Centralized MIMO radar multi-target tracking robust power distribution method for low interception

Abstract

The invention discloses a low-interception-oriented centralized MIMO radar multi-target tracking robust power distribution method, which comprises the following steps of: tracking a plurality of targets which are dispersedly distributed in a monitoring area by adopting a centralized MIMO radar working in a simultaneous multi-beam mode; according to the representation index of the target tracking precision, deriving the total interception probability of the centralized MIMO radar system by the enemy target formation as a low interception performance representation index; a centralized MIMO radar multi-target tracking robust power distribution optimization model oriented to low interception is established; and solving the optimization model by adopting a three-step solving strategy based on an interior point method and a gradient projection method, so that the radiation power vector with the optimal system performance is the optimal solution of the model. According to the method, the multi-target tracking precision and the low interception performance can be effectively improved at the initial stage of the track and under the condition of insufficient resources, and the system performance of the centralized MIMO radar is effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a robust power allocation method for low-interception centralized MIMO radar multi-target tracking. Background Art

[0002] In the field of electronic countermeasures, the low interception characteristics of radar are crucial and directly affect the concealment and survivability of the system. By reasonably scheduling and allocating the transmission resources of the radar system and reducing the probability of the radar transmission signal being intercepted by the enemy's passive detection equipment, the risk of the radar being hit by the anti-radiation of the enemy's combat system can be effectively reduced, thereby improving the combat effectiveness of the system. However, in the multi-target tracking task of the radar system, it is a more challenging task to maintain robust tracking of multiple targets while improving the system's low interception performance.

[0003] In order to meet these challenges, centralized MIMO radar provides an effective solution. Through centralized signal processing and resource management, centralized MIMO radar can achieve simultaneous detection and tracking of multiple targets, and has good information sharing and collaborative processing capabilities. However, in a complex electromagnetic environment, how to achieve low interception while performing robust power allocation to ensure effective tracking of multiple targets is still an urgent problem to be solved.

[0004] Existing power allocation methods are often based on ideal environmental assumptions, without considering the situation where the target tracking accuracy threshold cannot be met at the beginning of the track. Most of them directly adopt the resource minimization criterion as the core strategy of algorithm design, which makes it difficult to balance the contradiction between low interception requirements and tracking performance, and has certain limitations. Summary of the invention

[0005] Purpose of the invention: The purpose of the invention is to provide a robust power allocation method for centralized MIMO radar multi-target tracking with low interception.

[0006] Technical solution: The method for robust power allocation for low-interception centralized MIMO radar multi-target tracking of the present invention comprises the following steps:

[0007] Use centralized MIMO radar operating in simultaneous multi-beam mode to track multiple targets dispersed within the surveillance area;

[0008] The radiation power of the centralized MIMO radar system to each target is taken as the independent variable, and the predicted BCRLB matrix of the target state estimation error is derived. The root of the matrix is ​​taken as the characterization index of the target tracking accuracy, and the total interception probability of the centralized MIMO radar system by the enemy target formation is derived as the characterization index of the low interception performance.

[0009] Taking the given target tracking accuracy threshold requirement and the upper and lower limits of the centralized MIMO radar radiation power as constraints, and minimizing the probability of the centralized MIMO radar being intercepted by the enemy target formation as the optimization goal, a robust power allocation optimization model for centralized MIMO radar multi-target tracking with low interception is established.

[0010] A three-step solution strategy based on the interior point method and the gradient projection method is used to solve the optimization model, and the radiation power vector that optimizes the system performance while meeting the given target tracking accuracy threshold requirement and the centralized MIMO radar radiation power limit constraint is obtained as the optimal solution of the model.

[0011] Furthermore, the motion of multiple targets is described by the uniform linear motion model as follows:

[0012]

[0013] Where F represents the state transfer matrix, For the qth target in (k-1)T s The state vector at time, represents zero-mean Gaussian process noise, and its covariance matrix is

[0014]

[0015] Among them, q represents the zero-mean Gaussian process noise intensity, I 2 represents the second-order identity matrix.

