An interactive filtering method and system based on maximum relevant entropy and sparse communication

Abstract

The application discloses an interactive filtering method and system based on maximum correlation entropy and sparse communication, and the system comprises a target to be estimated module, a sensing module, a communication module, an initialization module, an interactive filtering module and a parameter design module; a nonlinear complex network dynamics model and a sensor measurement model of a multi-target tracking system are constructed; a scheduling mode of a component type dynamic event trigger mechanism is defined, which is used for scheduling a data transmission process, obtaining a measurement information model available at a filter end, and estimating a state of a target; a recursive form of an interactive filter under sparse communication is designed; a performance index function based on correlation entropy information is constructed to obtain a gain matrix of the interactive filter; state estimation of a nonlinear complex network under non-Gaussian noise, uncertain dynamic bias and limited resource constraints is realized, and the method can be applied to multi-target tracking, cooperative detection and cooperative attack and other task scenes in complex environments.

Description

Technical Field

[0001] This invention relates to state estimation techniques for complex networked systems, specifically to an interactive filtering method and system based on maximum correlation entropy and sparse communication. It is a nonlinear interactive filtering technique that is based on the maximum correlation entropy index and simultaneously meets the sparse communication requirements of the system. Background Technology

[0002] Complex networks typically consist of a set of interacting dynamic nodes, where each node is dynamically coupled to the others according to a specific topology. Complex networks can be used to characterize many complex large-scale systems in the real world; typical examples include social networks, transportation networks, power grids, neural networks, gene regulation networks, and infectious disease transmission networks. To gain a deeper understanding of the intrinsic structure of complex networks, one of the primary tasks is to obtain the system's state information. However, the large scale, strong coupling, and nonlinearity of these systems make this goal very difficult to achieve. A more feasible approach is to utilize available sensor measurements and design suitable state estimation algorithms to estimate the state of complex network systems.

[0003] Existing mature methods include Kalman filtering, H-infinity filtering, and set-membership filtering, which are mainly suitable for Gaussian noise or noise / interference with bounded energy and norm. However, in practical engineering, due to the combined effects of signal reflection and pulse electromagnetic interference, system noise often exhibits significant non-Gaussian characteristics, rendering the above methods unsuitable. Furthermore, in practical applications, system dynamics and sensor measurements are not only affected by noise but also easily influenced by unknown inputs (such as component failures and imperfect calibration). On the other hand, frequent data transmission in networked systems inevitably consumes a large amount of communication bandwidth resources, creating a heavy communication burden. While existing event-triggered mechanisms can save limited communication bandwidth resources, they are difficult to design differently based on the signal amplitude and required update frequency of each system component. Summary of the Invention

[0004] To address the shortcomings of the existing technologies, this invention provides an interactive filtering method and system based on maximum correlation entropy and sparse communication, which solves the state estimation problem of multi-target tracking systems with nonlinear complex network structures under non-Gaussian noise, uncertain dynamic bias, and limited resource constraints, thereby achieving rational utilization of limited resources and accurate estimation of system state.

[0005] This invention constructs a dynamic model of a complex network and a sensor measurement model based on actual engineering scenarios. By introducing a component-based dynamic event triggering mechanism, it ensures that each sensor component in the complex network system can independently schedule the data transmission process according to its own triggering conditions, making more flexible and rational use of limited communication resources. For non-Gaussian noise, a correlation entropy index is used to capture the higher-order statistics of the probability density function. Considering the influence of the component-based dynamic event triggering mechanism, the nonlinear characteristics of the system, and the uncertain dynamic bias, a recursive form of the interactive filter is constructed, and the upper bound matrix of the prediction error covariance matrix is ​​derived to assist in the design of the performance index function based on correlation entropy. Furthermore, the gain matrix of the filter is designed by maximizing the above-mentioned correlation entropy index function, thereby realizing the state estimation of nonlinear complex networks under non-Gaussian noise, uncertain dynamic bias, and limited resource constraints.

