Multi-extended target tracking method based on radar resource allocation

Abstract

The invention discloses a multi-extended target tracking method based on radar resource allocation, and the method comprises the steps: constructing a radar network non-cooperative game model according to the joint geometric precision attenuation factor of each extended target, carrying out the allocation of the extended targets of radar tracking, and obtaining an optimal radar tracking target allocation result; a radar network non-cooperative game model is constructed, a distribution problem is modeled as a multi-radar competition and cooperation relationship, and contour characteristics of an extended target are optimized and tracked, so that quicker response is realized, the resource utilization rate is optimized, and the accuracy and real-time performance of target tracking are improved; and after the distributed extended targets are measured by using the radars, constructing a joint association vector according to measurement results of the extended targets, obtaining joint states obtained by tracking the different extended targets by the radars, and performing fusion to obtain fusion results of the different extended targets so as to complete tracking of the multiple extended targets.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar resource management and multi-extended target tracking, and particularly relates to a multi-extended target tracking method based on radar resource allocation. Background Art

[0002] Radar resource management and multi-target tracking technologies are important research directions in modern radar systems. With the increasing demand for multi-extended target tracking in complex environments, traditional radar resource allocation and tracking methods face many challenges. Traditional target tracking methods usually assume that the target is a point target, ignoring the complex geometric characteristics of extended targets, which may lead to an increase in the error of target state estimation. In a complex clutter environment, the presence of multiple extended targets significantly increases the difficulty of radar in target association, resource allocation, and signal processing. Summary of the Invention

[0003] The purpose of the present invention is to provide a multi-extended target tracking method based on radar resource allocation.

[0004] The present invention provides a multi-extended target tracking method based on radar resource allocation, which includes the following steps:

[0005] Step 1: Obtain the combined geometric dilution of precision MGDOP of different extended targets respectively k , and its expression is:

[0006]

[0007] Where W is the number of key points on the shape contour of the extended target; M k is the number of radars tracking the extended target k; r ij , r i'j , r i”j are the distances between the radar and the contour key point j; α ij , α i'j , α i”j are the angles between the line connecting the radar and the contour key point j and the reference direction;

[0008] Construct a non-cooperative game model of the radar network to allocate the extended targets tracked by the radar, and obtain the optimal radar tracking target allocation result; k

[0009] Step 2: Use the radar to measure the allocated extended targets to obtain the measurement results of the extended targets;

[0010] Step 3: Construct a joint correlation vector; construct a factor graph for multi-extended target tracking based on the joint correlation vector, and predict and update the joint state of the extended target according to the factor graph to obtain the joint state at the current moment;

[0011] Step 4: Fuse the joint states obtained by different radars for tracking the same extended target to obtain the fusion result of multi-extended targets;

[0012] Step 5: Repeat Steps 1 to 4 to obtain the fusion results of different extended targets at different moments and complete the tracking of multi-extended targets.

[0013] Preferably, in Step 1, the objective function of the constructed non-cooperative game model of the radar network is:

[0014]

[0015] where U is the benefit; K i is the number of extended targets tracked by radar i; n max is the maximum threshold of the number of extended targets tracked by a single radar; n min is the minimum threshold of the number of radars tracking a single extended target; s ik is the tracking strategy of radar i for extended target k; M is the number of radars; K is the number of extended targets.

[0016] Preferably, in Step 1, the joint state includes the motion state and contour state of the extended target; the contour state of the extended target is constructed with the smallest ellipse containing the contour of the extended target where are the major semi-axis and minor semi-axis corresponding to the contour ellipse of extended target j at the current moment t, respectively; is the contour orientation angle.

[0017] Preferably, in Step 1, the endpoints of the major axis and minor axis of the ellipse are selected as the contour key points.