[0016] Furthermore, the centralized MIMO radar system extracts nonlinear measurement information of different targets from the echo signal, and the measurement model of multiple targets is expressed as:

[0017]

[0018] in, is the radar’s measurement information vector for target q, represents the nonlinear measurement function,

[0019]

[0020] in, and Respectively represent distance and angle measurement information;

[0021] represents zero-mean Gaussian measurement noise, whose covariance matrix is in and Represent the measurement variance of distance and angle respectively:

[0022]

[0023] Among them, -1 represents the inverse of the matrix, and β k,q They represent the radiation power and transmission signal bandwidth of the centralized MIMO radar to the target q in the kth frame, respectively, and T d represents the dwell time, B w Indicates the receive beamwidth.

[0024] Furthermore, the calculation method of the characterization index of target tracking accuracy is:

[0025] The Bayesian Fisher information matrix, that is, the inverse matrix of the BCRLB matrix is:

[0026]

[0027] in, is the Bayesian Fisher information matrix, and The Fisher information matrices representing the prior information and the measurement information are:

[0028]

[0029] in, is the inverse matrix of the Bayesian Fisher information matrix at the previous moment, is the Jacobian matrix of the observation function, is the covariance matrix of zero-mean Gaussian measurement noise;

[0030] Based on this, the Bayesian Fisher information matrix is ​​approximately calculated as:

[0031]

[0032] Then the target tracking accuracy characterization index is constructed as:

[0033]

[0034] in, is the target tracking accuracy characterization index, and Tr[·] represents the tracking operation.

[0035] Furthermore, the low interception performance characterization index is expressed as:

[0036]

[0037] in, It is a characterization index of low interception performance. represents the radar radiated power vector, is the probability that the centralized MIMO radar system is intercepted by target q in the kth frame, expressed as:

[0038]

[0039] Among them, T I 、p fa and G I represent the search time, false alarm rate and receiving antenna gain of the interception receiver respectively, G t is the transmit antenna gain of the centralized MIMO radar, λ is the signal wavelength, k 0 and T 0 are the Boltzmann constant and the receiver noise temperature, G IP , B I and F I represent the processing gain, system bandwidth and noise figure of the intercept receiver respectively, The distance the radar reaches the target.

[0040] Furthermore, the robust power allocation optimization model for low-interception centralized MIMO radar multi-target tracking is expressed as:

[0041]

[0042]

[0043] Among them, P min and P max They represent the minimum and maximum values ​​of the radiation power of the centralized MIMO radar to a single target, P total represents the total radiated power of the centralized MIMO radar, represents the tracking accuracy threshold of target q, p thre The threshold value representing the probability of interception.

[0044] Furthermore, the steps of solving the optimization model using a three-step solution strategy based on the interior point method and the gradient projection method are as follows:

[0045] (a) First, determine whether the original optimization model has a feasible solution and introduce an auxiliary judgment factor γ k , reconstructing the original model into:

[0046]

[0047]

[0048] When γ k >0, the original problem has no feasible solution; when γ k When ≤0, the original problem has a feasible solution;

[0049] (b) When γ k >0, the original problem is transformed into accelerating the reduction of target tracking error under the constraint of low interception performance, and the original optimization model is transformed into:

[0050]

[0051]

[0052] Among them, exp{·} represents exponential operation. The above formula is a convex optimization model, which is solved by the interior point method;

[0053] (c) When γ k When ≤0, the original problem has a feasible solution, and the optimization objective of the original problem is equivalently transformed into minimizing the radiation resource consumption of the centralized MIMO radar system, which can be reconstructed as:

[0054]

[0055]

[0056] The above formula is a convex optimization model, which can be solved using the gradient projection method.

[0057] The centralized MIMO radar multi-target tracking robust power allocation system for low interception of the present invention comprises:

[0058] A tracking scenario establishment unit for tracking multiple targets dispersed within a surveillance area using a centralized MIMO radar operating in a simultaneous multi-beam mode;

[0059] An index establishment unit is used to derive the predicted BCRLB matrix of the target state estimation error by taking the radiation power of the centralized MIMO radar system to each target as an independent variable, and to take the trace and root of the matrix as a characterization index of the target tracking accuracy, and to derive the total interception probability of the centralized MIMO radar system by the enemy target formation as a characterization index of low interception performance;

