and group structure information.

[0049] like Figure 2As shown, the actual trajectory of the group of targets is indicated by the small circles in the figure. ) indicates the target's birth location, triangle ( The area indicated by ) represents the location where the target disappears, and the solid dot represents the radar position (1000, 0). The movement of the target group is divided into three stages: Stage 1 (1s to 40s) contains four distinguishable targets. Target 1 and Target 2 form Target Group 1, and Target 3 and Target 4 form Target Group 2. Both groups are distinguishable and gradually move closer together, eventually overlapping and merging into one target group. Stage 2 (41s to 70s) contains four targets, which have merged into an indistinguishable target group. Stage 3 (71s to 100s) contains four targets, which split into two distinguishable target groups and move away from each other. Target 1 and Target 2 form Target Group 1, and Target 3 and Target 4 form Target Group 2. Because the distinguishability of the targets changes in the three stages, the number of targets is 4 and the number of target groups is 2 in both Stage 1 and Stage 3; in Stage 2, the number of centroids of the indistinguishable target groups is 1, and the number of target groups is 1.

[0050] like Figure 3 As shown, in the group target tracking trajectory, in stage one, there are two distinguishable group targets in the state space, each consisting of four distinguishable individual targets, and all four individual targets are tracked by the filter. In stage two, there are four individual targets in the state space, which together form an indistinguishable group target. According to the algorithm principle described in this invention, the filter needs to track the centroid of this indistinguishable group target, corresponding to... Figure 3 There is a tracking trajectory in the process; in stage three, the indistinguishable group target splits into four distinguishable individual targets, which form a distinguishable group target in pairs, and all four individual targets are tracked by the filter.

[0051] like Figure 4-5 As shown, the potential estimation and group target potential estimation results are good. The potential estimation and the potential estimation of both types of group targets are effective. There may be a small amount of error only when the group targets split, merge or the group target type changes, and the error can be eliminated quickly.

[0052] like Figure 6 As shown, the OSPA error in the three stages is small, and the error in each stage shows a convergence trend.

[0053] like Figure 7-10 As shown, the Monte Carlo simulation results show that the standard deviations of the noise in the target process are respectively... , , In this case, an OSPA comparison experiment was conducted between the GALMB and GLMB filters, performing 500 Monte Carlo simulations. Since the process noise covariance of individual targets directly affects the joint process noise covariance of the group targets in the SDE model, and the GLMB filter does not adequately model the internal motion of the group targets, the tracking error of the GLMB filter is significantly higher than that of the GALMB filter. Furthermore, the larger the process noise covariance, the worse the tracking performance of the GLMB filter, potentially even leading to divergence. When the process noise covariance is small, the GLMB filter can achieve stable tracking. The GALMB filter, on the other hand, maintains stable tracking performance in all three cases, with consistently smaller OSPA errors, and the OSPA errors converge across all three stages. The OSPA simulation curves of the two filters at time [time value missing] are shown below. and Two peaks appeared over a period of time afterward. This was because the group of targets split or merged, and there was a mutual transformation between distinguishable and indistinguishable group targets, which led to an increase in tracking error.

[0054] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for tracking partially resolvable group targets based on augmented label RFS, characterized in that, include: Obtain a set of measurement points, and determine the measurement points of distinguishable and indistinguishable targets. Cluster the measurement points of the indistinguishable targets and calculate the centroid as the equivalent measurement; The target state is recursively estimated using a GALMB filter to obtain a set of estimated target states; in the update step of the GALMB filter, the target type in the augmented label is updated by the Bernoulli element obtained from the update of the equivalent measurement. The target estimated state set is divided into groups, and the group structure of the filter labels is updated to obtain target trajectory, state and group structure information.

2. The partially resolvable group target tracking method based on augmented label RFS according to claim 1, characterized in that, Obtaining the measurement points for the distinguishable and indistinguishable targets includes: Using the set of measurement points, a first distance matrix is ​​constructed, and based on 3- The distance rule is used to calculate the standard deviation of the measurement noise in the radar field of view corresponding to each measurement point, and a 3- matrix; Through the first distance matrix and the 3- Construct a first adjacency matrix. If a group of measurement points located in the same connected component appears in the first adjacency matrix, then the group of measurement points is regarded as an indistinguishable target. If an independent measurement point appears in the first adjacency matrix, then the measurement point is regarded as a distinguishable target.