[0018] Preferably, in Step 1, the method for obtaining the optimal radar tracking target allocation result is as follows:

[0019] a. Set the initial tracking strategy of each radar i

[0020] b. Obtain the tracking strategy of radar i after p iterations

[0021]

[0022] where S is the strategy set of all radars; S i is the tracking strategy of radar i; is the tracking strategy of the remaining radars except radar i in the p-th iteration; is the benefit of unilaterally changing the tracking strategy of radar i; i ∈ {1, 2, …, M}; k ∈ {1, 2, …, K};

[0023] c. For the tracking strategy make a judgment. If the tracking strategy does not satisfy the constraint conditions C1 and C2, then adjust the benefit of radar i to the lowest;

[0024] d. If the benefit of radar i after the p-th iteration is equal to the benefit of radar i after the (p - 1)-th iteration, that is it means that radar i has found the optimal tracking strategy to maximize the target tracking benefit;

[0025] e. Allocate and measure the multi-extended target according to the optimal tracking strategies of each radar.

[0026] Preferably, in the third step, the method for updating the joint state of the extended target is as follows:

[0027] Evaluate through all measurement results to obtain the initial reliability of each associated variable; through iterative belief propagation, perform data association, measurement update, and external information update in sequence to achieve the estimation of the marginal posterior probability density; obtain the joint state of the extended target at the current moment according to the marginal posterior probability density.

[0028] Preferably, in the third step, the joint state at the current moment is expressed as follows:

[0029]

[0030] where is the covariance of the extended target k at the current moment; is the predicted covariance of the extended target k at the current moment; is the predicted joint state of the extended target k at the current moment; are the mean and covariance of the Gaussian distribution followed by the measurement update information respectively; I t is the number of measurement results at time t.

[0031] Preferably, in the fourth step, the fusion result of the multi-extended target is obtained as follows:

[0032]

[0033] where M k is the number of radars tracking the extended target k; ω iis the fusion weight of radar i; is the joint state of the extended target k obtained according to radar i.

[0034] Preferably, the method for obtaining the fusion weight is as follows:

[0035]

[0036] where is the detection probability of radar i for the extended target k; is the detection probability of radar num for the extended target k.

[0037] Preferably, in the third step, the joint association vector b t is constructed as follows:

[0038] According to the association variable construct the joint association vector at the current moment. The association variable is expressed as follows:

[0039]

[0040] where is the m-th measurement result at the current moment t.

[0041] The beneficial effects of the present invention are:

[0042] 1. The present invention allocates the tracking targets of radars by constructing a non-cooperative game model of a radar network, breaking through the limitation of traditional radar resource allocation for independent processing of multiple targets, considering clutter processing and data association. Compared with the traditional multi-extended target tracking scheme that does not consider resource allocation, the present invention can effectively solve the problem of allocation of limited resources, achieve faster response, optimize resource utilization rate, and further improve the accuracy and real-time performance of target tracking.

[0043] 2. The present invention optimizes the tracking for the contour characteristics of extended targets, fully considers the contour information of the targets in the radar allocation for the targets, and realizes the allocation and tracking of the targets by selecting the optimal joint geometric dilution of precision factor, and further efficiently completes the radar resource allocation and tracking tasks for multiple extended targets in a complex clutter environment. Description of the Drawings

[0044] Figure 1 is the overall flowchart of the present invention.

[0045] Figure 2 is a schematic diagram of different radar position combinations.

[0046] Figure 3Schematic diagram of the positional relationship between the radar and the key points of the extended target contour in the present invention.

[0047] Figure 4 Schematic diagram of the factor graph model in the present invention.

[0048] Figure 5 Flow chart of the fusion center for fusing the radar tracking results in the present invention. Detailed implementation manners

[0049] The present invention will be further described below with reference to the accompanying drawings.

[0050] As Figure 1 shown, a multi-extended target tracking method based on radar resource allocation includes the following steps:

[0051] Step 1: Model the joint state of the extended target

[0052] Construct a three-dimensional rectangular coordinate system and design the joint state of the extended target k at the current time t where is the motion state of the extended target j; is the contour state of the extended target j; represents a Gaussian distribution; is the mean; is the covariance. The motion state where is the position vector composed of the horizontal and vertical coordinates of the extended target in the Cartesian coordinate system; is the velocity vector of the extended target in the Cartesian coordinate system.

[0053] Model the contour state of the extended target with the smallest ellipse containing the extended target contour; the contour state of the extended target k at the current time t where are the major semi-axis and minor semi-axis corresponding to the contour ellipse of the extended target j at the current time t, respectively; is the contour orientation angle.

