A time-varying formation tracking control method and system for multi-sensor multi-target filtering

Abstract

This invention discloses a time-varying formation tracking control method and system based on multi-sensor multi-target filtering, relating to the field of multi-agent formation tracking. The method includes acquiring the communication topology between multiple agents, multiple targets, and multiple sensors; each agent carrying a sensor; establishing the state equations of all targets, the sensor observation models of all targets, and the state equations of each agent; based on the communication topology, the state equations of all targets, and the sensor observation models of the targets, using a filtering algorithm based on capacitive Kalman filtering to obtain the final state estimate and final error covariance of each target; and determining the time-varying formation control protocol for each agent based on the state equations of each agent and the final state estimate of each target. This invention achieves formation tracking of multiple non-cooperative targets by multiple agents.

Description

Technical Field

[0001] This invention relates to the field of multi-agent formation tracking technology, and in particular to a time-varying formation tracking control method and system with multi-sensor multi-target filtering. Background Technology

[0002] In recent years, formation tracking has attracted widespread attention and played an important role in both military and civilian fields. Formation tracking mainly utilizes information exchange between intelligent agents and the target's state to design control protocols, enabling the agents to track the target and maintain an ideal formation, where the formation is determined by a formation reference.

[0003] Multi-agent formation tracking of multiple targets is a hot topic in the field of formation tracking. XW Dong studied the average formation tracking problem for multiple targets, that is, the average state of all targets can be tracked by the agents in formation. He further proposed the necessary and sufficient conditions for multi-agents to achieve time-varying formation tracking of multiple targets, and the designed control protocol can be further applied to higher-order systems. JYHu proposed a control protocol for distributed time-varying formation tracking and considered the fully adaptive time-varying formation tracking problem with random noise in the states of multiple targets, and analyzed the stability and performance of the algorithm.

[0004] Compared to centralized filtering, distributed multi-sensor multi-target filtering offers advantages such as real-time performance, fault tolerance, and scalability. It can be categorized into two methods: data association (DA) and random finite set (RFS). Distributed filtering using RFS is computationally fast, but its theoretical research is still incomplete. After associating data using the DA method, distributed filtering of nonlinear systems can be performed using extended Kalman filtering (EKF), unscented Kalman filtering (UKF), and capacitive Kalman filtering (CKF). Since the weights of each capacitive point in the CKF method are identical and positive, the CKF method exhibits better stability than the UKF method. However, compared to the CKF method, the EKF method has lower accuracy when handling second-order nonlinear systems; therefore, the CKF method is widely used in nonlinear filtering algorithms.

[0005] However, in most real-world scenarios, the target's state is unknown, meaning the target is non-cooperative. Previous work by L Tian considered time-varying formation tracking problems where both the agent and the target experience unknown disturbances. Y Zhang combined multi-target filtering with the formation tracking problem, proposing a formation tracking control protocol for heterogeneous second-order systems, but neither of them considered the case of nonlinear observation models. Summary of the Invention

[0006] The purpose of this invention is to provide a time-varying formation tracking control method and system with multi-sensor multi-target filtering, which realizes formation tracking of multiple non-cooperative targets by multiple agents.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A time-varying formation tracking control method with multi-sensor and multi-target filtering includes:

[0009] The communication topology between multiple agents, multiple targets, and multiple sensors is acquired; each agent carries a sensor.

[0010] Establish the state equations for all targets, the sensor observation models for all targets, and the state equations for each agent;

[0011] Based on the communication topology, the state equations of all targets, and the sensor observation models of the targets, a distributed multi-sensor multi-target filtering method is designed based on capacitive Kalman filtering to obtain the final state estimate of each target.

[0012] The time-varying formation control protocol for each agent is determined based on the state equations of each agent and the final state estimates of each target.

[0013] Optionally, the sensor includes a radar sensor and an infrared sensor.

[0014] Optionally, the state equations for all the targets are expressed as:

[0015] Where, x k Let x represent the state of all targets at time k. k-1 This represents the state of all targets at time k-1. w represents the state transition matrix for all objectives. k-1 This indicates process noise.

