A radar network multi-target positioning and tracking method and system based on minimum error entropy in a complex electromagnetic environment

Abstract

This invention belongs to the field of radar network fusion positioning and tracking technology, and discloses a radar network multi-target positioning and tracking method and system based on minimum error entropy in complex electromagnetic environments. The method includes: constructing a multi-target motion state model based on the target state, state transition matrix, and motion process noise; generating a target state set and a target observation set based on the multi-target motion state model and random set description; calculating the equivalent position measurement likelihood function using the minimum error entropy algorithm based on the target state set and target observation set; calculating the multi-target joint likelihood function based on the equivalent position measurement likelihood function, the target motion state model, and amplitude feature information; calculating the multi-target posterior probability density based on the multi-target joint likelihood function; and clustering the multi-target posterior probability density to obtain the multi-target tracks and multi-target track states, thus completing the radar network multi-target positioning and tracking based on minimum error entropy in complex electromagnetic environments.

Description

Technical Field

[0001] This invention belongs to the field of radar network fusion positioning and tracking technology, and particularly relates to a radar network multi-target positioning and tracking method and system based on minimum error entropy in complex electromagnetic environments. Background Technology

[0002] In modern warfare, with the emergence and significant performance improvements of high-tech equipment such as hypersonic and stealth targets, coupled with the complexity of the battlefield electromagnetic environment, single radar information processing systems are increasingly inadequate in terms of processing speed, quality, capacity, and reliability, failing to meet the demands of modern warfare for multi-target air situation awareness. Furthermore, radar systems are significantly less effective against the powerful deception and suppression interference present on the modern battlefield, sometimes even failing completely, manifesting as outliers, clutter, and missed detections. Since distributed radar networking technology can fundamentally improve anti-jamming capabilities and the quality of information processing for multi-target signals under high density, research on radar networking, fusion, positioning, and tracking in complex electromagnetic environments is crucial. Summary of the Invention

[0003] To address the above problems, this invention provides a multi-target localization and tracking method for radar networks in complex electromagnetic environments based on minimum error entropy. The method includes: Step S1: Construct a multi-target motion state model based on the target state, state transition matrix, and motion process noise of the target motion; and generate a target state set and a target observation set based on the multi-target motion state model and random set description. Step S2: Based on the target state set and the target observation set, calculate the equivalent position measurement likelihood function using the minimum error entropy algorithm; Step S3: Calculate the multi-target joint likelihood function based on the equivalent position measurement likelihood function, the target motion state model, and amplitude feature information; Step S4: Introduce attribute measurement amplitude features and target identity, and calculate the multi-target posterior probability density based on the multi-target joint likelihood function; Step S5: Cluster the posterior probability density of the multi-target targets to obtain the multi-target tracks and track states, thus completing the radar networking multi-target positioning and tracking under complex electromagnetic environments based on minimum error entropy.

[0004] Optionally, in step S1, the formula for constructing a multi-target motion state model based on the target state of the target motion, the state transition matrix, and the motion process noise is as follows: ; in, for Constant target status, for Constant target status, Here is the state transition matrix. Here is the gain matrix. This is process noise.

[0005] Optionally, in step S1, generating the target state set and target observation set based on the multi-target motion state model and random set description specifically involves: Target state set: ; Target observation set: .

[0006] Optionally, in step S4, the multi-target posterior probability density is specifically as follows: ; in, For multi-objective posterior state probability distribution, A set of multi-target track labels. For the predicted multi-target track label space, To establish the mapping relationship between measurements and targets, For each mapping, the probability weights are... For predicting multi-target X-labels The validity indicator function takes a value of 0 or 1. For mapping Posterior distribution of multi-objective states under certain conditions.

[0007] Optionally, in the multi-objective posterior probability density formula: ; ; ; ; in, These are the probability weights corresponding to the posterior distribution of multiple objectives under the label-measurement mapping condition. For measuring Z and mapping The validity indicator function for multi-target track labels under certain conditions takes a value of 0 or 1. For mapping Normalized likelihood function of multi-objective state measurement under certain conditions. For a multi-objective posterior distribution, where These are the status and track labels for each target. These are target identity tags, primarily corresponding to RCS and echo intensity attributes. Let be the likelihood function for the objective. The track is tagged as The single-objective state normalized measurement likelihood, The detection probability of the target. Let be the likelihood function when the target has a measurement mapping. For a set of multi-objective states, It is the likelihood of the target echo point intensity.