[0054] Step 2: Radar resource allocation

[0055] Describe the allocation problem of a radar network composed of M radars for K extended targets as a non-cooperative game. Each radar is regarded as a participant, and its purpose is to maximize its own benefit. Represent the benefit of each participant changing its own strategy as a global function, and the purpose is to find the Nash equilibrium state of the game model. In the Nash equilibrium state, if the strategies of other participants remain unchanged, no participant can unilaterally increase its benefit by changing its own strategy. Construct a distributed radar network extended target allocation model based on the potential game. The strategy set S of all radars is expressed as:

[0056]

[0057] Among them, s ik is the tracking strategy of radar i for extended target k, i ∈ {1, 2, …, M}; k ∈ {1, 2, …, K}; M is the number of radars; K is the number of extended targets.

[0058] If the tracking strategy S of radar i i =

[1010] , that is, s i1 = 1, s i2 = 0, s i3 = 1, s i4 = 1, it means that radar i tracks extended target 1 and extended target 3.

[0059] For the problem of target allocation optimization criterion of this radar network, a decision-making mechanism based on GDOP (Geometric Dilution of Precision) is selected. GDOP represents the distance vector amplification factor between the target and the radar caused by ranging error and is used to measure the positioning accuracy; as Figure 2 shown, it represents the position uncertainty brought by the radar for measuring extended targets due to different positions. The larger the value of GDOP, the smaller the volume of the unit vector shape it represents, which is the result of the very similar angles from the target to the radar, indicating poor positioning accuracy. On the contrary, a better GDOP means a small value, representing a large volume of the unit vector shape, indicating high positioning accuracy and often achieving a better positioning effect.

[0060] As Figure 3 shown, in the problem of tracking and allocation of multiple extended targets by this radar network, in order to achieve the optimal tracking effect for multiple extended targets with shapes in the observation area, after allocating different radar combinations for each extended target, considering the property that the extended target has a contour, MGDOP (Combined Geometric Dilution of Precision) is proposed; MGDOP has a small computational amount and can effectively reduce the decision-making time to ensure that the radar completes the task of target allocation within the effective time. The expression of MGDOP for extended target k is:

[0061]

[0062] Among them, M k is the number of radars tracking extended target k; r ij , r i'j , r i”j are the distances between the radar and the contour key point j; α ij , α i'j , α i”jis the angle between the line connecting the radar and the contour key point j and the reference direction; j ∈ {1, 2, … W}; W is the number of key points on the extended target shape contour.

[0063] In this embodiment, the endpoints of the major axis and minor axis of the ellipse are used as the key points of the extended target; the x-axis direction is used as the reference direction.

[0064] Assume that each radar is rational and selects a tracking strategy S i is the strategy that enables itself to obtain the maximum benefit, that is, the MGDOP of the extended target being tracked is the smallest. Considering the limited radar resources, assume that the detection target ability of each radar has an upper limit n max , and at the same time, to ensure the tracking accuracy, the number of radars used to track the same extended target is not less than the lower limit n min . For the purpose of minimizing the sum of the MGDOPs of the multi-extended targets, the competitive optimal problem of the target allocation strategy selection in this radar network game model is expressed as the following objective function, that is:

[0065]

[0066] where, U is the benefit; K i is the number of extended targets tracked by radar i; n max is the maximum threshold of the number of extended targets tracked by a single radar; n min is the minimum threshold of the number of radars tracking a single extended target.

[0067] To sum up, the problem of extended target allocation and tracking in this radar network can be regarded as a non-cooperative game model where, M is the set of game participants, the radars; S i is the strategy of radar i, that is, the set of detected and tracked targets; u i is the benefit function of radar i, and its expression is:

[0068]

[0069] where, K i is the number of extended targets tracked by radar i; MGDOP i,k is the value of MGDOP of the extended target k observed by radar i.

[0070] Define this game model is a potential game, then there exists a pure strategy Nash equilibrium, and the influence generated by all participants by changing their own strategies can be expressed as a global potential function Φ. The potential function Φ is the sum of the precisions of all extended targets, and its expression is:

[0071]

[0072] Among them, Φ(S i , S -i ) is the potential function of the tracking strategy S i ; S -i is the tracking strategy of the remaining radars except radar i.