[0060] The optimization model building unit is used to establish a low-interception-oriented centralized MIMO radar multi-target tracking robust power allocation optimization model with given target tracking accuracy threshold requirements and centralized MIMO radar radiation power upper and lower limits as constraints and minimizing the probability of the centralized MIMO radar being intercepted by the enemy target formation as the optimization goal;

[0061] The optimization model solving unit is used to solve the optimization model by adopting a three-step solving strategy based on the interior point method and the gradient projection method, and obtain the radiation power vector that optimizes the system performance under the given target tracking accuracy threshold requirement and the centralized MIMO radar radiation power limit constraint as the optimal solution of the model.

[0062] An electronic device for storing and executing the method, comprising:

[0063] A memory storing executable program code;

[0064] a processor coupled to the memory;

[0065] The processor calls the executable program code stored in the memory to execute the steps of the method for robust power allocation for low-interception-oriented centralized MIMO radar multi-target tracking.

[0066] A computer-readable storage medium for storing and executing the method, wherein the computer-readable storage medium stores computer instructions, and when the computer instructions are called, the steps of the robust power allocation method for centralized MIMO radar multi-target tracking for low interception are executed.

[0067] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are: by dynamically optimizing the radiation power parameters of the centralized MIMO during multi-target tracking, the low-capture performance is maximized while meeting the given target tracking accuracy threshold requirements and the centralized MIMO radar radiation power limit constraints; a robust centralized MIMO radar radiation power optimization allocation is achieved, which can effectively improve the multi-target tracking accuracy and low-capture performance at the start of the track and when resources are insufficient, and effectively improve the system performance of the centralized MIMO radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is a flow chart of the method of the present invention;

[0069] Figure 2 It is a centralized MIMO radar and enemy target array diagram;

[0070] Figure 3 This is the radiation power distribution diagram of the centralized MIMO radar;

[0071] Figure 4 Tracking accuracy results for each target;

[0072] Figure 5 This is a comparison chart of the interception probability of centralized MIMO radar. DETAILED DESCRIPTION

[0073] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0074] Starting from the electronic countermeasure scenario, the present invention proposes a robust power allocation method for centralized MIMO radar multi-target tracking with low interception. Under the given target tracking accuracy threshold requirement and the centralized MIMO radar radiation power limit constraint, the total probability of the radar being intercepted by the enemy target formation is minimized as the optimization goal. The centralized MIMO radar radiation power parameters in the multi-target tracking process are adaptively optimized to improve the low interception performance of the centralized MIMO radar. Firstly, a centralized MIMO radar working in simultaneous multi-beam mode is considered on a two-dimensional plane to track multiple targets dispersed in the surveillance area. Secondly, a Bayesian Cramér-Rao Lower Bound (BCRLB) expression characterizing the multi-target tracking accuracy is constructed, and a closed-form expression for the total probability of the centralized MIMO radar's transmitted signal being intercepted by the enemy target formation is derived, and it is used as a characterization indicator of low intercept performance. On this basis, with the given target tracking accuracy threshold requirement and the centralized MIMO radar radiation power limit as constraints, and minimizing the total probability of the radar being intercepted by the enemy target formation as the optimization goal, a robust power optimization allocation model for centralized MIMO radar multi-target tracking for low intercept is established, and the centralized MIMO radar radiation power is adaptively and dynamically optimized to achieve the purpose of improving the low intercept performance.

[0075] like Figure 1 As shown, the method of the present invention comprises the following steps:

[0076] 1. Consider a radio transmitter operating in simultaneous multi-beam mode at (x C ,y C ) centralized MIMO radar to track Q independent point targets in the combat area, (x C ,y C ) is the position coordinate of the radar, where the initial position of the qth (q=1,2,…,Q)th target is The initial speed is Assume T s is the observation interval between two consecutive tracking frames, then the qth target is at kT s The state vector at time can be defined as Where T represents the transpose of the matrix, For the qth target in kT s The x-axis position at the time, For the qth target in kT s The x-axis velocity at the moment, For the qth target in kT s The y-axis position at the moment, For the qth target in kT sThe y-axis velocity at the moment . In each tracking frame, the centralized MIMO radar system dynamically dispatches the limited transmit power to Q targets to improve the system's multi-target tracking performance and low interception performance. To simplify the problem analysis, the following reasonable assumptions are made: (1) The tracks of Q independent targets are initialized, and the echo signal of each target can be separated and processed in parallel; (2) The centralized MIMO radar operates in simultaneous multi-beam mode and has the same dwell time for all targets; (3) The enemy targets are equipped with omnidirectional passive detection systems.