[0008] This invention also discloses a radar network multi-target positioning and tracking system based on minimum error entropy in complex electromagnetic environments, the system comprising: The model building module is used to construct a multi-target motion state model based on the target state, state transition matrix, and motion process noise of the target motion, and to generate a target state set and a target observation set based on the multi-target motion state model and random set description. The measurement likelihood function module is used to calculate the equivalent position measurement likelihood function based on the target state set and the target observation set using the minimum error entropy algorithm. The joint likelihood module is used to calculate a multi-objective joint likelihood function based on the equivalent position measurement likelihood function, the target motion state model, and amplitude feature information. The probability density calculation module is used to introduce attribute measurement amplitude features and target identity, and calculate the multi-target posterior probability density based on the multi-target joint likelihood function; The target localization and tracking module is used to cluster the posterior probability density of the multi-targets to obtain the multi-target tracks and track states, and to complete the multi-target localization and tracking of radar networks in complex electromagnetic environments based on minimum error entropy.

[0009] Optionally, in the model building module, the formula for the multi-objective motion state model is: ; in, for Constant target status, for Constant target status, Here is the state transition matrix. Here is the gain matrix. This is process noise.

[0010] Optionally, in the model building module: Target state set: ; Target observation set: .

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention proposes a multi-target fusion localization and tracking method for radar networks under complex electromagnetic environments based on error entropy. This method can be used to perceive scenarios in complex electromagnetic environments such as non-Gaussian noise, outliers, and missed detections. Existing methods suffer significant accuracy degradation in non-Gaussian noise environments such as outliers. This patented method employs a multi-target fusion tracking approach based on error entropy. It learns and approximates the error distribution in radar network measurements using a mixture of Gaussian kernel functions and establishes an optimization objective function for the mixture of error entropy, thereby obtaining the optimal estimate of the target state under the minimum error entropy criterion. Furthermore, it utilizes amplitude information from radar measurements to improve the ability to distinguish target measurements from clutter and other interference, increasing the accuracy of target-measurement correlation and obtaining the joint likelihood function of multi-target position and amplitude measurements. Then, based on a multi-target random finite set model within a Bayesian estimation framework, it obtains the joint posterior distribution of multi-target state and amplitude. To reduce the complexity of multi-target trajectory estimation, this patent finally presents a clustering method for multi-target density. By clustering, the trajectory of each target is obtained, avoiding the exponentially increasing computational complexity caused by the uncertainty of the correlation between the state and measurement of multiple targets, and improving the real-time performance of radar network data processing. Attached Figure Description

[0012] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart illustrating the method steps of the radar and communication detection multi-target tracking method with clutter density adaptive in an amphibious environment according to an embodiment of the present invention. Figure 2 This is a schematic diagram of multi-objective state and measurement modeling based on a label-based random finite set according to an embodiment of the present invention; Figure 3 This is the process for error entropy state estimation and equivalent likelihood calculation in an embodiment of the present invention. Detailed Implementation

[0013] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.

[0014] Example 1 like Figure 1 As shown, this embodiment provides a multi-target localization and tracking method for radar networks in complex electromagnetic environments based on minimum error entropy. The method includes: Step S1: Construct a multi-target motion state model based on the target state, state transition matrix, and motion process noise of the target motion; generate a target state set and a target observation set based on the multi-target motion state model and random set description.