[0073] The optimal solution that minimizes the sum of the accuracies of all detected targets is the pure-strategy Nash equilibrium of this game; if the tracking strategies of the remaining radars remain unchanged, unilaterally changing the tracking strategy of radar i has the same impact on its benefit function u i as the change in the potential function Φ, that is:

[0074] u i (S i , S -i ) - u i (S′ i , S -i ) = Φ(S i , S -i ) - Φ(S′ i , S -i )

[0075] Among them, S' i is a tracking strategy different from the tracking strategy S i .

[0076] By using the distributed best-response dynamic algorithm, it is ensured that this game model converges to the Nash equilibrium. In this game model, each radar is given a target allocation strategy with the aim of maximizing the benefit U defined in the objective function, and penalties are imposed on the selection of targets that do not meet the constraint conditions. The target allocation strategies that do not meet the C1 and C2 constraints will not be the pure-strategy Nash equilibrium of the game . The strategy combination that can minimize the error of the detected targets is a Pareto-optimal pure-strategy Nash equilibrium of the game , and the game has at least one feasible pure-strategy Nash equilibrium.

[0077] The competitive optimization problem of the target allocation strategy selection of this radar network is modeled as the following objective function, that is:

[0078]

[0079] Each radar selects a suitable target allocation strategy based on the constraint conditions C1 and C2 to track the extended target. The radar allocation method is as follows:

[0080] Run the iterative algorithm to obtain the optimal radar tracking target allocation result. Based on the best dynamic response, a low-complexity iterative target allocation strategy selection algorithm is designed to solve the pure-strategy Nash equilibrium of the designed game, and this algorithm can converge to the Nash equilibrium of the game after a finite number of iterations. In each round of the iterative process, all radars execute the best dynamic response algorithm in a certain order. While keeping the strategies of other radars unchanged, each radar finds the strategy that maximizes the target tracking benefit. Constraint C2 is executed in each iterative loop of the target allocation. If the allocation strategy does not meet the constraint conditions during the iteration process, a penalty mechanism is established to force it to make a new decision. Repeat the above process until convergence, that is, until the strategies of all radars remain unchanged. Finally, the non-cooperative game reaches the Nash equilibrium state; the specific process of the iterative algorithm is as follows: The Nash equilibrium of the game. In each round of the iterative process, all radars execute the best dynamic response algorithm in a certain order. While keeping the strategies of other radars unchanged, each radar finds the strategy that maximizes the target tracking benefit. Constraint C2 is executed in each iterative loop of the target allocation. If the allocation strategy does not meet the constraint conditions during the iteration process, a penalty mechanism is established to force it to make a new decision. Repeat the above process until convergence, that is, until the strategies of all radars remain unchanged. Finally, the non-cooperative game reaches the Nash equilibrium state; the specific process of the iterative algorithm is as follows:

[0081] (a) Set the initial tracking strategy of each radar i

[0082] (b) Obtain the tracking strategy of radar i after p iterations

[0083]

[0084] (c) Judge the tracking strategy If the tracking strategy does not meet the constraint conditions C1 and C2, then adjust the benefit of radar i to the lowest.

[0085] (d) If the benefit of radar i after p iterations is equal to the benefit of radar i after p - 1 iterations, that is it means that radar i has found the optimal tracking strategy that maximizes the target tracking benefit.

[0086] (e) Perform the above operations on all radars in turn until all radars have found the optimal tracking strategy that maximizes the target tracking benefit; allocate and measure the multi-extended targets according to the optimal tracking strategies of each radar.

[0087] Step 3: Construct the correlation variable

[0088] The measurement result generated by radar i at the current time t where is the m-th measurement result generated by radar i at the current time t; is the number of measurement results generated by radar i at the current time t; h(·) is the measurement function; is the joint state of K extended targets at the current time t; Assume the measurement result Generated by the extended target k, the measurement result model can be constructed as follows:

[0089]

[0090] where H is the matrix for extracting the position of the extended target, I2 is the 2D identity matrix; 0 is the zero matrix; is the contour orientation angle the rotation matrix formed by; is the multiplicative noise, a random variable obeying a zero-mean Gaussian distribution, and its norm is less than 1, and the covariance C of its corresponding Gaussian distribution q is set to I2 / 4; is the measurement noise of radar i.

