Low-interception-oriented robust power allocation method for centralized MIMO radar multi-target tracking

Abstract

The application discloses a centralized MIMO radar multi-target tracking robust power allocation method for low interception, which comprises the following steps: a centralized MIMO radar working in a simultaneous multi-beam mode is adopted to track multiple targets dispersedly distributed in a monitoring area; a total interception probability of the centralized MIMO radar system by an enemy target formation is derived as a low interception performance representation index according to a representation index of target tracking accuracy; a centralized MIMO radar multi-target tracking robust power allocation optimization model for low interception is established; and a three-step solving strategy based on an interior point method and a gradient projection method is adopted to solve the optimization model, so that a radiation power vector with optimal system performance is the optimal solution of the model. The application can effectively improve the multi-target tracking accuracy and the low interception performance in the track initiation stage and the case of insufficient resources, and effectively improves the system performance of the centralized MIMO radar.

Description

Technical Field

[0001] The present 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, a radar's low interception (LII) performance is crucial, directly impacting the system's stealth and survivability. By rationally allocating radar system transmission resources and reducing the probability of radar signals being intercepted by enemy passive detection equipment, the risk of radar being attacked by enemy combat systems' anti-radiation strikes can be effectively reduced, thereby improving the system's combat effectiveness. However, in radar system multi-target tracking missions, maintaining robust tracking of multiple targets while simultaneously improving the system's LII performance is a particularly challenging task.

[0003] Centralized MIMO radar offers an effective solution to these challenges. Through centralized signal processing and resource management, centralized MIMO radar enables simultaneous detection and tracking of multiple targets, while also offering enhanced information sharing and collaborative processing capabilities. However, achieving low interception while ensuring robust power allocation and effective tracking of multiple targets in complex electromagnetic environments remains a pressing challenge.

[0004] Existing power allocation methods are often based on ideal environmental assumptions and do not consider the situation where the target tracking accuracy threshold cannot be met at the initial stage 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] Objective of the invention: The objective of the present invention is to provide a robust power allocation method for multi-target tracking in a centralized MIMO radar with low interception.

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

[0007] Use a 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 used 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] A robust power allocation optimization model for low probability of intercept (LPI) of centralized MIMO radar multi-target tracking is established, which takes the minimum probability of interception of centralized MIMO radar by enemy target formation as the optimization objective and takes the given target tracking accuracy threshold requirement and the upper limit of centralized MIMO radar radiation power as the constraint condition.

[0010] The optimization model is solved by using a three-step solution strategy based on the interior point method and the gradient projection method, and the optimal radiation power vector that makes the system performance optimal under the given target tracking accuracy threshold requirement and the constraint of centralized MIMO radar radiation power is obtained as the optimal solution of the model.

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

[0012]

[0013] wherein F represents a state transition matrix, is the state vector of the qth target at the (k-1)T s time, represents a zero-mean Gaussian process noise, and the covariance matrix thereof is

[0014]

[0015] wherein ζ q represents a zero-mean Gaussian process noise intensity, and I2 represents a second-order unit matrix.

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

[0017]

[0018] wherein is the measurement information vector of the radar to the qth target, represents a nonlinear measurement function,

[0019]

[0020] wherein and represent distance and angle measurement information, respectively;

[0021] represents a zero-mean Gaussian measurement noise, and the covariance matrix thereof is wherein and represent the measurement variances of the distance and the angle, respectively:

[0022]

[0023] where -1 denotes the inverse of a matrix, and β k,q respectively denote the radiation power and the transmit signal bandwidth of the centralized MIMO radar to target q in the kth frame, T d denotes the dwell time, B w denotes the receive beam width.

