Radar networking multi-target positioning and tracking method and system in complex electromagnetic environment based on minimum error entropy

Abstract

The invention belongs to the technical field of radar networking fusion positioning and tracking, and discloses a radar networking multi-target positioning and tracking method and system in a complex electromagnetic environment based on minimum error entropy, and the method comprises the steps: constructing a multi-target motion state model based on the target state of target motion, a 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 the random set description; calculating an equivalent position measurement likelihood function by using a minimum error entropy algorithm based on the target state set and the target observation set; calculating a multi-target joint likelihood function based on the equivalent position measurement likelihood function, the target motion state model and the amplitude feature information; calculating a multi-target posterior probability density based on a multi-target joint likelihood function; and clustering the multi-target posterior probability density to obtain a multi-target track and a multi-target track state, and completing radar networking multi-target positioning tracking in the complex electromagnetic environment based on the minimum error entropy.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar networking fusion positioning and tracking, and in particular relates to a radar networking multi-target positioning and tracking method and system under a complex electromagnetic environment based on minimum error entropy. Background Art

[0002] In modern combat scenarios, with the emergence of high-tech equipment such as hypersonic and ultra-stealth targets and their performance greatly improved, as well as the complex electromagnetic environment of the battlefield, single radar information processing systems are gradually unable to adapt to the requirements of multi-target air situation in modern warfare in terms of information processing speed, information processing quality, information acquisition capacity and reliability. In addition, the performance of radar systems will be significantly reduced in the face of powerful deception and suppression interference on the battlefield today, and in severe cases, they will fail completely, and the measurement will be reflected in data wild values, clutter and missed detection. Since distributed radar networking technology can essentially improve the anti-interference capability and the information processing quality of multi-target signals under high density, it is crucial to study radar networking fusion positioning and tracking in complex electromagnetic environments. Summary of the invention

[0003] To solve the above problems, the present invention provides a radar network multi-target positioning and tracking method in a complex electromagnetic environment based on minimum error entropy, the method comprising:

[0004] Step S1, constructing a multi-target motion state model based on the target state, state transfer matrix, and motion process noise of the target motion, and generating a target state set and a target observation set based on the multi-target motion state model and random set description;

[0005] Step S2, based on the target state set and the target observation set, using a minimum error entropy algorithm to calculate an equivalent position measurement likelihood function;

[0006] Step S3, calculating a multi-target joint likelihood function based on the equivalent position measurement likelihood function, the target motion state model and the amplitude feature information;

[0007] Step S4, introducing the attribute measurement amplitude feature and the target identity, and calculating the multi-target posterior probability density based on the multi-target joint likelihood function;

[0008] Step S5: clustering the multi-target posterior probability density to obtain the multi-target track and multi-target track status, and completing the radar network multi-target positioning and tracking in a complex electromagnetic environment based on minimum error entropy.

[0009] Optionally, in step S1, the formula for constructing the multi-target motion state model based on the target state, state transfer matrix, and motion process noise of the target motion is:

[0010] X(k+1)=FX(k)+ΓW(k);

[0011] Among them, X(k+1) is the target state at time k+1, X(k) is the target state at time k, F is the state transfer matrix, Γ is the gain matrix, and W(k) is the process noise.

[0012] Optionally, in step S1, generating a target state set and a target observation set based on the multi-target motion state model and the random set description is specifically:

[0013] Target state set:

[0014]

[0015] Target observation set:

[0016]

[0017] Optionally, in step S4, the multi-target posterior probability density is specifically:

[0018]

[0019] in, is the multi-target posterior state probability distribution, is a set of multi-target track labels, is the predicted multi-target track label space, is the mapping relationship between measurement and target, is the probability weight corresponding to each mapping, is the predicted multi-target X label The legitimacy indicator function takes the value of 0 or 1, p (θ) is the posterior distribution of multiple target states under the mapping Θ condition.