[0091] Rotation matrix is expressed as:

[0092]

[0093] For each radar, assume that each measurement result generated by it is a false alarm or only comes from one extended target. The correlation variable b for the measurement result is used to indicate the source of the measurement result, and it is expressed as follows:

[0094]

[0095] where, is the correlation variable of the m-th measurement result at the current time t; is the m-th measurement result at the current time t. According to the correlation variable Construct the joint correlation vector from the initial time to the current time where, is the joint correlation vector at the current time t. For the given joint correlation vector b t , obtain the target correlation number vector corresponding to this joint correlation vector b t where, where, is the number of measurement results associated with the extended target k at the current time t, and k = 0 indicates that the measurement result is a false alarm.

[0096] Step 4: Construct a factor graph for multi-extended target tracking. Assume that the states of each extended target are independent of each other and follow a first-order Markov process. The joint state transition function f(C t |C t-1 ) of the extended target k at the current time t is decomposed into:

[0097]

[0098] where, is the joint state of K extended targets at the current time t.

[0099] Introduce the association variable into the joint posterior probability density function f(C 1:t , b 1:t | Z 1:t ). To reduce the computational complexity of solving the marginal posterior probability density of the extended target , factorize the joint posterior probability density function f(C 1:t , b 1:t | Z 1:t ) and construct a factor graph. The joint posterior probability density function f(C 1:t , b 1:t | Z 1:t ) is decomposed as:

[0100] f(C 1:t , b 1:t | Z 1:t ) ∝ f(Z 1:t ∣ C 1:t , b 1:t ) f(b 1:t ∣ C 1:t ) f(C 1:t )

[0101] where f(Z 1:t ∣ C 1:t , b 1:t ) is the global likelihood function; f(b 1:t ∣ C 1:t ) is the joint prior probability mass function of the association vector; f(C 1:t ) is the joint prior probability density function of the extended target state.

[0102] Factorize the joint prior probability density function f(C 1:t ), the joint prior probability mass function f(b 1:t ∣ C 1:t ), and the global likelihood function f(Z 1:t ∣ C 1:t , b 1:t ) respectively, and the process is as follows:

[0103] (a) Assume that the joint state estimate of the extended target and its prior probability density function are known, and factorize the joint prior probability density function f(c 1:t ) as follows:

[0104]

[0105] where Is the state transition function of the extended target k at time t'.

[0106] (b) The Poisson rate model is used to describe the number of measurement results generated by the extended target and the probability model corresponding to clutter. The joint prior probability mass function f(b 1:t ∣C 1:t ) is factorized as follows:

[0107]

[0108] Among them, Is the Poisson rate of the number of measurement results generated by the extended target k at time t'; n k (b t′ ) Is the number of correlation variables with value k in the joint correlation vector b t′ ; I t′ Is the number of measurement results at time t'; Is the measurement result The corresponding clutter mean; Is the Poisson probability selection function of the correlation variable;

[0109] (c) Factorize the global likelihood function f(Z 1:t ∣C 1:t ,b 1:t ):

[0110]

[0111] Among them, Is the likelihood selection function, which is expressed as:

[0112]

[0113] Among them, Is the joint prior probability density function of the measurement results; Is the measurement result The false alarm probability at time t'.

[0114] Through the factorization results of the global likelihood function f(Z 1:t ∣C 1:t ,b 1:t ), the joint prior probability mass function f(b 1:t ∣C 1:t ) and the joint prior probability density function f(C 1:t ), construct the factorization result of the joint posterior probability density function:

[0115]

[0116] Among them, The set of measurement result indices associated with the extended target k at time t'; 0} is the set of indices where the measurement result is a false alarm at time t'; is the prior probability density function of the measurement result; is defined as follows:

[0117]

[0118] The factor graph constructed according to the factorization result is as Figure 4 shown.

[0119] Step Five. Predict the motion state and contour state of the extended target k at the current time t, and the corresponding prediction confidence is expressed as:

[0120]

[0121] where, is the state confidence of the extended target k at the previous time t - 1.