[0006] The technical solution provided by this invention is as follows:

[0007] An interactive filtering method based on maximum correlation entropy and sparse communication is proposed to achieve state estimation of nonlinear complex networks under non-Gaussian noise, uncertain dynamic bias, and limited resource constraints. The method includes the following steps:

[0008] 1) Construct a nonlinear complex network dynamics model and a sensor measurement model for a multi-target tracking system;

[0009] The multi-target tracking system includes N coupled nodes, each node representing a target to be tracked, including vehicles, ships, or drones; the dynamic model of the multi-target tracking system is established as follows:

[0010]

[0011] in, This represents the state vector of the i-th node at time s, including the target's position and velocity information; its dimension is... D = [d ij ] N×N This represents the network coupling matrix, with element d. ij This indicates the degree of coupling between the state information of the i-th node and the j-th node; This represents the state vector of the j-th node at time s; This is a function used to describe the nonlinear characteristics of the target; This is a diagonal matrix representing internal coupling relationships, with its diagonal elements being... and B i，s Let represent the system matrix and the input matrix corresponding to the random bias of the i-th node, respectively; This represents process noise with zero mean, and its covariance is... z i，sThis represents the effect of random bias on the i-th node;

[0012] The sensor measurement model corresponding to the i-th node is constructed as follows:

[0013]

[0014] Among them, y i，s Indicates m-dimensional measurement output, v i，s This represents measurement noise with zero mean and covariance R. i，s >0; Let be the measurement matrix of the sensor corresponding to the i-th node at time s; all random variables are independent of each other;

[0015] 2) Define a component-based dynamic event triggering mechanism for scheduling the data transmission process, obtain the measurement information model available at the filter end, and estimate the state of the target;

[0016] The target is measured using the sensor measurement model established in step 1), and the measurement data is transmitted to the filter end via wireless communication. The transmission process of the measurement data of the sensor components is scheduled by a component-based dynamic event triggering mechanism to estimate the state of the target and obtain the state information of the target.

[0017] The available measurement information model is represented as follows:

[0018]

[0019] Where i is the node number; l is the sensor component number; and s is the time. The measurement information available at the filter terminal at time s. r i，s =[r i，1，s r i，2，s … r i，m，s ] T Λ i，s Indicates the variable λ i，1，s , λ i，2，s , …, λ i，m，s The diagonal matrix formed; I is the identity matrix; λ i，1，s , λ i，2，s , …, λ i，m，s Let y represent the binary variables corresponding to the 1st, ..., mth sensor components of the i-th node, respectively. Their values ​​are 1 when the trigger function is greater than zero, and 0 otherwise. i，s This is the measurement output of the i-th node at time s.

[0020] 3) Design the recursive form of the interactive filter under sparse communication;

[0021] Based on the target dynamics model and sensor measurement model established in step 1), and the available measurement information model established in step 2), an interactive filter structure is constructed, as shown below:

[0022]

[0023]

[0024] in, and K represents the one-step prediction and state estimate of the i-th node at time s, respectively; i，s This represents the gain matrix of the interactive filter to be designed;

[0025] 4) Construct a performance index function based on relevant entropy information to obtain the gain matrix of the interactive filter;

[0026] Construct a performance index function J(x) based on relevant entropy information i，s ), represented as:

[0027]

[0028] Among them, G χ (·) represents the Gaussian kernel function with bandwidth χ in the definition of maximum correlation entropy; and Let K represent the upper bound matrices of the prediction error covariance and the equivalent noise covariance, respectively. Their recursive expressions represent their relationship with the gain matrix K of the interactive filter. i，s Relationship;

[0029] 5) Design the gain matrix of the interactive filter based on the constructed performance index function to obtain the interactive filter;

[0030] Design the interactive filter gain matrix to maximize the performance index function established in step 4); including:

[0031] Calculate the performance index function J(x) i，s For x i，s The partial derivatives of , and let The gain matrix K of the interactive filter i，s Represented as:

[0032]

[0033] in,

[0034] 6) The designed interactive filter is used to realize the state estimation of complex networks.