[0020] Optionally, in the multi-objective posterior probability density formula:

[0021]

[0022]

[0023] Among them, w(I,ξ,θ) is the probability weight corresponding to the multi-target posterior distribution under the label and measurement mapping condition, is the legitimacy indicator function of the multi-target track labels under the conditions of measurement Z and mapping Θ, and its value is 0 or 1. is the normalized likelihood function of multi-target state measurement under mapping Θ, is the multi-target posterior distribution, where x, l are the state and track labels of each target, respectively, and d is the target identity label, which mainly corresponds to the RCS and echo intensity attributes. is the likelihood function of the target, is the normalized measurement likelihood of a single target state with track label l, is the detection probability of the target, is the likelihood function when the target exists in the measurement mapping, is a set of multiple target states, is the target echo trace intensity likelihood.

[0024] The present invention also discloses a radar network multi-target positioning and tracking system in a complex electromagnetic environment based on minimum error entropy, the system comprising:

[0025] A model building module is used to build a multi-target motion state model based on the target state, state transfer 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;

[0026] A measurement likelihood function module, used to calculate an equivalent position measurement likelihood function using a minimum error entropy algorithm based on the target state set and the target observation set;

[0027] A joint likelihood module, used to calculate a multi-target joint likelihood function based on the equivalent position measurement likelihood function, the target motion state model and amplitude feature information;

[0028] The probability density calculation module is used to introduce the attribute measurement amplitude characteristics and target identity, and calculate the multi-target posterior probability density based on the multi-target joint likelihood function;

[0029] The target positioning and tracking module is used to cluster the multi-target posterior probability density to obtain the multi-target track and multi-target track status, and complete the radar network multi-target positioning and tracking in a complex electromagnetic environment based on minimum error entropy.

[0030] Optionally, in the model building module, the multi-target motion state model formula is:

[0031] X(k+1)=FX(k)+ΓW(k);

[0032] Among them, X(k+1) is the target state at time k+1, X(k) is the target state at time k, F is the state transfer matrix, Γ is the gain matrix, and W(k) is the process noise.

[0033] Optionally, in the Model Building module:

[0034] Target state set:

[0035]

[0036] Target observation set:

[0037]

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] The present invention proposes a radar network multi-target fusion positioning and tracking method in a complex electromagnetic environment based on error entropy, which can perceive scenes in complex electromagnetic environments such as non-Gaussian noise, outliers, and missed detections. The existing methods have a serious impact on the tracking accuracy reduction in non-Gaussian noise environments such as outliers. The patented method adopts a multi-target fusion tracking method based on error entropy. Based on the mixed Gaussian kernel function, the error distribution in the radar network measurement is learned and approximated, and the optimization objective function of the mixed error entropy is established, so as to obtain the optimal estimate of the target state under the minimum error entropy criterion. Furthermore, the amplitude information in the radar measurement is used to improve the ability to distinguish between target measurement and interference such as clutter, improve the correlation accuracy of the target and measurement, and obtain the joint likelihood function of the multi-target position and amplitude measurement. Then, based on the multi-target random finite set model, the joint posterior distribution of the multi-target state and amplitude is obtained under the Bayesian estimation framework. In order to reduce the complexity of multi-target track estimation, this patent finally gives a multi-target density aggregation method, which obtains the track of each target through clustering, avoids the exponential growth of computational complexity caused by the uncertainty of multi-target state and measurement association, and improves the real-time performance of radar network data processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0041] Figure 1 A method step diagram of a clutter density adaptive radar and communication detection multi-target point trace fusion tracking method in an amphibious environment according to an embodiment of the present invention;

[0042] Figure 2 A schematic diagram of multi-target state and measurement modeling based on a random finite set of labels according to an embodiment of the present invention;

[0043] Figure 3 This is the error entropy state estimation and equivalent likelihood calculation process of an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0045] Embodiment 1

[0046] like Figure 1 As shown, this embodiment provides a radar network multi-target positioning and tracking method in a complex electromagnetic environment based on minimum error entropy, and the method includes:

[0047] Step S1, constructing a multi-target motion state model based on the target state, state transfer matrix, and motion process noise of the target motion, and generating a target state set and a target observation set based on the multi-target motion state model and random set description.