[0122] In the scenario of using the Gaussian hypothesis, the state confidence can be further expressed as:

[0123]

[0124] Derive the Gaussian form of the belief propagation algorithm on this factor graph. The expression of the prediction confidence is modified to:

[0125]

[0126] Obtain the predicted joint state and predicted covariance of the extended target according to the prediction confidence and their expressions are respectively:

[0127]

[0128] where, are the predicted motion state and predicted contour state; is the predicted covariance; are the state transition matrices of the motion state and contour state respectively; is the state transition matrix of the covariance; is zero - mean Gaussian noise.

[0129] Step 6. After predicting the states of all extended targets, iterative belief propagation is started. The states of each extended target are used to evaluate all measurement results to obtain the initial beliefs of each associated variable. Then, through data association, measurement update, and external information update, the belief update of the association situation is realized. The estimation of the marginal probability density is realized through iterative belief propagation on this cyclic factor graph, and the specific process is as follows:

[0130] Step 6-1. Data evaluation

[0131] Obtain the associated variable b of the measurement result generated by the radar for the extended target k m The corresponding evaluation belief Its expression is:

[0132]

[0133] where h k (x k , e k ; z m ) is the pseudo-likelihood function; is the innovation covariance matrix.

[0134] Step 6-2. Data association

[0135] Calculate the data association belief. Each extended target multiplies the evaluation beliefs of other measurement results to obtain the belief of the corresponding associated event Its expression is:

[0136]

[0137] Step 6-3. Update measurement results

[0138] The data association belief passes through the pseudo-likelihood function to obtain the measurement result update information Its expression is:

[0139]

[0140] Under the Gaussian assumption, each term in the summation of the above formula follows the following distribution:

[0141]

[0142] where is the linearized Jacobian matrix form of at .

[0143] Substituting the above formula into the measurement update formula, we can get: where are the mean and covariance of the Gaussian distribution, respectively, and are expressed as follows:

[0144]

[0145] Step 6-4. Update the state belief

[0146] When the iteration index q < Q, perform external information update. Through data association and measurement update, each extended target obtains the belief about the corresponding association situations of other extended targets, and thus updates the state belief. The updated state belief has the following expression:

[0147]

[0148] According to the predicted belief obtained above and the measurement update information the expression of the state belief

[0149]

[0150] Step 6-5. Extended target belief

[0151] Repeat Steps 6-1 to 6-4 for all measurement results of the radar until the iteration number q is equal to the preset iteration number Q; after Q times of iterative belief propagation, the marginal posterior probability density of each extended target is estimated, and finally the target belief at this moment is obtained, and its expression is:

[0152]

[0153] where N k is the normalization factor:

[0154]

[0155] Express the target belief in the following Gaussian form:

[0156]

[0157] According to obtain the joint state of the extended target at the current moment and the covariance

[0158]

[0159] Step 7. Each radar fuses the tracking results at the fusion center. A simple flowchart of information fusion at the fusion center is as shown in Figure 5 . At the fusion center, the tracking results of each radar are fused in combination with its own detection probability of the target. Radar i uses the GaBP algorithm (Genetic Algorithm - Backpropagation Algorithm) to track the allocated K i extended targets. The joint state obtained by radar i when tracking multiple extended targets at the current time t is where is the state estimate of extended target k obtained by radar i at the current time.

[0160] Next, the data between the M k radars that track the same extended target k at the current time t are fused, and the fusion result is expressed as Set the detection probability of each radar for extended target k as Assume that extended target k is tracked by radar i1 and radar i2 at the current time, that is, M k = 2. Then the fusion weight of radar i is Then the fusion result of extended target k at the current time t is Thus, at the current time, all extended targets form a joint feature vector The fusion result of multiple radars tracking multiple extended targets after allocation is obtained.

[0161] Step 8. Repeat Steps 2 to 7 to obtain the fusion results of different extended targets at different times, and complete the tracking of multiple extended targets.