[0016] Optionally, the sensor's observation model for all targets can be represented as:

[0017] in, Let h represent the observation model of sensor i for all targets at time k. i (x k ) represents the measurement function. This represents the measurement noise at time k;

[0018]

[0019]

[0020] Indicates about xk,s A continuously differentiable measurement function, x k,s Let represent the state of target s at time k, where s ranges from M+1 to N, M represents the number of agents, and NM represents the number of targets. This represents the relative distance between target s and sensor i at time k. This represents the relative angle between target s and sensor i at time k. This represents the distance measurement covariance between target s and sensor i at time k. This represents the covariance of the angle measurement noise between target s and sensor i at time k. This represents the relative distance between target s and sensor i′ at time k. Let represent the distance measurement covariance between target s and sensor i′ at time k. Sensor i and sensor i′ are located on the same agent. Sensor i is an infrared sensor, and sensor i′ is a radar sensor. Let D1 represent the set of radar sensors and D2 represent the set of infrared sensors.

[0021] Alternatively, the state equation of the agent can be expressed as:

[0022] in, This represents the state of agent c at time k. Let B represent the state of agent c at time k-1, Φ represent the state transition matrix of the agent, and B∈R. n×r Let r represent a matrix of rank r. This represents the time-varying formation control protocol for agent c.

[0023] Optionally, based on the communication topology, the state equations of all targets, and the sensor observation models of the targets, a distributed multi-sensor multi-target filtering method is designed based on capacitive Kalman filtering to obtain the final state estimate of each target, specifically including:

[0024] When the iteration number l = 0, Initialize to Initialize to This represents the state estimate of sensor i for all targets after l iterations at time k. Let represent the error covariance matrix of sensor i for all targets after l iterations at time k;

[0025] Through formula and Performing the l-th iteration, we obtain and The sensor at time k is obtained after L iterations. Obtain state estimates for all targets. and Consistent, all are And error covariance and Consistent, both are P k ;Will As the final state estimate, P k As the final error covariance;

[0026] Among them, w ii w represents the element in the i-th row and j-th column of the second weighted adjacency matrix. ij This represents the element in the i-th row and j-th column of the second weighted adjacency matrix, which is the weighted adjacency matrix of the directed graph formed by the sensors.

[0027] Wherein, the state estimates of sensor i for all targets at time k. And error covariance matrix The calculation process includes the following steps:

[0028] Initialization: At time k=0, for each sensor i, initialize the state estimate of sensor i for all targets. And error covariance matrix

[0029] According to the formula Calculate volume points

[0030] according to Get the spread

[0031] according to Determine the prior state estimate and prior estimate error covariance

[0032] According to the formula For volume point Update to obtain volume points

[0033] Based on volume points The predicted measurement value was calculated. Error covariance matrix Error covariance matrix

[0034] Based on the error covariance matrix And error covariance matrix Calculate the filter gain

[0035] Based on the measurements of all targets by sensor i at time k Filter gain Predicted measurement value Prior estimation error covariance And error covariance matrix The state estimates of sensor i for all targets at time k are calculated. And error covariance matrix

[0036] Optionally, the time-varying formation control protocol for intelligent agents is represented as:

[0037]

[0038] in, This represents the time-varying formation control protocol for agent c, where K is a constant gain matrix and π is the number of agents. cj This represents the element in the c-th row and j-th column of the first weighted adjacency matrix, π. cs Let represent the element in the c-th row and s-th column of the first weighted adjacency matrix. The first weighted adjacency matrix is ​​the weighted adjacency matrix in the directed graph composed of the agent and the target. This represents the state of agent c at time k-1. For agent c and the formation reference at time k-1 The relative states between them For agent j and the formation reference at time k-1 The relative states between them Let α be a convex combination of targets tracked by the agent formation at time k-1. s ,s∈V2 is satisfied V2 represents the target set, which is a positive constant. The formation tracking compensation signal for agent c at time k-1. This represents the final state of target s at time k-1.

[0039] This invention also discloses a time-varying formation tracking control system with multi-sensor multi-target filtering, comprising:

[0040] The communication topology determination module is used to obtain the communication topology relationships between multiple agents, multiple targets, and multiple sensors; each agent carries a sensor.