[0015] First, the target motion process is modeled. In practical applications, due to imperfect prior information and the random maneuvering of the target, establishing a completely accurate target motion model is difficult. This project, based on multiple basic motion models, describes the noise and uncertainty between the actual motion process and the target motion model through motion process noise and multi-model weighting methods. This approximates the actual motion process of the target while facilitating mathematical processing. The target state transition equation is: ; in, for Constant target status, for Constant target status, Here is the state transition matrix. Here is the gain matrix. This represents process noise. Different motion models have different transfer and gain matrices. For modeling the motion state of multiple targets, within a finite set statistical framework, the set of all individual target states is considered a set-valued state, while the set of all measurements obtained from a single observation is considered a set-valued measurement. After modeling the set-valued state and set-valued measurements as random finite sets, optimal Bayesian filtering techniques can be used to achieve time-varying multi-target estimation under conditions of correlation uncertainty, detection uncertainty, and false alarm clutter, thus deriving a multi-target Bayesian filter.

[0016] Multiple target states and measurements can be represented as sets. The target state set described by a random set (RFS) is as follows: ; As shown above, similarly, the observation set described by RFS is represented as follows: ; Given n objectives with state vectors x1, ..., xn, the multi-objective state random set can be represented as: In this embodiment, the multi-target tracking task requires establishing a mapping θ between target states and measurement sets. Using a specific measurement from the corresponding random measurement set, the likelihood function g for updating the target state is calculated, and the posterior estimate of each target state is solved within a Bayesian estimation framework. Therefore, the multi-platform multi-target RFS observation set can be represented as... .

[0017] This embodiment models the motion states, attribute categories, and multi-source signal information measurements of multiple targets. The modeling model is used to calculate the error entropy and equivalent likelihood based on the measurements. In this embodiment, the multi-target tracking task needs to establish a mapping θ relationship between the target state and the measurement set. Using a specific measurement from the corresponding random set of measurements, the likelihood function g for updating the target state is calculated, and the posterior estimate of each target state is solved within a Bayesian estimation framework.

[0018] Integrated processing of signal information within a random finite set framework can effectively improve the accuracy of target kinematic modeling, data association accuracy, and motion state estimation accuracy. This is particularly beneficial in scenarios with missed detections, dense clutter, and multiple targets at close range, where timely detection, stable tracking, and accurate classification based on a single sensor measurement are difficult to achieve. As shown below, the estimated trajectories of two targets overlap or alternate, making it impossible to distinguish between them and failing to meet performance requirements.

[0019] To integrate the measurement of multi-source signals, the dimensions of the state and measurement are first expanded. Assume the radar position measurement is... , It is the azimuth angle. The pitch angle, r For distance, the state vector is x=(x,l). Let l represent the position, velocity, and acceleration states along each coordinate axis, and l be the track label. Introducing attribute measurement amplitude features 'a' and target signal-to-noise ratio 'd', the dimensions of both measurements and states are expanded to obtain augmented measurements. augmented state Target identity (category, attribute) tags and track tags constitute a hybrid tag. After introducing identity tags, the state space is transformed from... Become ,in For identity labeling space. Measurement space is composed of Become ,in This is the attribute measurement space. The target's identity is a static attribute, meaning the target type does not change over time. However, due to the influence of target pose, environmental changes, etc., the target recognition result is represented by a probability vector, indicating the probability that the target belongs to a certain class. To avoid potential misjudgments caused by hard decision-making, we use a probability vector to represent the target type, i.e., soft decision-making.

[0020] Step S2: Based on the target state set and the target observation set, calculate the equivalent position measurement likelihood function using the minimum error entropy algorithm. ,in, It is the measurement error variance matrix of sensor n. It is the measurement error entropy matrix of sensor n.

[0021] The minimum error entropy algorithm used in this invention has a recursive framework. In this embodiment, an iterative algorithm for multi-sensor fusion estimation under non-Gaussian noise is proposed. It is constructed and recursively computed when the hybrid correlation cost is related to the state estimation.

[0022] To improve numerical stability, this embodiment proposes a fusion estimation algorithm within the information filter framework. Assume the Fisher information matrix is... Information vector is The state estimate can be written as The estimation error is The state prediction can be calculated based on the state transition equation. and variance prediction .