3. The partially resolvable group target tracking method based on augmented label RFS according to claim 1, characterized in that, Calculating the centroid includes: ； in, For equivalent measurement of indistinguishable targets, The quantity measured for this indistinguishable target. For measurement index, For the measurement of this indistinguishable target.

4. The partially resolvable group target tracking method based on augmented label RFS according to claim 1, characterized in that, The target state includes: The state transitions of the group of targets are determined by using the stochastic differential module of single-target motion and the joint stochastic differential model of group targets: ； in, For the Markov transition density of the group's objective state, The repulsive force control matrix, for The set of states of the target within the subgroup at time step. for The set of states of the target within the subgroup at time step. Let be the subgroup state transition matrix. Let the vector be the joint repulsive force vector of the subgroups. This refers to the noise in the joint process of subgroup objectives.

5. The partially resolvable group target tracking method based on augmented label RFS according to claim 1, characterized in that, The prediction steps of the GALMB filter include: ； ； ； ； in, For multi-objective prior probability density functions, for The parameter set of the target still exists at all times. For survival target tags The prior existence probability of the corresponding target. Let this be the prior probability density of the target. Let be the parameter set of the probability density function of the newborn target. Tags for freshmen goals The prior existence probability of the corresponding target. Let this be the prior probability density of the target. Predictive step augmentation tags The probability of the existence of the corresponding Bernoulli component. To broaden labels after prediction steps The state probability density corresponding to the Bernoulli component. The prior probability density normalization factor, for Moment Tags The corresponding target is The probability density of time that still exists. For tags The Markov transition density corresponding to the target state, For tags The corresponding target is The posterior probability density at time t; The update steps include: ； ； ； ； ； ； ； in, Let be the posterior probability density function. For measurement set, Let be the parameter set of the posterior probability density function. For target tags, For the target label space after the prediction step, for A family of sets consisting of all subsets of . For mapping The set, For indicator functions, when The value is 1 if it is true, and 0 otherwise. For the tag The state probability density of the Bernoulli component, For a subset of tags and measurement allocation The combined weights, To measure the normalization factor of the likelihood, For tags Corresponding target in measurement allocation The conditional probability density under the following conditions The state of an individual's goals. For prediction step label The prior state probability density corresponding to the target. To measure the likelihood function, The target is in a state The probability of being detected by the sensor at any time. This represents the state probability density when the target is not detected. For space Towards space The mapping, For the tag The corresponding target was observed and measured by the sensor. The probability density, Assign function to measurement label Assigned to measurement set In Measurement The intensity of Poisson clutter. Assign instructions for measurement. Indicates label Assigned to the Individual measurements; This indicates that no measurement has been assigned.

6. The partially resolvable group target tracking method based on augmented label RFS according to claim 1, characterized in that, The augmentation tags include: ； in, For the moment of the target's birth, For the index of the target at the current time, For the centroid of the group target, For the index of group targets, It is a marker used to indicate the type of group objective. For the group target index space, For the target type space, To broaden the label, To broaden the individual identity attributes of the target in the tag, To broaden the group identity attributes of the target in the tag.

7. The partially resolvable group target tracking method based on augmented label RFS according to claim 1, characterized in that, The group structure partitioning of the target estimated state set includes: Based on the target estimated state set, construct the second distance matrix and the second adjacency matrix; Set a target threshold. When the Mahalanobis distance between targets in the second distance matrix is ​​less than the target threshold, it proves that there is an edge between the targets. Then, the second adjacency matrix is ​​used to partition the group structure.

8. The partially resolvable group target tracking method based on augmented label RFS according to claim 7, characterized in that, Constructing the second distance matrix includes: ； ； in, This is the second distance matrix. For the target posterior state and Mahalanobis distance, It is the identity matrix. Here is the posterior covariance matrix of the state estimate. Estimate the quantity for the target.

9. A partially resolvable group target tracking system based on augmented label RFS implemented according to any one of claims 1-8, characterized in that, include: The sensor module is used to acquire a set of measurement points; The measurement processing module is used to judge the set of measurement points, obtain the measurement points of distinguishable and indistinguishable targets, cluster the measurement points of indistinguishable targets, and calculate the centroid as an equivalent measurement. The state estimation module is used to recursively estimate the target state using a GALMB filter to obtain a set of estimated target states. In the update step of the GALMB filter, the target type in the augmented label is updated using the equivalent measurement; The group structure analysis module is used to divide the target estimated state set into group structures and update the group structure of the filter labels to obtain target trajectory, state and group structure information.

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