[0077] In the kth frame, the motion of the qth target can be approximately described by the uniform linear motion model:

[0078]

[0079] Where F represents the state transfer matrix, For the qth target in (k-1)T s The state vector at time, represents zero-mean Gaussian process noise, and its covariance matrix is

[0080]

[0081] Among them, q represents the zero-mean Gaussian process noise intensity, I 2 represents the second-order identity matrix.

[0082] Using parallel signal processing technology and maximum likelihood estimation methods, the centralized MIMO radar system can extract nonlinear measurement information of different targets from the echo signal. In this case, the measurement model of target q can be expressed as:

[0083]

[0084] in, is the radar’s measurement information vector for target q, represents the nonlinear measurement function, where

[0085]

[0086] in, and Respectively represent the distance and angle measurement information. In formula (3), represents zero-mean Gaussian measurement noise, whose covariance matrix is in and Represent the measurement variance of distance and angle respectively:

[0087]

[0088] Among them, -1 represents the inverse of the matrix, and β k,q They represent the radiation power and transmission signal bandwidth of the centralized MIMO radar to the target q in the kth frame, respectively, and T d represents the dwell time, B w Indicates the receive beamwidth.

[0089] 2. Taking the radiation power of each target of the centralized MIMO radar system as the independent variable, the predicted BCRLB matrix of the target state estimation error is derived, and its trace root is taken as the characterization index of the target tracking accuracy. The total interception probability of the centralized MIMO radar system by the enemy target formation is derived as the characterization index of the low interception performance. The specific calculation steps are as follows:

[0090] The Bayesian Fisher information matrix of the target q in the kth frame, that is, the inverse matrix of the BCRLB matrix, can be calculated as follows:

[0091]

[0092] in, is the Bayesian Fisher information matrix, and The Fisher information matrices representing the prior information and the measurement information are:

[0093]

[0094] in, is the inverse matrix of the Bayesian Fisher information matrix at the previous moment, is the Jacobian matrix of the observation function, is the covariance matrix of the zero-mean Gaussian measurement noise.

[0095] Based on this, the Bayesian Fisher information matrix can be approximately calculated as:

[0096]

[0097] Then the target tracking accuracy characterization index can be constructed as:

[0098]

[0099] in, is the target tracking accuracy characterization index, and Tr[·] represents the tracking operation.

[0100] The closed-form expression of the total probability of the radar system being intercepted by the enemy target formation is used as the evaluation index of low interception performance. The interception of the radar signal by the enemy target is a joint probability problem in the time domain, spatial domain, frequency domain and power domain. Since the interception receiver is omnidirectional, the probability of the centralized MIMO radar system being intercepted by target q in the kth frame can be calculated as:

[0101]

[0102] in, is the probability of the centralized MIMO radar system being intercepted by target q in the kth frame, T I 、p fa and G I represent the search time, false alarm rate and receiving antenna gain of the interception receiver respectively, G t is the transmit antenna gain of the centralized MIMO radar, λ is the signal wavelength, k 0 and T 0 are the Boltzmann constant and the receiver noise temperature, G IP , B I and F I represent the processing gain, system bandwidth and noise figure of the intercept receiver respectively, The distance the radar reaches the target.

[0103] Assuming that the enemy target formation can communicate in real time through the data link, the total probability of the centralized MIMO radar being intercepted by the enemy target formation, that is, the low interception performance characterization index, can be expressed as:

[0104]

[0105] in, It is a characterization index of low interception performance. represents the radar radiated power vector.