[0023] The objective function of error entropy Taking the derivative with respect to the target state x, the optimal estimate is obtained. Satisfy the following equation: ; Among them, the normalized error vector Variables in the formula and The error entropy matrix for the predicted state and the error entropy matrix for multi-sensor measurements, respectively, can be calculated as follows: ; ; in, Represents the Gaussian kernel function. It is the sensor measurement error vector The elements in.

[0024] Under this estimation, the equivalent likelihood function can be obtained as: in, It is the measurement error variance matrix of sensor n. This is the measurement error entropy matrix of sensor n. Under the condition of the equivalent measurement likelihood function, the posterior information matrix of the target motion state can be calculated as: ; in, It is the linearized measurement matrix of sensor n. If the measurement error entropy matrix of sensor n is given, then the posterior estimation vector of the target motion state can be calculated as follows: ; Thus, the posterior state estimate of the target is obtained. .

[0025] Step S3: Based on the equivalent position measurement likelihood function The target motion state model and amplitude feature information are used to calculate the multi-objective joint likelihood function, providing a foundation for calculating the multi-objective posterior state distribution with attribute dimension expansion. For example... Figure 3 As shown, assuming the target identity or category is represented by its expected signal-to-noise ratio d, and introducing the attribute measurement amplitude feature a and the target identity d, and assuming the target motion state x is independent of identity d, the single-target likelihood can be decomposed into: ; The first part of the right-hand side represents the likelihood of the motion state, and the second part represents the likelihood of the attribute state. The attribute likelihood ratio is: .

[0026] Step S4: Introduce attribute measurement amplitude features and target identity, and calculate the multi-target posterior probability density based on the multi-target joint likelihood function.

[0027] The target state under attribute union can be used as a function Therefore, the target prediction state under attribute assistance is: For multi-source signal information measurement, the target state likelihood function under attribute assistance is: ; The first part of the right-hand side represents the multi-source motion state likelihood, including radar range, angle, ESM angle measurement, etc. The multi-source measurement likelihood is equal to the product of the individual measurement likelihoods. (In the context of correlation...) Under the given conditions, the posterior state distribution of the target is: ; ; ; The multi-objective posterior probability density is: ; in, For multi-objective posterior state probability distribution, A set of multi-target track labels. For the predicted multi-target track label space, To establish the mapping relationship between measurements and targets, For each mapping, the probability weights are... For prediction of multiple objectives Label The validity indicator function takes a value of 0 or 1. For mapping Posterior distribution of multi-objective states under certain conditions.

[0028] ; ; ; .

[0029] in, These are the probability weights corresponding to the posterior distribution of multiple objectives under the label-measurement mapping condition. For measuring Z and mapping The validity indicator function for multi-target track labels under certain conditions takes a value of 0 or 1. For mapping Normalized likelihood function of multi-objective state measurement under certain conditions. For a multi-objective posterior distribution, where These are the status and track labels for each target. The target identity tag mainly corresponds to the RCS and echo intensity attributes. Let be the likelihood function for the objective. The track is tagged as The single-objective state normalized measurement likelihood, The detection probability of the target. Let be the likelihood function when the target has a measurement mapping. For a set of multi-objective states, It is the likelihood of the target echo point intensity.

[0030] Step S5: Cluster the posterior probability density of the multi-target targets to obtain the multi-target tracks and track states, thus completing the radar networking multi-target positioning and tracking under complex electromagnetic environments based on minimum error entropy.

[0031] Clustering of multi-target densities yields multi-target tracks and their corresponding states. A multi-Bernoulli stochastic finite set model is employed, and within a Bayesian framework, the updated posterior probability density is assumed to be: ; Multi-target track tags The state parameters below can be simplified to ,in: ; ; .

[0032] Example 2 A radar network multi-target positioning and tracking system based on minimum error entropy in complex electromagnetic environments, the system comprising: The model building module is used to construct a multi-target motion state model based on the target state, state transition matrix, and motion process noise of the target motion, and to generate a target state set and a target observation set based on the multi-target motion state model and random set description.