[0035] In practical implementation, this invention also designs an interactive filtering system based on maximum correlation entropy and sparse communication to implement the above method. The system includes six modules: a target to be estimated module, a perception module, a communication module, an initialization module, an interactive filtering module, and a parameter design module. The target to be estimated module represents the target of interest for which state estimation is required. In multi-target tracking scenarios, the target of interest can be a ground vehicle convoy, a maritime ship formation, or an aerial UAV cluster. The perception module observes the target of interest and obtains measurement signals in the form of distance, angle, and signal reception strength. The communication module transmits the measurement signals. In this invention, a component-based dynamic event triggering mechanism is used to schedule this transmission process to achieve sparse communication. The initialization module sets the initial values ​​and parameters of the filtering algorithm. The interactive filtering module runs the interactive filter and updates the state estimate and the corresponding upper bound of the error covariance matrix. The parameter design module maximizes the performance index function based on correlation entropy and determines the filtering gain matrix of the interactive filter.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] This invention proposes an interactive filtering method based on maximum correlation entropy and sparse communication. By introducing a component-based dynamic event triggering mechanism, the data transmission process of each sensor component is independently scheduled. This sparse communication approach saves limited network communication resources, and by maximizing the correlation entropy index function, the influence of non-Gaussian noise is effectively suppressed. This ensures the accuracy of state estimation for complex networks while making reasonable use of limited resources. The interactive filtering method designed in this invention can be applied to mission scenarios such as multi-target tracking, cooperative detection, and cooperative strike in complex environments. Attached Figure Description

[0038] Figure 1 This is a system structure block diagram of the method for implementing the present invention as used in an embodiment of the present invention.

[0039] Figure 2 This is a flowchart of the interactive filtering method based on maximum correlation entropy and sparse communication provided by the present invention. Detailed Implementation

[0040] The present invention will be further illustrated below with reference to the accompanying drawings and embodiments, but the scope of the invention is not limited in any way.

[0041] This invention provides an interactive filtering method based on maximum correlation entropy and sparse communication, and the system structure for implementing the interactive filtering algorithm in this invention is as follows: Figure 1As shown, the entire system comprises six modules: the target to be estimated module, the perception module, the communication module, the initialization module, the interactive filtering module, and the parameter design module. Specifically, the target to be estimated module represents the target of interest for which state estimation is required. In multi-target tracking scenarios, the target of interest can be a ground vehicle convoy, a maritime ship formation, or an aerial drone cluster. The perception module observes the target of interest, obtaining measurement signals such as distance, angle, and signal reception strength. The communication module transmits the measurement signals; this invention employs a component-based dynamic event triggering mechanism to schedule this transmission process, achieving sparse communication. The initialization module sets the initial values ​​and parameters of the filtering algorithm. The interactive filtering module runs the interactive filter, thereby updating the state estimate and the corresponding upper bound of the error covariance matrix. The parameter design module maximizes the performance index function based on correlation entropy to determine the filtering gain matrix of the interactive filter.

[0042] The overall process of the interactive filtering method based on maximum correlation entropy and sparse communication provided by this invention is as follows: Figure 2 As shown, the process includes six steps. First, a dynamic model and sensor measurement model of the complex network are constructed based on the actual engineering scenario, serving as prior knowledge for subsequent filter design. Then, a scheduling method based on a component-based dynamic event triggering mechanism is defined to save limited communication resources through sparse communication. Next, the recursive form of the interactive filter under sparse communication is designed based on the available measurement information. Then, considering the effects of sparse communication and non-Gaussian noise, a performance index function based on relevant entropy information is constructed, and the gain matrix of the interactive filter is designed accordingly. Finally, the designed interactive filter is run to obtain the state estimate of the complex network.