[0048] First, the target motion process is modeled. In practical applications, it is difficult to establish a completely accurate target motion model due to the imperfection of prior information and the random maneuver of the target. This project is based on a variety of basic motion models. It describes the noise and uncertainty between the actual motion process and the target motion model through motion process noise and multi-model weighting methods. While approximating the actual motion process of the target, it is also convenient for mathematical processing. The target state transfer equation is:

[0049] X(k+1)=FX(k)+GW(k);

[0050] Among them, X(k+1) is the target state at time k+1, X(k) is the target state at time k, F is the state transfer matrix, G is the gain matrix, and W(k) is the process noise. Different motion models have different transfer matrices and gain matrices. For the modeling of multi-target motion states, all individual target state sets are regarded as a set-valued state in the finite set statistics framework, and all measurement value sets obtained from one observation are regarded as set-valued measurements. After modeling the set-valued state and set-valued measurement as random finite sets, the optimal Bayesian filtering technology can be used to realize the time-varying number of multi-target estimation under the conditions of association uncertainty, detection uncertainty and false alarm clutter, and the multi-target Bayesian filter is derived.

[0051] Multiple target states and measurements can be expressed in the form of a set. The target state set described by a random set (RFS) is expressed as follows:

[0052]

[0053] The state space is shown above. Similarly, the observation set described by RFS is expressed as follows:

[0054]

[0055] The state vectors of the n targets are x1,...,xn respectively, and the multi-target state random set can be expressed as X = {x1,...,xn n In this embodiment, the multi-target tracking task is to establish a mapping θ relationship between the target state and the measurement set, use a specific measurement in the corresponding measurement random set 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. Therefore, the multi-platform multi-target RFS observation set can be expressed as {Z1,...Z m}.

[0056] This embodiment models the multi-target motion states, attribute categories, and multi-source signal information measurements, and 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, and use a specific measurement in the corresponding measurement random set 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.

[0057] Integrated processing of signal information within the framework of random finite sets can effectively improve the accuracy of target kinematic modeling, data association accuracy, and motion state estimation accuracy, especially in conditions such as missed detection, dense clutter, and close-range multi-target scenarios, where it is difficult to achieve timely detection, stable tracking, and accurate classification based on single sensor measurements. The following is the Bayesian filter tracking result of two close-range targets. It can be seen that the estimated tracks of the two targets overlap or alternate with each other, making it impossible to distinguish the targets and difficult to meet the index requirements.

[0058] In order to integrate the measurement of multi-source signal information, the state and measurement are first expanded. Assume that the radar position measurement is z = θ a ,θ e ,r T ,θ a is the azimuth angle, θ e is the pitch angle, r is the distance, the state vector x=(x,l), is the position, velocity and acceleration state of each coordinate axis, and l is the track label. Introducing the attribute measurement amplitude feature a and the target signal-to-noise ratio d, the measurement and state are expanded to obtain the augmented measurement Augmented State The target identity (category, attribute) label and the track label form a mixed label (d, l). After the introduction of the identity label, the state space is composed of becomes in is the identity label space. The measurement space is becomes in is the attribute measurement space. The identity of the target is a static attribute, that is, the target type does not change over time, but due to the influence of the target posture and environmental changes, the target recognition result is expressed in the form of a probability vector to represent the possibility that the target belongs to a certain category. In order to avoid the misjudgment caused by hard decisions, the target type is expressed by probability vector, that is, soft decision.

[0059] Step S2: Based on the target state set and the target observation set, use the minimum error entropy algorithm to calculate the equivalent position measurement likelihood function Among them, R k,n is the measurement error variance matrix of sensor n, Λ k·n is the measurement error entropy matrix of sensor n.

[0060] The minimum error entropy algorithm used in the present invention has a recursive framework. In this embodiment, an iterative algorithm for multi-sensor fusion estimation under non-Gaussian noise is proposed. When the mixed correlation cost is related to the state estimation, it is constructed and recursively calculated.

[0061] In order to improve numerical stability, this embodiment proposes a fusion estimation algorithm under the information filter framework. Assume that the Fisher information matrix is ​​V k-1 The information vector is v k-1 , the state estimate can be written as The estimated error is The state prediction can be calculated based on the state transfer equation And the variance prediction P k|k-1 .