[0041] The state equation and observation model establishment module is used to establish the state equations of all targets, the sensor observation models of all targets, and the state equations of each agent.

[0042] The final state estimate and final error covariance determination module of the target is used to design a distributed multi-sensor multi-target filtering method based on the communication topology, the state equations of all targets and the sensor observation model of the target, to obtain the final state estimate of each target.

[0043] The agent time-varying formation control protocol determination module is used to determine the time-varying formation control protocol of each agent based on the state equation of each agent and the final state estimate of each target.

[0044] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0045] This invention discloses a time-varying formation tracking control method and system based on multi-sensor multi-target filtering. Based on communication topology, the state equations of all targets, and the sensor observation models of the targets, a distributed multi-sensor multi-target filtering method is designed based on capacitive Kalman filtering to obtain the final state estimates of each target. A time-varying formation control protocol for each agent is determined according to its state equation and the final state estimates of each target. Based on the time-varying formation control protocol of each agent, formation tracking of multiple non-cooperative targets by multiple agents is achieved. The sensors and agents are distributed, meaning that individual sensors and agents only utilize information from their neighbors, exhibiting good scalability and self-organization, enabling distributed operation and improving computational and information utilization efficiency. Attached Figure Description

[0046] 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.

[0047] Figure 1 This is a schematic diagram of the time-varying formation tracking control method with multi-sensor multi-target filtering according to the present invention;

[0048] Figure 2 This is a schematic diagram of the states of each target provided in the embodiments of the present invention;

[0049] Figure 3 This is a schematic diagram of the directed communication topology between an agent and a target provided in an embodiment of the present invention;

[0050] Figure 4 This is a schematic diagram illustrating the state estimation error of a target by a sensor on an intelligent agent, provided in an embodiment of the present invention.

[0051] Figure 5This is a schematic diagram illustrating the formation tracking error of each agent towards multiple targets, provided in an embodiment of the present invention.

[0052] Figure 6 The states of multiple agents and multiple targets at time t = 20s are provided in the embodiments of the present invention;

[0053] Figure 7 The states of multiple agents and multiple targets at time t = 40s are provided in the embodiments of the present invention;

[0054] Figure 8 The states of multiple agents and multiple targets at time t = 60s are provided in the embodiments of the present invention;

[0055] Figure 9 The states of multiple agents and multiple targets at time t = 80s are provided in the embodiments of the present invention;

[0056] Figure 10 This is a schematic diagram of the structure of a time-varying formation tracking control system with multi-sensor multi-target filtering according to the present invention. Detailed Implementation

[0057] 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.

[0058] The purpose of this invention is to provide a time-varying formation tracking control method and system with multi-sensor multi-target filtering, which realizes formation tracking of multiple non-cooperative targets by multiple agents.

[0059] 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.

[0060] like Figure 1 As shown, the time-varying formation tracking control method with multi-sensor multi-target filtering of the present invention includes the following steps.

[0061] Step 101: Obtain the communication topology between multiple agents, multiple targets, and multiple sensors; each agent carries a sensor.

[0062] The sensors include radar sensors and infrared sensors.

[0063] The topological structure of the interactions between agents, targets, and sensor systems can be described by two graphs G1 = (V, ε, Π) and G2 = (D, χ, W), where V and D represent the sets of all agent, target, and sensor nodes, ε ∈ V × V and χ ∈ D × D are the edge sets of the system, and Π and W are the weighted adjacency matrices of the system, with Π denoted as the first weighted adjacency matrix and W denoted as the second weighted adjacency matrix. A directed edge (j, i) ∈ ε or (j, i) ∈ χ means that node i can receive data from node j. In this case, node j is called an inner neighbor node of node i, and the set of inner neighbors of node i is N. i It can be represented as N i ={j:(j,i)∈εor(j,i)∈χ}, Ν i The number of nodes in the middle is |N i |

[0064] Assume the system contains M agents, NM targets, M radar sensors, and M1 infrared sensors, where M ≥ M1. V1 = {1, ..., M} represents the set of agents, V2 = {M+1, ..., N} represents the set of targets, and V = V1 ∪ V2. D1 = {1, ..., M} and D2 = {M+1, ..., M+M1} represent the sets of radar sensors and infrared sensors, respectively, and D = D1 ∪ D2.