[0024] Further, the target tracking accuracy characterization index is calculated as:

[0025] The inverse of the Bayesian Fisher information matrix, i.e., the BCRLB matrix, is:

[0026]

[0027] where, is the Bayesian Fisher information matrix, and denote the Fisher information matrices of the prior information and the measurement information respectively:

[0028]

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

[0030] Based on this, the Bayesian Fisher information matrix is approximated as:

[0031]

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

[0033]

[0034] where, is the tracking accuracy characterization index of the target, Tr[·] denotes the trace operation.

[0035] Further, the low intercept performance characterization index is represented as:

[0036]

[0037] where, is the low intercept performance characterization index, denotes the radar radiation power vector, The probability that the centralized MIMO radar system is intercepted by target q in the kth frame is expressed as:

[0038]

[0039] where T I , p fa and G I represent the search time, false alarm rate and receive antenna gain of the intercept receiver, respectively, G t is the transmit antenna gain of the centralized MIMO radar, λ represents the signal wavelength, k0 and T0 represent the Boltzmann constant and receiver noise temperature, respectively, G IP , B I and F I represent the processing gain, system bandwidth and noise factor of the intercept receiver, respectively, is the distance from the radar to the target.

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

[0041]

[0042]

[0043] where P min and P max represent the minimum and maximum values of the radiated power of the centralized MIMO radar to a single target, respectively, P total represents the total radiated power of the centralized MIMO radar, represents the tracking accuracy threshold of target q, p thre represents the threshold of the intercepted probability.

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

[0045] (a) First, it is judged whether the original optimization model has a feasible solution, an auxiliary judgment factor γ k is introduced, and the original model is reconstructed as:

[0046]

[0047]

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

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

[0050]

[0051]

[0052] Wherein, exp{·} represents exponential operation, the above formula is a convex optimization model, and an interior point method is used for solving;

[0053] (c) When γ k When γ ≤ 0, the original problem has a feasible solution, and the optimization target of the original problem is equivalent to minimizing the radiation resource consumption of the centralized MIMO radar system, and is reconstructed as:

[0054]

[0055]

[0056] The above formula is a convex optimization model, and a gradient projection method is used for solving.

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

[0058] A tracking scene establishing unit is used for tracking a plurality of targets distributed in a monitoring area by using a centralized MIMO radar working in a simultaneous multi-beam mode.

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

[0060] An optimization model establishing unit is used for taking a given target tracking accuracy threshold requirement and an upper and lower limit of the radiation power of the centralized MIMO radar as constraint conditions, taking the probability of interception of the centralized MIMO radar by an enemy target formation as an optimization target, and establishing a multi-target tracking robust power distribution optimization model for low interception of the centralized MIMO radar.

[0061] An optimization model solving unit is used for solving the optimization model by using a three-step solving strategy based on an interior point method and a gradient projection method, so as to obtain an optimal solution of the model, that is, an optimal radiation power vector of the system under the condition that the given target tracking accuracy threshold requirement and the radiation power limit constraint of the centralized MIMO radar are met.

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

[0063] a memory storing executable program codes;

[0064] a processor coupled with the memory;

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

[0066] A computer-readable storage medium for storing and executing the method, the computer-readable storage medium storing computer instructions, the computer instructions being invoked to execute the steps of the low-interception-oriented centralized MIMO radar multi-target tracking robust power allocation method.

[0067] Beneficial effects: Compared with the prior art, the significant technical effects of the present application are: by dynamically optimizing the radiation power parameters of centralized MIMO in the multi-target tracking process, the low-interception performance is maximized under the conditions of meeting the given target tracking accuracy threshold requirement and the centralized MIMO radar radiation power limit constraint; the robust centralized MIMO radar radiation power optimization allocation is realized, which can effectively improve the multi-target tracking accuracy and low-interception performance under the conditions of track initiation stage and insufficient resources, and effectively improves the system performance of the centralized MIMO radar. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 The method flowchart of the present application;

[0069] Figure 2 The centralized MIMO radar and enemy target array diagram;

[0070] Figure 3 The centralized MIMO radar radiation power allocation diagram;

[0071] Figure 4 The target tracking accuracy results;

[0072] Figure 5 The centralized MIMO radar interception probability comparison diagram. DETAILED DESCRIPTION

[0073] The present application will be described in detail below in combination with the drawings and specific embodiments.