[0062] The error entropy objective function x k Derivative the target state x, optimal estimate Satisfies the following equation:

[0063]

[0064] Where, the normalized error vector Variables in formulas and A k,n They are the error entropy matrix of the predicted state and the error entropy matrix of multi-sensor measurement, which can be calculated as:

[0065]

[0066] Among them, G σ represents the Gaussian kernel function, is the sensor measurement error vector ζ k，n The elements in .

[0067] Under this estimation, the equivalent likelihood function can be obtained as:

[0068]

[0069] Among them, R k，n is the measurement error variance matrix of sensor n, Λ k·n is the measurement error entropy matrix of sensor n. Under the condition of equivalent measurement likelihood function, the posterior information matrix of the target motion state can be calculated as:

[0070]

[0071] in, is the linearized measurement matrix of sensor n, Λ k，n is the measurement error entropy matrix of sensor n, then the target motion state posterior estimation vector can be calculated as:

[0072]

[0073] Thus, we can obtain the posterior state estimate of the target

[0074] Step S3: Based on the equivalent position measurement likelihood function The target motion state model and amplitude feature information calculate the multi-target joint likelihood function, providing a basis for the calculation of the multi-target posterior state distribution of attribute expansion. Figure 3 As shown in Figure 1, assuming that the target identity or category is represented by its expected signal-to-noise ratio d, the attribute measurement amplitude feature a and the target identity d are introduced. Assuming that the target motion state x is independent of the identity d, the single target likelihood can be decomposed into:

[0075]

[0076] The former on the right side of the equation is the motion state likelihood, the latter is the attribute state likelihood, and the attribute likelihood ratio is:

[0077]

[0078] Step S4: Introduce attribute measurement amplitude features and target identity, and calculate multi-target posterior probability density based on multi-target joint likelihood function.

[0079] The target state under the attribute union can be expressed by the function p(x , d) indicates that, then, the target prediction state under attribute assistance is:

[0080]

[0081] For multi-source signal information measurement, the attribute-assisted target state likelihood function is:

[0082]

[0083] The former on the right side of the equation is the multi-source motion state likelihood, including radar distance, angle, ESM angle measurement, etc. The multi-source measurement likelihood is equal to the product of the likelihoods of each measurement. Under the condition of association q, the target posterior state distribution is:

[0084]

[0085] The multi-target posterior probability density is:

[0086]

[0087] in, is the multi-target posterior state probability distribution, is a set of multi-target track labels, is the predicted multi-target track label space, is the mapping relationship between measurement and target, is the probability weight corresponding to each mapping, For multi-target prediction Label The legality indicator function takes the value of 0 or 1. is the posterior distribution of multiple target states under the mapping Θ condition.

[0088]

[0089] Among them, w (I,q) is the probability weight corresponding to the multi-target posterior distribution under the label and measurement mapping condition, is the legitimacy indicator function of the multi-target track labels under the conditions of measurement Z and mapping Θ, and its value is 0 or 1. is the normalized likelihood function of multi-target state measurement under mapping Θ, is the multi-target posterior distribution, where x and l are the status and track labels of each target respectively, and d is the target identity label mainly corresponding to the RCS and echo intensity attributes. is the likelihood function of the target, is the normalized measurement likelihood of a single target state with track label l, P d t (x,l) is the detection probability of the target, is the likelihood function when the target exists in the measurement mapping, is a set of multiple target states, is the target echo trace intensity likelihood.

[0090] Step S5: clustering the multi-target posterior probability density to obtain the multi-target track and multi-target track status, and completing the radar network multi-target positioning and tracking in a complex electromagnetic environment based on minimum error entropy.

[0091] Cluster the multi-target density to obtain the multi-target tracks and corresponding states. Using the multi-Bernoulli random finite set model, assuming that under the Bayesian framework, the updated posterior probability density is:

[0092]

[0093] The state parameters under the multi-target track label (l) can be simplified to π = {(r (l) ,p (l) )},in:

[0094]

[0095] Embodiment 2

[0096] A radar network multi-target positioning and tracking system in a complex electromagnetic environment based on minimum error entropy, the system comprising:

[0097] The model building module is used to build a multi-target motion state model based on the target state, state transfer 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.