[0065] Define Π = [π] ij ] N×N For element π ij A weighted adjacency matrix where all elements are non-negative, π ij The communication weight of the directed edge (j,i), j,i∈V, is given by formula (1).

[0066]

[0067] Among them, b j and a ij Here, we can take 1 for all values.

[0068] Step 102: Establish the state equations for all targets, the sensor observation models for all targets, and the state equations for each agent.

[0069] The state equation of the target s (s∈V2) can be expressed as:

[0070] x k,s =Φ s x k-1,s +w k-1,s (2)

[0071] Where, x k,s ∈R n Let n be the state of target s at time k, and let n be x. k,s Dimensions. Φs =Φ∈R n×n Let w be the state transition matrix. k-1,s ∈R n With a mean of 0 and a covariance matrix of R k-1,s Process noise. Define x k =[(x k,M+1 ) T ,...,(x k,N ) T ] T Let K be the state of all targets at time k. Then the state equations of all targets can be expressed as:

[0072]

[0073] in, Let w be the state transition matrix. k-1 =[(w k-1,M+1 ) T ,...,(w k-1,N ) T ] T With a mean of 0 and a covariance matrix of R k-1 =diag{R k-1,M+1 ,...,R k-1,N Process noise.

[0074] Assume all sensors are located on M agents, each agent carrying one radar sensor and one or zero infrared sensors. The observation model of sensor i (i∈D) on target s at time k is as follows:

[0075]

[0076] in, Let be the measurement value of sensor i (i∈D) on target s. For a question about x k,s A continuously differentiable measurement function, With a mean of 0, the covariance matrix is Measurement noise. Among them,

[0077]

[0078] in, and Let be the relative distance and relative angle between target s and sensor i at time k, respectively. and Let be the covariances of the distance and angle measurement noise of sensor i to target s at time k. Let i′ be the radar sensor located on the same agent as infrared sensor i. and Let be the relative distance between target s and sensor i′ at time k, and be the distance measurement covariance, respectively.

[0079] make Let x be the measurement value of sensor i (i∈D) for all targets at time k. Then, the measurement value of sensor i for all targets x k =[(x k,M+1 ) T ,...,(x k,N ) T ] T The observation model can be expressed as:

[0080]

[0081] in, For measurement functions, With a mean of 0, the covariance matrix is Measurement noise.

[0082] The mean is 0, and the covariance matrix is Measurement noise.

[0083] The state equation of agent c, c∈V1 at time k can be expressed as:

[0084]

[0085] in, Let B be the state of agent c at time k, where B∈R n×r Let r be a matrix. A time-varying formation control protocol for agent c.

[0086] Step 103: Based on the communication topology, the state equations of all targets, and the sensor observation models of the targets, design a distributed multi-sensor multi-target filtering method based on capacitive Kalman filtering to obtain the final state estimate of each target.

[0087] 1: Initialization

[0088] At k = 0, for each sensor i (i ∈ D), the state estimate of i (i ∈ D) for all targets is initialized according to formulas (8) and (9). And error covariance matrix

[0089]

[0090]

[0091] 2. Prediction Step

[0092] Calculate the volume point according to formula (10).

[0093]

[0094] in, and Let e ​​represent the state estimate and error covariance matrix of sensor i (i∈D) for all targets at time k-1, respectively. e = 1,...,2n. For ξ s The e-th element, ξ s The values ​​are shown in formula (11).

[0095]

[0096] Using formula (12) to determine the volume point Further predictions are made to obtain the propagation through the measurement equation.

[0097]

[0098] The prior state estimate can be obtained using formulas (13) and (14). and prior estimate error covariance

[0099]

[0100]

[0101]

[0102] in, This represents the covariance matrix among the state estimates of all targets. Let M+1 be the covariance matrix of the target M+1.

[0103] 3. Update Steps

[0104] A new set of volume points is obtained by using the volume points obtained from the prediction step and formula (15).

[0105]

[0106] The predicted measurement value can be calculated using formulas (16), (17), and (18). And error covariance matrix

[0107]

[0108]

[0109]

[0110] in, This represents the covariance matrix among all targets.