[0106] 3. Establish a robust power allocation optimization model for centralized MIMO radar multi-target tracking with low interception:

[0107] Taking the given target tracking accuracy threshold requirement and the upper and lower limits of the centralized MIMO radar radiation power as constraints, and minimizing the total probability of the centralized MIMO radar being intercepted by the enemy target formation as the optimization goal, a robust power allocation optimization model for centralized MIMO radar multi-target tracking with low interception is established, as shown in the following formula:

[0108]

[0109] Among them, P min and P max They represent the minimum and maximum values ​​of the radiation power of the centralized MIMO radar to a single target, Ptotal represents the total radiated power of the centralized MIMO radar, represents the tracking accuracy threshold of target q, p thre Indicates the threshold of interception probability. The first constraint in formula (12) indicates the dynamic range limit of centralized MIMO radar radiation power; the second constraint indicates the total radiation power limit of centralized MIMO radar; the third constraint indicates the target tracking accuracy constraint of the kth frame; the last constraint indicates that the interception probability of centralized MIMO radar needs to be less than the set threshold.

[0110] 4. A three-step decomposition method based on the interior point method and gradient projection method is used to solve the optimization model (12).

[0111] (a) First, determine whether the original optimization model has a feasible solution and introduce an auxiliary judgment factor γ k , the original optimization model is reconstructed as follows:

[0112]

[0113] The above optimization model is a convex optimization model, which can be solved by the interior point method. k >0, the original problem has no feasible solution, that is, it is impossible to find an optimization result that satisfies all constraints at the same time. At this time, the original optimization problem can be transformed into accelerating the target tracking error reduction under the low interception performance constraint, so as to satisfy the multi-target tracking accuracy constraint and the low interception performance constraint as soon as possible. k When ≤0, the original problem has a feasible solution.

[0114] (b) When γ k >0, the original problem can be transformed into accelerating the target tracking error reduction under the constraint of low interception performance. Considering that the enemy target has different distance, speed, and threat level, each target has a different tracking accuracy threshold. The original optimization model in formula (12) can be transformed as follows:

[0115]

[0116] Where exp{·} represents exponential operation. The above formula is a convex optimization model, which can be solved by interior point method.

[0117] (c) When γ k When ≤0, the original problem has a feasible solution. To reduce the complexity of problem solving, the optimization objective of the original problem can be equivalently transformed into minimizing the radiation resource consumption of the centralized MIMO radar system. Formula (12) can be reconstructed as follows:

[0118]

[0119] The above formula is a convex optimization model, which can be solved by gradient projection method.

[0120] Simulation results:

[0121] Assume that there are Q = 3 targets scattered on a two-dimensional plane. The initial state of target 1 is [-40km, 0.42km / s, 78km, -0.42km / s], the initial state of target 2 is [25km, 0.2km / s, 70km, -0.4km / s], and the initial state of target 3 is [10km, -0.km / s, 55km, -0.4km / s]. The initial position of the centralized MIMO radar is [0km, 0km]. Assume that the radar observation interval T s = 1s, and the tracking process lasts for 30s. The maximum radiated power of the centralized MIMO radar transmitter is P max =1000W, the minimum radiated power is P min =10W.

[0122] Centralized MIMO radar and enemy target array as shown below Figure 2 As shown in Figure 1, enemy targets are located in different monitoring units of the centralized MIMO radar and have different priorities. The tracking accuracy threshold requirements increase from far to near. Figure 3 As shown in the figure, it can be seen that the centralized MIMO radar allocates more resources to target 3 with high tracking accuracy threshold requirements at the beginning, followed by target 2. After the tracking errors of targets 1 and 2 decrease, more resources are allocated to target 1. In the later stage of the tracking sequence, when all targets can meet the tracking accuracy threshold requirements, the radar also allocates more resources to target 3 with the highest requirements.

[0123] The target tracking root mean square error (RMSE) is calculated as follows:

[0124]

[0125] Among them, N MC is the number of Monte Carlo experiments, is the estimated position of the target obtained in the nth Monte Carlo experiment. Here, let N MC =200.

[0126] Figure 4 The target tracking accuracy results of the method proposed in the present invention are given. It can be seen from the figure that the centralized MIMO radar can quickly meet the tracking accuracy threshold requirements of each target.