[0098] First, the target motion process is modeled. In practical applications, it is difficult to establish a completely accurate target motion model due to the imperfection of prior information and the random maneuver of the target. This project is based on a variety of basic motion models. It describes the noise and uncertainty between the actual motion process and the target motion model through motion process noise and multi-model weighting methods. While approximating the actual motion process of the target, it is also convenient for mathematical processing. The target state transfer equation is:

[0099] X(k+1)=FX(k)+GW(k);

[0100] Among them, X(k+1) is the target state at time k+1, X(k) is the target state at time k, F is the state transfer matrix, G is the gain matrix, and W(k) is the process noise. Different motion models have different transfer matrices and gain matrices.

[0101] For the modeling of multi-target motion states, the set of all individual target states is regarded as a set-valued state in the finite set statistics framework, and the set of all measurement values ​​obtained from one observation is regarded as a set-valued measurement. After modeling the set-valued state and set-valued measurement as random finite sets, the optimal Bayesian filtering technology can be used to realize the time-varying number of multi-target estimation under the conditions of association uncertainty, detection uncertainty and false alarm clutter, and the multi-target Bayesian filter can be derived.

[0102] Multiple target states and measurements can be expressed in the form of a set. The target state set described by a random set (RFS) is expressed as follows:

[0103]

[0104] The state space is shown above. Similarly, the observation set described by RFS is expressed as follows:

[0105]

[0106] The state vectors of the n targets are x1,...,xn respectively, and the multi-target state random set can be expressed as X = {x1,...,xn n}.

[0107] Therefore, the multi-platform multi-target RFS observation set can be expressed as {Z1,...Z m This project models the motion states, attribute categories, and information measurements of multiple targets and multiple sources of signals. The modeling model is used to calculate error entropy and equivalent likelihood based on the measurements.

[0108] 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 measurement random set 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.

[0109] Integrated processing of signal information within the framework of random finite sets can effectively improve the accuracy of target kinematic modeling, data association accuracy, and motion state estimation accuracy, especially under conditions such as missed detection, dense clutter, and close-range multi-target scenarios, where it is difficult to achieve timely detection, stable tracking, and accurate classification based on single sensor measurements.

[0110] The following are the Bayesian filtering tracking results of two close targets. It can be seen that the estimated tracks of the two targets overlap or alternate with each other, making it impossible to distinguish the targets and difficult to meet the index requirements.

[0111] In order to integrate the measurement of multi-source signal information, the state and measurement are first expanded. Assume that the radar position measurement is z = θ a ,θ e ,r T ,θ a is the azimuth angle, θ e is the pitch angle, r is the distance, and the state vector is the position, velocity and acceleration state of each coordinate axis, and l is the track label. Introducing the attribute measurement amplitude feature a and the target signal-to-noise ratio d, the measurement and state are expanded to obtain the augmented measurement Augmented State

[0112] The target identity (category, attribute) label and the track label form a mixed label (d, l). After the introduction of the identity label, the state space is composed of becomes in is the identity label space. The measurement space is becomes in is the attribute measurement space. The identity of the target is a static attribute, that is, the target type does not change over time, but due to the influence of the target posture and environmental changes, the target recognition result is expressed in the form of a probability vector to represent the possibility that the target belongs to a certain category. In order to avoid the misjudgment caused by hard decisions, the target type is expressed by probability vector, that is, soft decision.

[0113] A 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 Among them, R k,n is the measurement error variance matrix of sensor n, Λ k·n is the measurement error entropy matrix of sensor n.

[0114] like Figure 2 As shown, the minimum error entropy algorithm used in the present invention has a recursive framework.

[0115] In this embodiment, an iterative algorithm for multi-sensor fusion estimation under non-Gaussian noise is proposed.

[0116] When a mixture-dependent cost is associated with the state estimate, it is constructed and recursively computed.

[0117] In order to improve numerical stability, this embodiment proposes a fusion estimation algorithm under the information filter framework. Assume that the Fisher information matrix is ​​V k-1 The information vector is v k-1 , the state estimate can be written as The estimated error is The state prediction can be calculated based on the state transfer equation And the variance prediction P k|k-1 .