[0043] The specific implementation of the technical solution of the present invention includes the following steps:

[0044] 1) Construct the target dynamics model and sensor measurement model;

[0045] Suppose a multi-target tracking system described by a complex network includes N coupled nodes, each node representing a target to be tracked (such as a ground vehicle, a ship at sea, or an aerial drone), and its dynamic model is as follows:

[0046]

[0047] in, This represents the state vector of the i-th node at time s, including information such as the target's position and velocity, with dimension O(n). D = [d ij ] N×N Denotes the network coupling matrix, d ijThese are elements in the network coupling matrix, used to describe the degree of coupling of state information between the i-th node and the j-th node; This represents the state vector of the j-th node at time s; A function describing the nonlinear characteristics of the state vector of a multi-target tracking system, satisfying... as well as Where u and v represent any feasible dimensional state vector, κ is a known matrix used to approximate the nonlinear characteristics of the target. s Given a positive scalar for describing the approximation error of the target's nonlinear characteristics, it indicates that the target has Lipschitz-like nonlinear characteristics; This is a diagonal matrix representing internal coupling relationships, with its diagonal elements being... and B i，s Let represent the system matrix and the input matrix corresponding to the random bias of the i-th node, respectively. This represents process noise with zero mean, and its covariance is... z i，s Let represent the effect of random bias on the i-th node, and its dynamic characteristics are as follows:

[0048] z i，s+1 =(G i，s +ΔG i，s )z i，s +η i，s

[0049] Among them, z i，s+1 G represents the random bias effect experienced by the i-th node at time s+1; i，s Let η represent the known bias transition matrix. i，s This represents noise with zero mean and covariance S. i，s >0, ΔG i，s Represents a perturbation term that satisfies the following properties:

[0050]

[0051] Where τ i Let I be a given positive scalar, I be the identity matrix, E{·} denote the expected value of the random variable, and the superscript T denotes the transpose operation.

[0052] The sensor measurement model corresponding to the i-th node is constructed as follows:

[0053]

[0054] Where y i，s Indicates m-dimensional measurement output, v i，s This represents measurement noise with zero mean and covariance R.i，s >0; Let be the measurement matrix of the sensor corresponding to the i-th node at time s. Assume variables... η i，s v i，s , z i，0 Each of them is independent of the others.

[0055] For simplicity, the following symbols are defined: This represents the augmented state vector of the i-th node; This represents the system matrix after augmentation of the i-th node; This indicates the uncertainty of the system matrix after the i-th node is augmented; This represents the augmented internal coupling matrix of the i-th node; This represents a function used to describe the nonlinear characteristics of the augmented i-th node; This represents the process noise after the augmentation of the i-th node; Let represent the measurement matrix after augmentation at the i-th node. The following augmentation dynamics model can be established:

[0056]

[0057] y i，s =C i，s x i，s +v i，s

[0058] 2) Define the scheduling method of the component-based dynamic event triggering mechanism, schedule the data transmission process, obtain the measurement information model available at the filter end, and estimate the state of the target;

[0059] To obtain the target's state information, the sensor measurement model established in step 1) is used to observe the target. The measurement data is then transmitted wirelessly to the filter terminal to estimate the target's state. To achieve sparse communication, a component-based dynamic event triggering mechanism is used to schedule the data transmission process. The triggering function is shown below:

[0060]

[0061] in y i，l，s This represents the measurement output corresponding to the l-th sensor component at the i-th node. Represents the latest transmitted measurement information before time s; π i，l and ρ i，l These represent the preset trigger threshold and the adjustable parameter, respectively; auxiliary variable ξ i，l，s The initial value is ξ i，l，0≥0, and has the following kinetic characteristics:

[0062]

[0063] Where δ i，l This represents the preset parameters. Further define the binary variable λ. i，l，s Let l = 1, ..., m, where m represents the number of sensor components; the value is 1 when the trigger function is greater than zero, and 0 otherwise. Then, the available measurement information model at time s satisfies the following relationship, expressed as:

[0064]

[0065] in, This provides the measurement information available at the filter end. r i，s =[r i，1，s r i，2，s … r i，m，s ] T Λ i，s Indicates the variable λ i，l，s That is, λ i，1，s , λ i，2，s , …, λ i，m，s A diagonal matrix formed.