[0074] The application is based on the electronic countermeasure scene, and a centralized MIMO radar multi-target tracking robust power allocation method for low interception is provided. Under the conditions of meeting 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 target, the centralized MIMO radar radiation power parameter in the multi-target tracking process is adaptively optimized and designed, so as to improve the low interception performance of the centralized MIMO radar. Firstly, considering a centralized MIMO radar working in a simultaneous multi-beam mode in a two-dimensional plane, the radar tracks multiple targets dispersedly distributed in a monitoring area; secondly, a Bayesian Cramér-Rao Lower Bound (BCRLB) expression representing the multi-target tracking accuracy is constructed, a closed-form expression of the total probability of the centralized MIMO radar transmitting signals being intercepted by the enemy target formation is derived, and the total probability is taken as a low interception performance characterization index; on this basis, under the conditions of the given target tracking accuracy threshold requirement and the centralized MIMO radar radiation power limit, the total probability of the radar being intercepted by the enemy target formation is minimized as the optimization target, a centralized MIMO radar multi-target tracking robust power optimization allocation model for low interception is established, the centralized MIMO radar radiation power is adaptively and dynamically optimized, and the purpose of improving the low interception performance is achieved.

[0075] As shown in Figure 1 , the method comprises the following steps:

[0076] 1. Considering a centralized MIMO radar working in a simultaneous multi-beam mode and located at (x C ,y C ), the radar tracks Q independent point targets in a combat area, (x C ,y C ) is the position coordinate of the radar, wherein the initial position of the qth (q = 1, 2, …, Q) target is , the initial velocity is , let T s be the observation interval between two consecutive tracking frames, then the state vector of the qth target at kT s time can be defined as , wherein T represents the transpose of the matrix, is the x-axis position of the qth target at kT s time, is the x-axis velocity of the qth target at kT s time, is the y-axis position of the qth target at kT s time, is the y-axis velocity of the qth target at kT sThe y-axis velocity at time k. In each tracking frame, the centralized MIMO radar system dynamically schedules the limited transmit power to Q targets to improve the system's multi-target tracking performance and low probability of intercept performance. To simplify the problem analysis, the following reasonable assumptions are made: (1) the tracks of Q independent targets are initialized, and the echo signals of each target can be separated and processed in parallel; (2) the centralized MIMO radar works in the simultaneous multi-beam mode, and has the same dwell time for all targets; (3) the enemy targets are all 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 transition matrix, is the state vector of the qth target at the (k-1)T s time, represents a zero-mean Gaussian process noise, and its covariance matrix is

[0080]

[0081] where ζ q represents the zero-mean Gaussian process noise intensity, and I2 represents the second-order unit matrix.

[0082] Using parallel signal processing technology and maximum likelihood estimation method, the centralized MIMO radar system can extract the 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] where, is the measurement information vector of the radar to target q, represents a nonlinear measurement function, where

[0085]

[0086] where, and represent the distance and angle measurement information, respectively. In equation (3), represents a zero-mean Gaussian measurement noise, and its covariance matrix is where and represent the measurement variances of the distance and angle, respectively:

[0087]

[0088] where -1 denotes the inverse of a matrix, and β k,q denote the radiation power and the transmit signal bandwidth of the kth frame of the target q by the centralized MIMO radar, respectively, d denote the dwell time, B w denote the receive beamwidth.