[0111] Calculate the filter gain using formula (19)

[0112]

[0113] Combine the measurements of all targets by sensor i at time k. Filter gain Predicted measurement value Prior estimation error covariance Error covariance matrix The state estimates of sensor i for all targets at time k can be calculated using formulas (20) and (21). And error covariance matrix

[0114]

[0115]

[0116] 4. Consistent Iteration

[0117] The element w in the i-th row and j-th column of the sensor's communication topology W ij The values ​​are shown in formula (22).

[0118]

[0119] Let l (l=1,...,L) be the iteration number of the l-th iteration, where L is greater than the radius of the sensor communication topology. Assume... and Let be the state estimates and error covariance matrix of sensor i for all targets after l iterations at time k. When l = 0, and Initialize to Formulas (23) and (24) can be used to obtain the result after l iterations. and

[0120]

[0121]

[0122] After a total of L iterations, the sensor at time k... Obtain state estimates for all targets. and error covariance To reach a consensus, all are and P k ,in, P k =diag(P k,M+1 ,...,P k,N ), and P k,s These are the final state estimate and error covariance of the target s (s∈V2), respectively.

[0123] Step 104: Determine the time-varying formation control protocol for each agent based on the state equations of each agent and the final state estimates of each target.

[0124] Based on the time-varying formation control protocol of each agent, the formation tracking of multiple non-cooperative targets by multiple agents is realized.

[0125] Based on step 103 P k,s , s(s∈V2), calculate the time-varying formation control protocol in the state equation (7) of agent c. As shown in formula (25).

[0126]

[0127] in, This represents the time-varying formation control protocol for agent c, where K is a constant gain matrix and π is the number of agents. cj This represents the element in the c-th row and j-th column of the first weighted adjacency matrix, π. cs Let represent the element in the c-th row and s-th column of the first weighted adjacency matrix. The first weighted adjacency matrix is ​​the weighted adjacency matrix in the directed graph composed of the agent and the target. This represents the state of agent c at time k-1. For agent c and the formation reference at time k-1 The relative states between them For agent j and the formation reference at time k-1 The relative states between them Let α be a convex combination of targets tracked by the agent formation at time k-1. s ,s∈V2 is satisfied V2 represents the target set, which is a positive constant. The formation tracking compensation signal for agent c at time k-1. This represents the final state of target s at time k-1.

[0128] To meet The matrix.

[0129] In a specific implementation, the initial positions of 10 agents c = 1, 2, ..., 10 are all [-150; -150; 10; 10]. The state equation of the agents is formula (7), where, Each agent carries one radar sensor and one or zero infrared sensors. The state equations for the three targets are given by equation (2), where R... k-1,s =0.05I4, T=1 is the sensor sampling time, The sensor's observation model is given by formula (4). At time k∈[1,100], the target's state is as follows: Figure 2 As shown, target1 represents target 1, target2 represents target 2, and target3 represents target 3.

[0130] The directed communication topology between the agent and the target is as follows: Figure 3 As shown, circles represent agents, and triangles represent targets. The error in the state estimation of the target by the sensors on the agent represents this. like Figure 4 As shown, Figure 4 The horizontal axis represents time, and the vertical axis represents the state estimation error. The formation tracking error of each agent for multiple targets is... like Figure 5 As shown, Figure 5 The horizontal axis represents time, and the vertical axis represents the formation tracking error. Figures 6-9 The states of multiple agents and multiple objectives are defined at times t = 20s, 40s, 60s, and 80s. (Integration) Figures 6-9 Changes in motion trajectory and Figure 4 , Figure 5 The error variation shows that the multi-agent system can estimate the state of multiple non-cooperative targets and perform formation tracking of multiple targets. This example verifies the effectiveness of the proposed method.