Claims

1. A multi-extended target tracking method based on radar resource allocation, characterized in that: The following steps are involved: Step 1: Obtain the joint geometrical dilution of precision factors MGDOP for different extended targets k , whose expression is: Where W is the number of key points on the extended target shape contour; M k is the number of radars tracking the extended target k; r ij 、r i'j 、r i”j is the distance between the radar and the contour key point j; α ij , α i'j , α i”j is the angle between the line connecting the radar and the contour key point j and the reference direction; According to the joint geometric dilution of precision MGDOP k Construct a radar network non-cooperative game model to allocate the extended targets tracked by radar and obtain the optimal radar tracking target allocation result; Step 2: Use the radar to measure the assigned extended target and obtain the measurement result of the extended target; Step 3: Construct a joint correlation vector; construct a factor graph for tracking multiple extended targets based on the joint correlation vector, and predict and update the joint state of the extended targets according to the factor graph to obtain the joint state at the current moment; Step 4: Fusing the joint states obtained by different radars tracking the same extended target to obtain a fusion result of multiple extended targets; Step 5: Repeat steps 1 to 4 to obtain the fusion results of different extended targets at different times and complete the tracking of multiple extended targets.

2. The method for tracking multiple extended targets based on radar resource allocation according to claim 1, characterized in that: In the step 1, the objective function of the radar network non-cooperative game model constructed is: Among them, U is the income; K i is the number of extended targets tracked by radar i; n max The maximum threshold for the number of extended targets tracked by a single radar; n min The minimum threshold for the number of radars that track a single extended target; ik is the tracking strategy of radar i for extended target k; M is the number of radars; K is the number of extended targets.

3. The method for tracking multiple extended targets based on radar resource allocation according to claim 1, characterized in that: In step 1, the joint state Includes the motion state and contour state of the extended target; constructs the contour state of the extended target with the minimum ellipse that contains the contour of the extended target in, are the major and minor semi-axes of the contour ellipse of the extended target j at the current time t; is the contour orientation angle.

4. The method for tracking multiple extended targets based on radar resource allocation according to claim 3, characterized in that: In the step 1, the endpoints of the major axis and the minor axis of the ellipse are selected as contour key points.

5. The method for tracking multiple extended targets based on radar resource allocation according to claim 1, characterized in that: In the step 1, the method for obtaining the optimal radar tracking target allocation result is as follows: a. Set the initial tracking strategy for each radar i b. Obtain the tracking strategy of radar i after p iterations Among them, S is the strategy set of all radars; S i is the tracking strategy of radar i; is the tracking strategy of the remaining radars except radar i in the pth iteration; is the benefit of unilaterally changing the tracking strategy of radar i; i∈{1,2,…M}; k∈{1,2,…,K}; c. Tracking strategy Make a judgment, if the tracking strategy If the constraints C1 and C2 are not met, the revenue of radar i will be Adjust to lowest setting; d. If the revenue of radar i after p iterations is equal to the revenue of radar i after p-1 iterations, that is It means that radar i finds the optimal tracking strategy that maximizes the target tracking benefit; e. Allocate and measure multiple extended targets according to the optimal tracking strategy of each radar.

6. The method for tracking multiple extended targets based on radar resource allocation according to claim 1, characterized in that: In step 3, the method for updating the joint state of the extended target is as follows: The initial reliability of each associated variable is obtained by evaluating all measurement results. Through iterative reliability propagation, data association, measurement update and external information update are performed in sequence to estimate the marginal posterior probability density. The joint state of the extended target at the current moment is obtained according to the marginal posterior probability density.

7. The method for tracking multiple extended targets based on radar resource allocation according to claim 1, characterized in that: In step 3, the current joint state It is expressed as follows: in, is the covariance of the extended target k at the current moment; is the predicted covariance of the extended target k at the current moment; is the predicted joint state of the extended target k at the current moment; and are the mean and covariance of the Gaussian distribution obeyed by the measurement update information; I t is the number of measurement results at time t.

8. The method for tracking multiple extended targets based on radar resource allocation according to claim 1, characterized in that: In step 4, the fusion result of multiple extended targets The method to obtain is as follows: Among them, M k is the number of radars tracking the extended target k; ω i is the fusion weight of radar i; is the joint state of the extended target k acquired by radar i.

9. The method for tracking multiple extended targets based on radar resource allocation according to claim 8, characterized in that: The method for obtaining the fusion weight is as follows: in, is the detection probability of radar i for extended target k; is the detection probability of radar num for extended target k.

10. The method for tracking multiple extended targets based on radar resource allocation according to claim 1, characterized in that: In step 3, a joint correlation vector b is constructed. t The method is as follows: According to the associated variable Construct the joint association vector for the current moment Associated variables It is expressed as follows: in, is the mth measurement result at the current time t.

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