[0089] 2. Taking the radiation power of each target by the centralized MIMO radar system as the independent variable, the prediction BCRLB matrix of the target state estimation error is derived, and the trace of the matrix is taken as the root to serve 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, and the specific calculation steps are as follows:

[0090] The Bayesian Fisher information matrix of the kth frame of the target q, i.e., the inverse matrix of the BCRLB matrix, can be calculated as follows:

[0091]

[0092] where, is the Bayesian Fisher information matrix, and denote the Fisher information matrices of the prior information and the measurement information, respectively:

[0093]

[0094] where, is the inverse matrix of the Bayesian Fisher information matrix at the previous time, 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] The tracking accuracy characterization index of the target can be constructed as:

[0098]

[0099] where, is the tracking accuracy characterization index of the target, and Tr[·] denotes the trace operation.

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

[0101]

[0102] wherein, is the probability of the centralized MIMO radar system being intercepted by the target q in the kth frame, T I , p fa and G I represent the search time, the false alarm rate and the receiving antenna gain of the interception receiver respectively, G t is the transmitting antenna gain of the centralized MIMO radar, λ represents the signal wavelength, k0 and T0 represent the Boltzmann constant and the receiver noise temperature respectively, G IP , B I and F I represent the processing gain, the system bandwidth and the noise coefficient of the interception receiver respectively, is the distance from the radar to the target.

[0103] It is assumed that the enemy target formation can communicate in real time through the data link. The total probability of the centralized MIMO radar system being intercepted by the enemy target formation, i.e. the low-interception performance characterization index, can be represented as:

[0104]

[0105] wherein, is the low-interception performance characterization index, represents the radar radiation power vector.

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

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

[0108]

[0109] wherein, P min and P max represent the minimum and maximum values of the radiation power of the centralized MIMO radar to a single target respectively, P totalPtotal(k) denotes the total radiated power of the centralized MIMO radar, p denotes the tracking accuracy threshold of target q thre Pia denotes the threshold of the probability of interception. The first constraint condition in equation (12) denotes the dynamic range limit of the radiated power of the centralized MIMO radar; the second constraint condition denotes the total radiated power limit of the centralized MIMO radar; the third constraint condition denotes the tracking accuracy constraint of the kth frame target; and the last constraint condition denotes that the probability of interception of the centralized MIMO radar needs to be less than a set threshold.

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

[0111] (a) First, it is judged whether the original optimization model has a feasible solution, and an auxiliary judgment factor γ is introduced 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. When γ k > 0, the original problem has no feasible solution, that is, it is impossible to find an optimization result that satisfies all the constraints at the same time, and at this time, the original optimization problem can be transformed into accelerating the target tracking error decline under the constraint of low interception performance, so as to meet the multi-target tracking accuracy constraint and the low interception performance constraint as soon as possible; when γ k ≤ 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 decline under the constraint of low interception performance. Considering that different distances, speeds and threat degrees of enemy targets result in different tracking accuracy thresholds of each target, the original optimization model in equation (12) can be transformed as follows:

[0115]

[0116] Wherein, exp{·} denotes the exponential operation, and the above equation is a convex optimization model, which can be solved by the interior point method.

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

[0118]

[0119] The above formula is a convex optimization model, and a gradient projection method can be used for solving.

[0120] Simulation results:

[0121] Suppose that there are Q=3 targets scattered in 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]. It is assumed that the radar observation interval T s =1s, and the tracking duration is 30s. The maximum radiation power of the transmitter of the centralized MIMO radar is P max =1000W, and the minimum radiation power is P min =10W.

[0122] The arrangement of the centralized MIMO radar and the enemy targets is shown in Figure 2 . The enemy targets are in different monitoring units of the centralized MIMO radar, have different priority, and the tracking accuracy threshold requirement is successively high from far to near. The radiation power distribution diagram of the centralized MIMO radar is shown in Figure 3 . As can be seen from the diagram, the centralized MIMO radar allocates more resources to target 3 with high tracking accuracy threshold requirement at the initial time, and then to target 2. After the tracking error of target 1 and 2 is reduced, more resources are allocated to target 1. In the later tracking sequence, when all targets can meet the tracking accuracy threshold requirement, the radar also allocates more resources to target 3 with the highest requirement.