[0127] Figure 5 A comparison chart of interception probability of centralized MIMO radar with different methods is given. Figure 5It can be seen that the algorithm proposed in the present invention can maintain good low interception performance in the entire tracking process, avoid excessive radiation resources at the initial stage of tracking resulting in too high a probability of interception, avoid radiating more resources after the tracking accuracy threshold constraint is met, resulting in a waste of resources, and increase the risk of being intercepted by the enemy's passive detection system, which verifies the effectiveness of the algorithm proposed in the present invention.

[0128] The working principle and working process of the invention are as follows:

[0129] The present invention considers a centralized MIMO radar working in a simultaneous multi-beam mode on a two-dimensional plane to track multiple targets dispersed in the surveillance area. For the scenario of this centralized MIMO radar tracking multiple targets, firstly, the centralized MIMO radar radiation power parameter is used as the independent variable to construct a BCRLB expression characterizing the multi-target tracking accuracy, derive a closed-form expression of the total probability of the centralized MIMO radar transmitting signal being intercepted by the enemy target formation, and use it as a low interception performance characterization index; then, with the given target tracking accuracy threshold requirement and the centralized MIMO radar radiation power limit as constraints, and minimizing the total probability of the radar being intercepted by the enemy target formation as the optimization goal, a centralized MIMO radar multi-target tracking robust power optimization allocation model for low interception is established; finally, a three-step solution strategy based on the interior point method and the gradient projection method is used to solve the optimization model. By solving the optimization model, the radiation power vector P that optimizes the system performance under the given target tracking accuracy threshold requirement and the centralized MIMO radar radiation power limit constraint is obtained. k is the optimal solution of the model.

Claims

1. A robust power allocation method for low-interception centralized MIMO radar multi-target tracking, characterized in that: The following steps are involved: Use centralized MIMO radar operating in simultaneous multi-beam mode to track multiple targets dispersed within the surveillance area; The radiation power of the centralized MIMO radar system to each target is taken as the independent variable, and the predicted BCRLB matrix of the target state estimation error is derived. The root of the matrix is ​​taken as the characterization index of the target tracking accuracy, and the total interception probability of the centralized MIMO radar system by the enemy target formation is derived as the characterization index of the low interception performance. Taking the given target tracking accuracy threshold requirement and the upper and lower limits of the centralized MIMO radar radiation power as constraints, and minimizing the probability of the centralized MIMO radar being intercepted by the enemy target formation as the optimization goal, a robust power allocation optimization model for centralized MIMO radar multi-target tracking with low interception is established. A three-step solution strategy based on the interior point method and the gradient projection method is used to solve the optimization model, and the radiation power vector that optimizes the system performance while meeting the given target tracking accuracy threshold requirement and the centralized MIMO radar radiation power limit constraint is obtained as the optimal solution of the model.

2. The method for robust power allocation for low-interception centralized MIMO radar multi-target tracking according to claim 1, characterized in that: The motion of multiple targets is described by the uniform linear motion model: Where F represents the state transfer matrix, For the qth target in (k-1)T s The state vector at time, represents zero-mean Gaussian process noise, and its covariance matrix is Among them, q represents the zero-mean Gaussian process noise intensity, and I2 represents the second-order identity matrix.

3. The method for robust power allocation for low-interception centralized MIMO radar multi-target tracking according to claim 1, characterized in that: The centralized MIMO radar system extracts nonlinear measurement information of different targets from the echo signal. The measurement model of multiple targets is expressed as: in, is the radar’s measurement information vector of target q, represents the nonlinear measurement function, in, and Respectively represent distance and angle measurement information; represents zero-mean Gaussian measurement noise, whose covariance matrix is in and Represent the measurement variance of distance and angle respectively: Among them, -1 represents the inverse of the matrix, and β k,q They represent the radiation power and transmission signal bandwidth of the centralized MIMO radar to the target q in the kth frame, respectively, and T d represents the dwell time, B w Indicates the receive beamwidth.