[0033] First, the target motion process is modeled. In practical applications, due to imperfect prior information and the random maneuvering of the target, establishing a completely accurate target motion model is difficult. This project, based on multiple basic motion models, describes the noise and uncertainty between the actual motion process and the target motion model through motion process noise and multi-model weighting methods. This approximates the actual motion process of the target while facilitating mathematical processing. The target state transition equation is: ; in, for Constant target status, for Constant target status, Here is the state transition matrix. Here is the gain matrix. This represents process noise. Different motion models have different transfer matrices and gain matrices.

[0034] For modeling the motion state of multiple targets, within a finite set statistical framework, the set of all individual target states is considered a set-valued state, while the set of all measurements obtained from a single observation is considered a set-valued measurement. By modeling the set-valued state and set-valued measurements as random finite sets, optimal Bayesian filtering techniques can be used to estimate the time-varying number of multiple targets under conditions of association uncertainty, detection uncertainty, and false alarm clutter, thus deriving a multi-target Bayesian filter.

[0035] Multiple target states and measurements can be represented as sets. The target state set described by a random set (RFS) is as follows: ; As shown above, similarly, the observation set described by RFS is represented as follows: ; Given n objectives with state vectors x1, ..., xn, the multi-objective state random set can be represented as: .

[0036] Therefore, a multi-platform, multi-objective RFS observation set can be represented as This project modeled the motion states, attribute categories, and multi-source signal information measurements of multiple targets. The modeling model was used to calculate the error entropy and equivalent likelihood based on the measurements.

[0037] In this embodiment, the multi-target tracking task needs to establish a mapping θ relationship between the target state and the measurement set, use a specific measurement in the corresponding random set of measurements to calculate the likelihood function g of the target state update, and solve the posterior estimate of each target state in the Bayesian estimation framework.

[0038] Integrated processing of signal information within a framework of random finite sets can effectively improve the accuracy of target kinematic modeling, data association accuracy, and motion state estimation accuracy. This is especially useful in scenarios with missed detections, dense clutter, and multiple targets at close range, where it is difficult to achieve timely detection, stable tracking, and accurate classification based on measurements from a single sensor.

[0039] As shown below, it can be seen that the estimated trajectories of the two targets overlap or alternate, making it impossible to distinguish the targets and making it difficult to meet the target requirements.

[0040] To integrate the measurement of multi-source signals, the dimensions of the state and measurement are first expanded. Assume the radar position measurement is... , It is the azimuth angle. The pitch angle, r For distance, the state vector is x=(x,l). Let l represent the position, velocity, and acceleration states along each coordinate axis, and l be the track label. Introducing attribute measurement amplitude features 'a' and target signal-to-noise ratio 'd', the dimensions of both measurements and states are expanded to obtain augmented measurements. augmented state .

[0041] Target identity (category, attribute) tags and track tags constitute a hybrid tag. After introducing identity tags, the state space is transformed from... Become ,in For identity labeling space. Measurement space is composed of Become ,in This is the attribute measurement space. The target's identity is a static attribute, meaning the target type does not change over time. However, due to the influence of target pose, environmental changes, etc., the target recognition result is represented by a probability vector, indicating the probability that the target belongs to a certain class. To avoid potential misjudgments caused by hard decision-making, we use a probability vector to represent the target type, i.e., soft decision-making.

[0042] The measurement likelihood function module is used to calculate the equivalent position measurement likelihood function based on the target state set and the target observation set using the minimum error entropy algorithm. ,in, It is the measurement error variance matrix of sensor n. It is the measurement error entropy matrix of sensor n.

[0043] like Figure 2 As shown, the minimum error entropy algorithm used in this invention has a recursive framework.

[0044] In this embodiment, an iterative algorithm for multi-sensor fusion estimation under non-Gaussian noise is proposed.

[0045] When the mixed-related costs are associated with the state estimate, they are constructed and recursively calculated.

[0046] To improve numerical stability, this embodiment proposes a fusion estimation algorithm within the information filter framework. Assume the Fisher information matrix is... Information vector is The state estimate can be written as The estimation error is The state prediction can be calculated based on the state transition equation. and variance prediction .

[0047] The objective function of error entropy Taking the derivative with respect to the target state x, the optimal estimate is obtained. Satisfy the following equation: ; Among them, the normalized error vector .