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

[0124]

[0125] Wherein, N MC is the number of Monte Carlo experiments, is the estimated position of the target in the nth Monte Carlo experiment, and here, N MC =200.

[0126] Figure 4 The tracking accuracy results of each target of the method are given, and as can be seen from the diagram, the centralized MIMO radar can quickly complete the tracking accuracy threshold requirement of each target.

[0127] Figure 5 The comparison diagram of the interception probability of the centralized MIMO radar of different methods is given, and from Figure 5As can be seen, the algorithm can keep good low-interception performance in the whole tracking process, avoid high interception probability caused by too much radiation resource in the initial tracking stage, avoid resource waste caused by too much radiation resource after the tracking accuracy threshold constraint is met, and increase the risk of interception by the enemy passive detection system, thereby verifying the effectiveness of the algorithm.

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

[0129] The application considers a centralized MIMO radar working in a simultaneous multi-beam mode in a two-dimensional plane, and tracks multiple targets dispersedly distributed in a monitoring area. For the scene of tracking multiple targets by the centralized MIMO radar, firstly, taking the radiation power parameter of the centralized MIMO radar as an independent variable, a BCRLB expression representing the tracking accuracy of multiple targets is constructed, a closed-form expression of the total probability that the transmitted signal of the centralized MIMO radar is intercepted by the enemy target formation is derived, and the expression is taken as a low-interception performance representation index; then, taking the given target tracking accuracy threshold requirement and the radiation power limit of the centralized MIMO radar as constraint conditions, and taking the minimization of the total probability that the radar is intercepted by the enemy target formation as an optimization target, a centralized MIMO radar multi-target tracking robust power optimization allocation model facing low interception is established; finally, a three-step solving strategy based on the interior point method and the gradient projection method is adopted to solve the optimization model. Through solving the optimization model, the radiation power vector P k is obtained as the optimal solution of the model.

Claims

1. A low-interception-oriented centralized MIMO radar multi-target tracking robust power allocation method, characterized in that, The method comprises the following steps: A centralized MIMO radar working in a simultaneous multi-beam mode is used to track multiple targets scattered in a monitoring area; A prediction BCRLB matrix of a target state estimation error is derived with the radiated power of the centralized MIMO radar system to each target as an independent variable, and a root of a trace of the prediction BCRLB matrix is taken as a characterization index of target tracking accuracy, and a total interception probability of the centralized MIMO radar system by an enemy target formation is derived as a low-interception performance characterization index; A robust power distribution optimization model of the centralized MIMO radar for multiple target tracking facing low interception is established with a given target tracking accuracy threshold requirement and an upper and lower limit of the radiated power of the centralized MIMO radar as constraint conditions, and a probability of interception of the centralized MIMO radar by the enemy target formation as an optimization target; A three-step solving strategy based on an interior point method and a gradient projection method is used to solve the optimization model, and a radiated power vector that is optimal for the system performance under the condition of meeting the given target tracking accuracy threshold requirement and the radiated power limit constraint of the centralized MIMO radar is obtained as an optimal solution of the model.

2. The low-interception-oriented centralized MIMO radar multi-target tracking robust power allocation method according to claim 1, characterized in that, The motion of the multiple targets is described by a uniform straight-line motion model as follows: where F denotes the state transition matrix, the state vector of the qth target at the (k - 1)T s moment, denotes zero-mean Gaussian process noise with covariance matrix where ζ q denotes the zero-mean Gaussian process noise intensity, I2denotes the second-order identity matrix.