[0118] The error entropy objective function x k Derivative the target state x, optimal estimate Satisfies the following equation:

[0119]

[0120] Where, the normalized error vector

[0121] Variables in formulas and Λ k，n They are the error entropy matrix of the predicted state and the error entropy matrix of multi-sensor measurement, which can be calculated as:

[0122]

[0123] Among them, G σ represents the Gaussian kernel function, is the sensor measurement error vector ζ k,n The elements in .

[0124] Under this estimation, the equivalent likelihood function can be obtained as:

[0125]

[0126] Among them, R k，n is the measurement error variance matrix of sensor n, Λ k·n is the measurement error entropy matrix of sensor n.

[0127] Under the condition of equivalent measurement likelihood function, the posterior information matrix of the target motion state can be calculated as:

[0128]

[0129] in, is the linearized measurement matrix of sensor n, Λ k，n is the measurement error entropy matrix of sensor n, then the target motion state posterior estimation vector can be calculated as:

[0130]

[0131] Thus, we can obtain the posterior state estimate of the target

[0132] A joint likelihood module for measuring the likelihood function based on the equivalent position The target motion state model and amplitude feature information calculate the multi-target joint likelihood function, providing a basis for the calculation of the multi-target posterior state distribution of attribute expansion. Figure 3 As shown in Figure 1, assuming that the target identity or category is represented by its expected signal-to-noise ratio d, the attribute measurement amplitude feature a and the target identity d are introduced. Assuming that the target motion state x is independent of the identity d, the single target likelihood can be decomposed into:

[0133]

[0134] The former on the right side of the equation is the motion state likelihood, the latter is the attribute state likelihood, and the attribute likelihood ratio is:

[0135]

[0136] The probability density calculation module is used to introduce the attribute measurement amplitude characteristics and target identity, and calculate the multi-target posterior probability density based on the multi-target joint likelihood function.

[0137] The target state under the attribute union can be expressed by the function p(x , d) indicates that, then, the target prediction state under attribute assistance is:

[0138]

[0139] For multi-source signal information measurement, the attribute-assisted target state likelihood function is:

[0140]

[0141] The former on the right side of the equation is the multi-source motion state likelihood, including radar distance, angle, ESM angle measurement, etc. The multi-source measurement likelihood is equal to the product of the likelihoods of each measurement. Under the condition of association q, the target posterior state distribution is:

[0142]

[0143] The multi-target posterior probability density is:

[0144]

[0145] in, is the multi-target posterior state probability distribution, is a set of multi-target track labels, is the predicted multi-target track label space, is the mapping relationship between measurement and target, is the probability weight corresponding to each mapping, For multi-target prediction Label The legality indicator function takes the value of 0 or 1. is the posterior distribution of multiple target states under the mapping Θ condition.

[0146]

[0147]

[0148] Among them, w(I, ξ, θ) is the probability weight corresponding to the multi-target posterior distribution under the label and measurement mapping condition, is the legitimacy indicator function of the multi-target track labels under the conditions of measurement Z and mapping Θ, and its value is 0 or 1. is the normalized likelihood function of multi-target state measurement under mapping θ, is the multi-target posterior distribution, where x, l are the state and track labels of each target, respectively, and d is the target identity label, which mainly corresponds to the RCS and echo intensity attributes. is the likelihood function of the target, is the normalized measurement likelihood of a single target state with track label l, is the detection probability of the target, is the likelihood function when the target exists in the measurement mapping, is a set of multiple target states, is the target echo trace intensity likelihood.

[0149] The target positioning and tracking module is used to cluster the multi-target posterior probability density to obtain the multi-target track and multi-target track status, and complete the radar network multi-target positioning and tracking in a complex electromagnetic environment based on minimum error entropy.

[0150] Cluster the multi-target density to obtain the multi-target tracks and corresponding states. Using the multi-Bernoulli random finite set model, assuming that under the Bayesian framework, the updated posterior probability density is:

[0151]

[0152] The state parameters under the multi-target track label (l) can be simplified to π = {(r (l) ,p (l) )},in:

[0153]

[0154] The embodiments of the present disclosure are 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 the embodiments of the present disclosure should be included in the scope of protection of the present disclosure.