[0048] Variables in the formula and The error entropy matrix for the predicted state and the error entropy matrix for multi-sensor measurements, respectively, can be calculated as follows: ; ; in, Represents the Gaussian kernel function. It is the sensor measurement error vector The elements in.

[0049] Under this estimation, the equivalent likelihood function can be obtained as: in, It is the measurement error variance matrix of sensor n. It is the measurement error entropy matrix of sensor n.

[0050] Under the condition of the equivalent measurement likelihood function, the posterior information matrix of the target's motion state can be calculated as follows: ; in, It is the linearized measurement matrix of sensor n. If the measurement error entropy matrix of sensor n is given, then the posterior estimation vector of the target motion state can be calculated as follows: ; Thus, the posterior state estimate of the target is obtained. .

[0051] The joint likelihood module is used to measure the likelihood function based on the equivalent position. The target motion state model and amplitude feature information are used to calculate the multi-objective joint likelihood function, providing a foundation for calculating the multi-objective posterior state distribution with attribute dimension expansion. For example... Figure 3 As shown, assuming the target identity or category is represented by its expected signal-to-noise ratio d, and introducing the attribute measurement amplitude feature a and the target identity d, and assuming the target motion state x is independent of identity d, the single-target likelihood can be decomposed into: ; The first part of the right-hand side represents the likelihood of the motion state, and the second part represents the likelihood of the attribute state. The attribute likelihood ratio is: .

[0052] The probability density calculation module is used to introduce attribute measurement amplitude features and target identity, and calculate the multi-target posterior probability density based on the multi-target joint likelihood function.

[0053] The target state under attribute union can be used as a function Therefore, the target prediction state under attribute assistance is: For multi-source signal information measurement, the target state likelihood function under attribute assistance is: ; The first part of the right-hand side represents the multi-source motion state likelihood, including radar range, angle, ESM angle measurement, etc. The multi-source measurement likelihood is equal to the product of the individual measurement likelihoods. (In the context of correlation...) Under the given conditions, the posterior state distribution of the target is: ; ; ; The multi-objective posterior probability density is: ; in, For multi-objective posterior state probability distribution, A set of multi-target track labels. For the predicted multi-target track label space, To establish the mapping relationship between measurements and targets, For each mapping, the probability weights are... For prediction of multiple objectives Label The validity indicator function takes a value of 0 or 1. For mapping Posterior distribution of multi-objective states under certain conditions.

[0054] ; ; ; .

[0055] in, These are the probability weights corresponding to the posterior distribution of multiple objectives under the label-measurement mapping condition. For measuring Z and mapping The validity indicator function for multi-target track labels under certain conditions takes a value of 0 or 1. For mapping Normalized likelihood function of multi-objective state measurement under certain conditions. For a multi-objective posterior distribution, where These are the status and track labels for each target. These are target identity tags, primarily corresponding to RCS and echo intensity attributes. Let be the likelihood function for the objective. The track is tagged as The single-objective state normalized measurement likelihood, The detection probability of the target. Let be the likelihood function when the target has a measurement mapping. For a set of multi-objective states, It is the likelihood of the target echo point intensity.

[0056] The target localization and tracking module is used to cluster the posterior probability density of the multi-targets to obtain the multi-target tracks and track states, and to complete the multi-target localization and tracking of radar networks in complex electromagnetic environments based on minimum error entropy.

[0057] Clustering of multi-target densities yields multi-target tracks and their corresponding states. A multi-Bernoulli stochastic finite set model is employed, and within a Bayesian framework, the updated posterior probability density is assumed to be: ; Multi-target track tags The state parameters below can be simplified to ,in: ; ; .