[0066] 3) Design the recursive form of the interactive filter under sparse communication;

[0067] Based on the target dynamics model and sensor measurement model established in step 1) and the available measurement information model established in step 2), the following interactive filter structure is constructed:

[0068]

[0069]

[0070] in and K represents the one-step prediction and state estimate of the i-th node at time s, respectively; i，s This represents the gain matrix of the interactive filter to be designed.

[0071] 4) Construct a performance index function based on relevant entropy information to obtain the gain matrix of the interactive filter;

[0072] To design the gain matrix K of the interactive filter in step 3). i，s The performance index function J(x) based on relevant entropy information is constructed as follows. i，s ):

[0073]

[0074] Among them, G χ (·) represents the Gaussian kernel function with bandwidth χ in the definition of maximum correlation entropy; and Let K represent the upper bound matrices of the prediction error covariance and the equivalent noise covariance, respectively. Their recursive expressions represent their relationship with the gain matrix K of the interactive filter. i，s Relationship;

[0075] Its recursive expression is as follows:

[0076]

[0077]

[0078]

[0079]

[0080]

[0081] Ξ i，l，s =δ i，l Ξ i，l，s-1 +π i，l

[0082] in α i，j (j = 1, 2, ..., 5) are given positive scalars representing the scaling coefficients involved in the upper bound matrix of the prediction error covariance; β i，j (j = 1, 2) is a given positive scalar representing the scaling coefficients involved in the upper bound matrix of the filter error covariance; Ξ i，l，s Describing the auxiliary variable ξ i，l，s The upper bound of , whose initial value is Ξ i，l，0 =ξ i，l，0 ; tr{·} represents the trace of a matrix; the superscript -1 represents the reciprocal of a scalar or the inverse of a matrix.

[0083] 5) Design the gain matrix of the interactive filter and optimize the performance index function;

[0084] Design the interactive filter gain matrix to maximize the performance index function established in step 4); including:

[0085] Calculate the performance index function J(x) i，s For x i，s The partial derivatives of , and let have to

[0086]

[0087] in Considering Ui，s Includes unknown variable x i，s Predict in one step To approximate x i，s The following gain matrix form, which is easy to calculate, can be obtained:

[0088]

[0089] in

[0090] 6) Run the designed interactive filter to obtain the state estimate of the complex network.

[0091] Based on the filter gain matrix designed in the previous step, running the interactive filter for sparse communication designed in step 3) can yield the state estimate of each node in the complex network.

[0092] Based on the specific implementation methods and implementation cases described above, state estimation of nonlinear complex networks under non-Gaussian noise, uncertain dynamic bias, and finite resource constraints can be achieved.

[0093] It should be noted that the purpose of disclosing the embodiments is to help further understand the present invention. However, those skilled in the art will understand that various substitutions and modifications are possible without departing from the scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the embodiments, and the scope of protection of the present invention is defined by the scope of the claims.