4. The method for robust power allocation for low-interception centralized MIMO radar multi-target tracking according to claim 1, characterized in that: The calculation method of the characterization index of target tracking accuracy is: The Bayesian Fisher information matrix, that is, the inverse matrix of the BCRLB matrix is: in, is the Bayesian Fisher information matrix, and The Fisher information matrices representing the prior information and the measurement information are: in, is the inverse matrix of the Bayesian Fisher information matrix at the previous moment, is the Jacobian matrix of the observation function, is the covariance matrix of zero-mean Gaussian measurement noise; Based on this, the Bayesian Fisher information matrix is ​​approximately calculated as: Then the target tracking accuracy characterization index is constructed as: in, is the target tracking accuracy characterization index, and Tr[·] represents the tracking operation.

5. The method for robust power allocation for low-interception centralized MIMO radar multi-target tracking according to claim 1, characterized in that: The low interception performance characterization index is expressed as: in, It is a characterization index of low interception performance. represents the radar radiated power vector, is the probability that the centralized MIMO radar system is intercepted by target q in the kth frame, expressed as: Among them, T I 、p fa and G I represent the search time, false alarm rate and receiving antenna gain of the interception receiver respectively, G t is the transmit antenna gain of the centralized MIMO radar, λ is the signal wavelength, k0 and T0 are the Boltzmann constant and receiver noise temperature respectively, G IP , B I and F I represent the processing gain, system bandwidth and noise figure of the intercept receiver respectively, The distance the radar reaches the target.

6. The method for robust power allocation for low-interception centralized MIMO radar multi-target tracking according to claim 1, characterized in that: The robust power allocation optimization model for centralized MIMO radar multi-target tracking with low interception is expressed as: Among them, P min and P max They represent the minimum and maximum values ​​of the radiation power of the centralized MIMO radar to a single target, P total represents the total radiated power of the centralized MIMO radar, represents the tracking accuracy threshold of target q, p thre The threshold value representing the probability of interception.

7. The method for robust power allocation for low-interception centralized MIMO radar multi-target tracking according to claim 1, characterized in that: The steps of solving the optimization model using a three-step solution strategy based on the interior point method and the gradient projection method are as follows: (a) First, determine whether the original optimization model has a feasible solution and introduce an auxiliary judgment factor γ k , reconstructing the original model into: When γ k >0, the original problem has no feasible solution; when γ k When ≤0, the original problem has a feasible solution; (b) When γ k When >0, the original problem is transformed into accelerating the reduction of target tracking error under the constraint of low interception performance, and the original optimization model is transformed into: Among them, exp{·} represents exponential operation. The above formula is a convex optimization model, which is solved by the interior point method; (c) When γ k When ≤0, the original problem has a feasible solution, and the optimization objective of the original problem is equivalently transformed into minimizing the radiation resource consumption of the centralized MIMO radar system, which can be reconstructed as: The above formula is a convex optimization model, which can be solved using the gradient projection method.

8. A robust power allocation system for centralized MIMO radar multi-target tracking for low interception, characterized in that: include: A tracking scenario establishment unit for tracking multiple targets dispersed within a surveillance area using a centralized MIMO radar operating in a simultaneous multi-beam mode; An index establishment unit is used to derive the predicted BCRLB matrix of the target state estimation error by taking the radiation power of the centralized MIMO radar system to each target as an independent variable, and to take the trace and root of the matrix as a characterization index of the target tracking accuracy, and to derive the total interception probability of the centralized MIMO radar system by the enemy target formation as a characterization index of low interception performance; The optimization model building unit is used to establish a low-interception-oriented centralized MIMO radar multi-target tracking robust power allocation optimization model with given target tracking accuracy threshold requirements and centralized MIMO radar radiation power upper and lower limits as constraints and minimizing the probability of the centralized MIMO radar being intercepted by the enemy target formation as the optimization goal; The optimization model solving unit is used to solve the optimization model by adopting a three-step solving strategy based on the interior point method and the gradient projection method, and obtain the radiation power vector that optimizes the system performance under the given target tracking accuracy threshold requirement and the centralized MIMO radar radiation power limit constraint as the optimal solution of the model.

9. An electronic device, characterized in that: The device comprises: A memory storing executable program code; a processor coupled to the memory; The processor calls the executable program code stored in the memory to execute the steps of the robust power allocation method for low-interception centralized MIMO radar multi-target tracking as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, which, when called, are used to execute the steps of the robust power allocation method for low-interception centralized MIMO radar multi-target tracking as described in any one of claims 1-7.

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