[0058] This disclosure is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A multi-target localization and tracking method for radar networks under complex electromagnetic environments based on minimum error entropy, characterized in that, The method specifically includes: Step S1: Construct a multi-target motion state model based on the target state, state transition matrix, and motion process noise of the target motion; and generate a target state set and a target observation set based on the multi-target motion state model and random set description. Step S2: Based on the target state set and the target observation set, calculate the equivalent position measurement likelihood function using the minimum error entropy algorithm; Step S3: Calculate the multi-target joint likelihood function based on the equivalent position measurement likelihood function, the target motion state model, and amplitude feature information; Step S4: Introduce attribute measurement amplitude features and target identity, and calculate the multi-target posterior probability density based on the multi-target joint likelihood function; Step S5: Cluster the posterior probability density of the multi-target targets to obtain the multi-target tracks and track states, thus completing the radar network multi-target positioning and tracking under complex electromagnetic environment based on minimum error entropy.

2. The radar networking multi-target localization and tracking method based on minimum error entropy in complex electromagnetic environments as described in claim 1, characterized in that, In step S1, the formula for constructing a multi-target motion state model based on the target state, state transition matrix, and motion process noise is as follows: ； in, for Constant target status, for Constant target status, Here is the state transition matrix. Here is the gain matrix. This is process noise.

3. The radar networking multi-target positioning and tracking method based on minimum error entropy in complex electromagnetic environments, as described in claim 2, is characterized in that... In step S1, generating the target state set and target observation set based on the multi-target motion state model and random set description specifically involves: Target state set: ； Target observation set: 。 4. The radar networking multi-target localization and tracking method based on minimum error entropy in complex electromagnetic environments as described in claim 1, characterized in that, In step S4, the multi-objective posterior probability density is specifically as follows: ； in, For multi-objective posterior state probability distribution, A set of multi-target track labels. For the predicted multi-target track label space, To establish the mapping relationship between measurements and targets, For each mapping, the probability weights are... For predicting multi-target X-labels The validity indicator function takes a value of 0 or 1. For mapping Posterior distribution of multi-objective states under given conditions It is a set of multi-objective states.

5. The radar networking multi-target localization and tracking method based on minimum error entropy in complex electromagnetic environments as described in claim 4, characterized in that, In the multi-objective posterior probability density formula, in, These are the probability weights corresponding to the posterior distribution of multiple objectives under the label-measurement mapping condition. For measuring Z and mapping The validity indicator function for multi-target track labels under certain conditions takes a value of 0 or 1. For mapping Normalized likelihood function of multi-objective state measurement under certain conditions. For a multi-objective posterior distribution, where These are the status and track labels for each target. d These are target identity tags, primarily corresponding to RCS and echo intensity attributes. Let be the likelihood function for the objective. The track is tagged as l The single-objective state normalized measurement likelihood, The detection probability of the target. Let be the likelihood function when the target has a measurement mapping. It is the likelihood of the target echo point intensity.

6. A radar network multi-target positioning and tracking system based on minimum error entropy in complex electromagnetic environments, the system being used to implement the radar network multi-target positioning and tracking method according to any one of claims 1-5, characterized in that, The system includes: The model building module is used to construct a multi-target motion state model based on the target state, state transition matrix, and motion process noise of the target motion, and to generate a target state set and a target observation set based on the multi-target motion state model and random set description. The measurement likelihood function module is used to calculate the equivalent position measurement likelihood function based on the target state set and the target observation set using the minimum error entropy algorithm. The joint likelihood module is used to calculate a multi-objective joint likelihood function based on the equivalent position measurement likelihood function, the target motion state model, and amplitude feature information. The probability density calculation module is used to introduce attribute measurement amplitude features and target identity, and calculate the multi-target posterior probability density based on the multi-target joint likelihood function; The target localization and tracking module is used to cluster the posterior probability density of the multi-targets to obtain the multi-target tracks and track states, and to complete the multi-target localization and tracking of radar networks in complex electromagnetic environments based on minimum error entropy.

7. The radar network multi-target positioning and tracking system based on minimum error entropy in complex electromagnetic environments as described in claim 6, characterized in that, In the model building module, the formula for the multi-objective motion state model is: ； in, for Constant target status, for Constant target status, Here is the state transition matrix. Here is the gain matrix. This is process noise.

8. The radar network multi-target positioning and tracking system based on minimum error entropy in complex electromagnetic environments as described in claim 7, characterized in that, In the model building module: Target state set: ； Target observation set: 。

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