Claims

1. An interactive filtering method based on maximum correlation entropy and sparse communication, characterized in that, Design an interactive filter to achieve state estimation of nonlinear complex networks under non-Gaussian noise, uncertain dynamic bias, and limited resource constraints; including the following steps: 1) Construct a nonlinear complex network dynamics model and a sensor measurement model for a multi-target tracking system; The multi-target tracking system includes N coupled nodes, each node representing a target to be tracked, including vehicles, ships, or drones; the dynamic model of the multi-target tracking system is established as follows: in, This represents the state vector of the i-th node in a multi-target tracking system at time s, including the target's position and velocity information; its dimension is... D = [d ij ] N×N This represents the network coupling matrix, with element d. ij This indicates the degree of coupling between the state information of the i-th node and the j-th node; This represents the state vector of the j-th node at time s; A function describing the nonlinear characteristics of the state vector in a multi-target tracking system; This is a diagonal matrix representing internal coupling relationships, with its diagonal elements being... and B i,s Let ζ represent the system matrix and the input matrix corresponding to the random bias of the i-th node, respectively; i,s This represents process noise with zero mean, and its covariance is... z i,s This represents the effect of random bias on the i-th node; The sensor measurement model corresponding to the i-th node is constructed as follows: Among them, y i,s Indicates m-dimensional measurement output, v i,s This represents measurement noise with zero mean and covariance R. i,s >0; Let be the measurement matrix of the sensor corresponding to the i-th node at time s; all random variables are independent of each other; 2) Define a component-based dynamic event triggering mechanism for scheduling the data transmission process, obtain the measurement information model available at the filter end, and estimate the state of the target; The target is measured using the sensor measurement model established in step 1), and the measurement data is transmitted to the filter end via wireless communication. The transmission process of the measurement data of the sensor components is scheduled by a component-based dynamic event triggering mechanism to estimate the state of the target and obtain the state information of the target. The available measurement information model is represented as follows: Where i is the node number; l is the sensor component number; and s is the time. The measurement information available at the filter terminal at time s. r i,s =[r i,1,s r i,2,s … r i,m,s ] T Λ i,s Indicates the variable λ i,1,s ,λ i,2,s ,…,λ i,m,s The diagonal matrix formed; I is the identity matrix; λ i,1,s ,λ i,2,s ,…,λ i,m,s Let y represent the binary variables corresponding to the 1st, ..., mth sensor components of the i-th node; i,s The measurement output of the i-th node at time s; 3) Design the recursive form of the interactive filter under sparse communication; Based on the target dynamics model and sensor measurement model established in step 1), and the available measurement information model established in step 2), an interactive filter structure is constructed, as shown below: in, and K represents the one-step prediction and state estimate of the i-th node at time s, respectively; i,s This represents the gain matrix of the interactive filter to be designed; 4) Construct a performance index function based on relevant entropy information to obtain the gain matrix of the interactive filter; Construct a performance index function J(x) based on relevant entropy information i,s ), represented as: Among them, G χ (·) represents the Gaussian kernel function with bandwidth χ in the definition of maximum correlation entropy; and Let K represent the upper bound matrices of the prediction error covariance and the equivalent noise covariance, respectively. Their recursive expressions are derived from the gain matrix K of the interactive filter. i,s Relationship; 5) Design the gain matrix of the interactive filter based on the constructed performance index function to obtain the interactive filter; Design the interactive filter gain matrix to maximize the performance index function established in step 4); including: Calculate the performance index function J(x) i,s For x i,s The partial derivatives of , and let The gain matrix K of the interactive filter i,s Represented as: in, 6) The designed interactive filter is used to realize the state estimation of complex networks.

2. The interactive filtering method based on maximum correlation entropy and sparse communication as described in claim 1, characterized in that, In step 1), the i-th node in the multi-target tracking system is affected by a random bias, and its dynamic characteristics are expressed as follows: With i,s+1 =(G i,s +ΔG i,s )With i,s +η i,s Among them, z i,s+1 G represents the random bias effect experienced by the i-th node at time s+1; i,s Let η represent the known bias transition matrix. i,s This represents noise with zero mean and covariance S. i,s >0, ΔG i,s Represents a perturbation term that satisfies the following properties: Where τ i Given a positive scalar, I is the identity matrix, E{·} denotes the expected value of the random variable, and the superscript T denotes the transpose operation; And nonlinear functions satisfy as well as Where u and v are dimensional vector, Given a matrix, κ s For a given positive scalar.