Claims

1. A radar network multi-target positioning and tracking method in a complex electromagnetic environment based on minimum error entropy, characterized in that: The method specifically comprises: Step S1, constructing a multi-target motion state model based on the target state, state transfer matrix, and motion process noise of the target motion, and generating 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, using a minimum error entropy algorithm to calculate an equivalent position measurement likelihood function; Step S3, calculating a multi-target joint likelihood function based on the equivalent position measurement likelihood function, the target motion state model and the amplitude feature information; Step S4, introducing the attribute measurement amplitude feature and the target identity, and calculating the multi-target posterior probability density based on the multi-target joint likelihood function; Step S5: clustering the multi-target posterior probability density to obtain the multi-target track and multi-target track status, and completing the radar network multi-target positioning and tracking in a complex electromagnetic environment based on minimum error entropy.

2. The radar network multi-target positioning and tracking method based on minimum error entropy in a complex electromagnetic environment according to claim 1 is characterized in that: In step S1, the formula for constructing a multi-target motion state model based on the target state, state transfer matrix, and motion process noise of the target motion is: X(k+1)=FX(k)+ΓW(k); Among them, X(k+1) is the target state at time k+1, X(k) is the target state at time k, F is the state transfer matrix, Γ is the gain matrix, and W(k) is the process noise.

3. The radar network multi-target positioning and tracking method based on minimum error entropy in a complex electromagnetic environment according to claim 2 is characterized in that: In the step S1, generating a target state set and a target observation set based on the multi-target motion state model and the random set description is specifically as follows: Target state set: Target observation set:

4. The radar network multi-target positioning and tracking method based on minimum error entropy in a complex electromagnetic environment according to claim 1 is characterized in that: In step S4, the multi-target posterior probability density is specifically: in, is the multi-target posterior state probability distribution, is a set of multi-target track labels, is the predicted multi-target track label space, is the mapping relationship between measurement and target, is the probability weight corresponding to each mapping, is the predicted multi-target X label The legitimacy indicator function takes the value of 0 or 1, p (θ) is the posterior distribution of multiple target states under the mapping Θ condition.

5. The radar network multi-target positioning and tracking method based on minimum error entropy in a complex electromagnetic environment according to claim 4 is characterized in that: In the multi-target posterior probability density formula, Among them, w (I，ξ，θ) is the probability weight corresponding to the multi-target posterior distribution under the label and measurement mapping condition, is the legitimacy indicator function of the multi-target track labels under the conditions of measurement Z and mapping Θ, and its value is 0 or 1. is the normalized likelihood function of multi-target state measurement under mapping Θ, is the multi-target posterior distribution, where x, l are the state and track labels of each target, respectively, and d is the target identity label, which mainly corresponds to the RCS and echo intensity attributes. is the likelihood function of the target, is the normalized measurement likelihood of a single target state with track label l, is the detection probability of the target, is the likelihood function when the target exists in the measurement mapping, is a set of multiple target states, is the target echo trace intensity likelihood.

6. A radar network multi-target positioning and tracking system in a complex electromagnetic environment based on minimum error entropy, the system is used to implement the radar network multi-target positioning and tracking according to any one of claims 1 to 5, characterized in that: The system includes: A model building module is used to build a multi-target motion state model based on the target state, state transfer 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; A measurement likelihood function module, used to calculate an equivalent position measurement likelihood function using a minimum error entropy algorithm based on the target state set and the target observation set; A joint likelihood module, used to calculate a multi-target 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 the attribute measurement amplitude characteristics and target identity, and calculate the multi-target posterior probability density based on the multi-target joint likelihood function; The target positioning and tracking module is used to cluster the multi-target posterior probability density to obtain the multi-target track and multi-target track status, and complete the radar network multi-target positioning and tracking in a complex electromagnetic environment based on minimum error entropy.

7. The radar network multi-target positioning and tracking system based on minimum error entropy in a complex electromagnetic environment according to claim 6, characterized in that: In the model building module, the multi-target motion state model formula is: X(k+1)=FX(k)+ΓW(k); Among them, X(k+1) is the target state at time k+1, X(k) is the target state at time k, F is the state transfer matrix, Γ is the gain matrix, and W(k) is the process noise.

8. The radar network multi-target positioning and tracking system based on minimum error entropy in a complex electromagnetic environment according to claim 7, characterized in that: In the model building module: Target state set: Target observation set:

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