[0131] According to specific embodiments provided by the present invention, the following technical achievements are disclosed: The present invention proposes a distributed multi-sensor multi-target filtering method. Based on the assumption that the agent carries sensors and all targets can be measured by each sensor, the results after associating target measurements and target trajectories using the DA method are studied. Furthermore, based on the state estimates of multiple targets obtained by the distributed multi-sensor multi-target filtering method, a time-varying formation tracking control protocol is proposed to achieve time-varying formation tracking of multiple non-cooperative targets by multiple agents. The main advantages are as follows: 1) The present invention proposes a distributed multi-sensor multi-target filtering method to estimate the state of multiple targets. 2) Based on the state estimates obtained by filtering, a time-varying formation tracking control protocol is proposed to achieve formation tracking of multiple non-cooperative targets by multiple agents. 3) The designed sensor and agent system are all distributed, meaning that individual sensors and agents only utilize information from their neighbors. It has good scalability and self-organization, can operate in a distributed manner, and improves computational and information utilization efficiency.

[0132] Figure 10 This is a schematic diagram of the structure of a time-varying formation tracking control system with multi-sensor multi-target filtering according to the present invention, as shown below. Figure 10 As shown, a time-varying formation tracking control system with multi-sensor multi-target filtering includes:

[0133] The communication topology determination module 201 is used to obtain the communication topology relationship between multiple intelligent agents, multiple targets and multiple sensors; each intelligent agent carries a sensor.

[0134] The state equation and observation model establishment module 202 is used to establish the state equations of all targets, the sensor observation models of all targets, and the state equations of each agent.

[0135] The final state estimate and final error covariance determination module 203 is used to design a distributed multi-sensor multi-target filtering method based on the communication topology, the state equations of all targets and the sensor's observation model of the targets, to obtain the final state estimate of each target.

[0136] The agent time-varying formation control protocol determination module 204 is used to determine the time-varying formation control protocol of each agent based on the state equation of each agent and the final state estimate of each target.

[0137] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0138] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A time-varying formation tracking control method with multi-sensor multi-target filtering, characterized in that, include: The communication topology between multiple agents, multiple targets, and multiple sensors is acquired; each agent carries a sensor. Establish the state equations for all targets, the sensor observation models for all targets, and the state equations for each agent; Based on the communication topology, the state equations of all targets, and the sensor observation models of the targets, a distributed multi-sensor multi-target filtering method is designed based on capacitive Kalman filtering to obtain the final state estimate of each target. The time-varying formation control protocol for each agent is determined based on the state equations of each agent and the final state estimates of each target. The time-varying formation control protocol for intelligent agents is represented as follows: in, This represents the time-varying formation control protocol for agent c, where K is a constant gain matrix and π is the number of agents. cj This represents the element in the c-th row and j-th column of the first weighted adjacency matrix, π. cs Let represent the element in the c-th row and s-th column of the first weighted adjacency matrix. The first weighted adjacency matrix is ​​the weighted adjacency matrix in the directed graph composed of the agent and the target. This represents the state of agent c at time k-1. For agent c and the formation reference at time k-1 The relative states between them For agent j and the formation reference at time k-1 The relative states between them Let α be a convex combination of targets tracked by the agent formation at time k-1. s To meet The positive constant s ∈ V2, where V2 represents the target set. The formation tracking compensation signal for agent c at time k-1. Let M represent the final state of target s at time k-1; M represents the number of agents; and NM represents the number of targets.

2. The time-varying formation tracking control method with multi-sensor multi-target filtering according to claim 1, characterized in that, The sensors include radar sensors and infrared sensors.

3. The time-varying formation tracking control method with multi-sensor multi-target filtering according to claim 2, characterized in that, The state equations for all the targets are expressed as follows: Where, x k Let x represent the state of all targets at time k. k-1 This represents the state of all targets at time k-1. w represents the state transition matrix for all objectives. k-1 This indicates process noise.

4. The time-varying formation tracking control method with multi-sensor multi-target filtering according to claim 3, characterized in that, The sensor's observation model for all targets is represented as follows: in, Let h represent the observation model of sensor i for all targets at time k. i (x k ) represents the measurement function. This represents the measurement noise at time k; Indicates about x k,s A continuously differentiable measurement function, x k,s This represents the state of target s at time k, where s ranges from M+1 to N. This represents the relative distance between target s and sensor i at time k. This represents the relative angle between target s and sensor i at time k. This represents the distance measurement covariance between target s and sensor i at time k. This represents the covariance of the angle measurement noise between target s and sensor i at time k. This represents the relative distance between target s and sensor i′ at time k. Let represent the distance measurement covariance between target s and sensor i′ at time k. Sensor i and sensor i′ are located on the same agent. Sensor i is a radar sensor, and sensor i′ is an infrared sensor. Let D1 represent the set of radar sensors and D2 represent the set of infrared sensors.