3. The interactive filtering method based on maximum correlation entropy and sparse communication as described in claim 2, characterized in that, In step 1), an augmented dynamics model is established, expressed as: y i,s =C i,s x i,s +n i,s Wherein, the symbol x is defined. i,s : This represents the augmented state vector of the i-th node; Represents the system matrix after augmentation of the i-th node; This indicates the uncertainty of the system matrix after the i-th node is augmented; This represents the augmented internal coupling matrix of the i-th node; This represents a function used to describe the nonlinear characteristics of the augmented i-th node; This represents the process noise after the augmentation of the i-th node; Let represent the measurement matrix after augmentation of the i-th node.

4. The interactive filtering method based on maximum correlation entropy and sparse communication as described in claim 3, characterized in that, In step 2), a component-based dynamic event triggering mechanism is used to schedule the data transmission process to achieve sparse communication. Its triggering function is expressed as follows: in, y i,l,s This represents the measurement output corresponding to the l-th sensor component at the i-th node. Represents the latest transmitted measurement information before time s; π i,l and ρ i,l These represent the preset trigger threshold and the adjustable parameter, respectively; auxiliary variable ξ i,l,s The initial value is ξ i,l,0 ≥0, and having kinetic properties, is expressed as: Where, δ i,l Indicates preset parameters; The available measurement information model at time s satisfies the following relationship, expressed as: Here, a binary variable λ is defined. i,l,s When the trigger function is greater than zero, its value is 1, otherwise it is 0; This provides the measurement information available at the filter end. r i,s =[r i,1,s r i,2,s … r i,m,s ] T Λ i,s Indicates the variable λ i,1,s ,λ i,2,s ,…,λ i,m,s A diagonal matrix formed.

5. The interactive filtering method based on maximum correlation entropy and sparse communication as described in claim 1, characterized in that, In step 4), the upper bound matrix of the prediction error covariance and the upper bound matrix of the equivalent noise covariance are... and The recursive expressions are respectively expressed as: X i,l,s =d i,l X i,l,s-1 +p i,l in, α i,j (j=1,2,…,5) are given positive scalars, representing the scaling coefficients involved in the upper bound matrix of the prediction error covariance; β i,j (j=1,2) is a given positive scalar representing the scaling coefficients involved in the upper bound matrix of the filter error covariance; Ξ i,l,s Describing the auxiliary variable ξ i,l,s The upper bound of the initial value is Ξ i,l,0 =ξ i,l,0 ; tr{·} represents the trace of a matrix; the superscript -1 represents the reciprocal of a scalar or the inverse of a matrix.

6. The interactive filtering method based on maximum correlation entropy and sparse communication as described in claim 5, characterized in that, U in step 5) i,s Includes unknown variable x i,s One-step prediction Approximate x i,s Furthermore, a gain matrix form that is easier to calculate is obtained, expressed as: in, 7. An interactive filtering system based on maximum correlation entropy and sparse communication for implementing the method of claim 1, characterized in that it comprises: The module to be estimated includes a target estimation module, a sensing module, a communication module, an initialization module, an interactive filtering module, and a parameter design module; among which: The target to be estimated module is used to represent the target of interest that needs to be state estimated in a multi-target tracking scenario; The sensing module is used to observe the target of interest and obtain measurement signals; The communication module is used to measure signal transmission and realize sparse communication; The initialization module is used to set the initial values ​​and parameters of the filtering algorithm; The interactive filtering module is used to run interactive filters, thereby updating the state estimates and the corresponding upper bound of the error covariance matrix; The parameter design module is used to maximize the performance index function based on correlation entropy to determine the filter gain matrix of the interactive filter.

8. The interactive filtering system based on maximum correlation entropy and sparse communication as described in claim 7, characterized in that, Targets of interest include ground vehicle convoys, maritime ship formations, and aerial drone swarms.

9. The interactive filtering system based on maximum correlation entropy and sparse communication as described in claim 7, characterized in that, The measured signals include distance, angle, and signal reception strength.

10. The interactive filtering system based on maximum correlation entropy and sparse communication as described in claim 7, characterized in that, The communication module specifically employs a component-based dynamic event-triggered mechanism to schedule the transmission process, thereby achieving sparse communication.

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