5. The time-varying formation tracking control method with multi-sensor multi-target filtering according to claim 4, characterized in that, The state equation of the agent is expressed as: in, This represents the state of agent c at time k. Let B represent the state of agent c at time k-1, Φ represent the state transition matrix of the agent, and B∈R. n×r Let r represent a matrix of rank r. This represents the time-varying formation control protocol for agent c.

6. The time-varying formation tracking control method with multi-sensor multi-target filtering according to claim 5, characterized in that, Based on the aforementioned communication topology, the state equations of all targets, and the sensor observation models of the targets, a distributed multi-sensor multi-target filtering method is designed based on capacitive Kalman filtering to obtain the final state estimate of each target, specifically including: When the iteration number l = 0, Initialize to P k i,l Initialize to P represents the state estimate of sensor i for all targets after l iterations at time k. k i,l Let represent the error covariance matrix of sensor i for all targets after l iterations at time k; Through formula and Performing the l-th iteration, we obtain and P k i,l Until after L iterations, the sensor at time k State estimates for all targets and Consistent, all are And the error covariance P k i,L and P k j,L Consistent, both are P k ;Will As the final state estimate, P k As the final error covariance; N i Let i be the set of its internal neighbor nodes; Among them, w ii w represents the element in the i-th row and i-th column of the second weighted adjacency matrix. ij This represents the element in the i-th row and j-th column of the second weighted adjacency matrix, which is the weighted adjacency matrix of the directed graph formed by the sensors. Wherein, the state estimates of sensor i for all targets at time k. And error covariance matrix P k i The calculation process includes the following steps: Initialization: At time k=0, for each sensor i, initialize the state estimate of sensor i for all targets. And error covariance matrix P0 i ; According to the formula Calculate volume points For ξ s The e-th element, e = 1,...,2n, ξ s The formula for determining the value is: s∈V2, n is x k,s The dimension; according to Get the spread according to Determine the prior state estimate and prior estimate error covariance According to the formula For volume point Update to obtain volume points Based on volume points The predicted measurement value was calculated. Error covariance matrix Error covariance matrix Based on the error covariance matrix And error covariance matrix Calculate the filter gain Based on the measurements of all targets by sensor i at time k Filter gain Predicted measurement value Prior estimation error covariance And error covariance matrix The state estimates of sensor i for all targets at time k are calculated. And error covariance matrix P k i .

7. A time-varying formation tracking control system with multi-sensor multi-target filtering, characterized in that, include: The communication topology determination module is used to obtain the communication topology relationships between multiple agents, multiple targets, and multiple sensors; each agent carries a sensor. The state equation and observation model establishment module is used to establish the state equations of all targets, the sensor observation models of all targets, and the state equations of each agent. The final state estimate and final error covariance determination module of the target is used to design a distributed multi-sensor multi-target filtering method based on the communication topology, the state equations of all targets and the sensor observation model of the target, to obtain the final state estimate of each target. The agent time-varying formation control protocol determination module is used to determine the time-varying formation control protocol of each agent based on the state equation of each agent and the final state estimate of each target. The time-varying formation control protocol for intelligent agents is represented as follows: in, This represents the time-varying formation control protocol for agent c, where K is a constant gain matrix and π is the number of agents. cj This represents the element in the c-th row and j-th column of the first weighted adjacency matrix, π. cs Let represent the element in the c-th row and s-th column of the first weighted adjacency matrix. The first weighted adjacency matrix is ​​the weighted adjacency matrix in the directed graph composed of the agent and the target. This represents the state of agent c at time k-1. For agent c and the formation reference at time k-1 The relative states between them For agent j and the formation reference at time k-1 The relative states between them Let α be a convex combination of targets tracked by the agent formation at time k-1. s To meet The positive constant s ∈ V2, where V2 represents the target set. The formation tracking compensation signal for agent c at time k-1. Let M represent the final state of target s at time k-1; M represents the number of agents; and NM represents the number of targets.

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