3. The low-interception-oriented centralized MIMO radar multi-target tracking robust power allocation method according to claim 1, characterized in that, Nonlinear measurement information of different targets is extracted from echo signals by the centralized MIMO radar system, and a measurement model of the multiple targets is expressed as follows: wherein, is the radar's measurement information vector for target q, denotes a nonlinear measurement function, wherein and respectively represent distance, angular measurement information; denotes zero-mean Gaussian measurement noise with covariance matrix where and denote the range and angle measurement variances, respectively: where -1 denotes the inverse of a matrix, and β k,q denote the transmitted signal bandwidth and the dwell time, respectively, d denote the transmitted signal bandwidth and the dwell time, respectively, w denote the transmitted signal bandwidth and the dwell time, respectively, 4. The low-interception-oriented centralized MIMO radar multi-target tracking robust power allocation method according to claim 1, characterized in that, A calculation method of the characterization index of target tracking accuracy is as follows: An inverse matrix of a Bayesian Fisher information matrix, i.e., a BCRLB matrix, is as follows: where is the Bayesian Fisher information matrix, and denote the Fisher information matrices of the prior information and the measurement information, respectively: wherein, is the inverse of the Bayesian Fisher information matrix at the previous time instant, is the Jacobian matrix of the observation function, is the covariance matrix of the zero-mean Gaussian measurement noise; Based on this, an approximate calculation of the Bayesian Fisher information matrix is as follows: A tracking accuracy characterization index of the target is constructed as follows: wherein, is the target tracking accuracy characterization indicator, and Tr[·] denotes the trace operation.

5. The low-interception oriented centralized MIMO radar multi-target tracking robust power allocation method according to claim 1, characterized in that, A low-interception performance characterization index is expressed as follows: wherein, is a low probability of intercept performance characterization indicator, represents a radar radiated power vector, is the probability that a centralized MIMO radar system is intercepted by target q in the kth frame, expressed as: where T I , p fa and G I represent the search time, false alarm rate and receive antenna gain of the intercept receiver, respectively, G t is the transmit antenna gain of the centralized MIMO radar, λ represents the signal wavelength, k0 and T0 represent 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, is the radar range to the target.

6. The low-interception oriented centralized MIMO radar multi-target tracking robust power allocation method according to claim 1, characterized in that, An expression of the robust power distribution optimization model of the centralized MIMO radar for multiple target tracking facing low interception is as follows: where P min and P max denote the minimum and maximum of the radiated power of a single target by the centralized MIMO radar, respectively, P total denotes the total radiated power of the centralized MIMO radar, denotes the threshold of the tracking accuracy of the target q, p thre denotes the threshold of the probability of interception.

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

8. A low-interception oriented centralized MIMO radar multi-target tracking robust power allocation system, characterized in that, The method comprises the following steps: A centralized MIMO radar working in a simultaneous multi-beam mode is used to track multiple targets scattered in a monitoring area by a tracking scene establishment unit; A prediction BCRLB matrix of a target state estimation error is derived with the radiated power of the centralized MIMO radar system to each target as an independent variable by an index establishment unit, and a root of a trace of the prediction BCRLB matrix is taken as a characterization index of target tracking accuracy, and a total interception probability of the centralized MIMO radar system by an enemy target formation is derived as a low-interception performance characterization index; A robust power distribution optimization model of the centralized MIMO radar for multiple target tracking facing low interception is established by an optimization model establishment unit with a given target tracking accuracy threshold requirement and an upper and lower limit of the radiated power of the centralized MIMO radar as constraint conditions, and a probability of interception of the centralized MIMO radar by the enemy target formation as an optimization target. An optimization model solving unit is configured to solve the optimization model by using a three-step solving strategy based on an interior point method and a gradient projection method, so as to obtain an optimal solution of the model, which is a 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.

9. An electronic device, comprising: The device comprises: a memory storing executable program codes; a processor coupled with the memory; the processor invokes the executable program codes stored in the memory to execute the steps of the low-interception-oriented centralized MIMO radar multi-target tracking robust power allocation method according to 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 invoked, are configured to execute the steps of the low-interception-oriented centralized MIMO radar multi-target tracking robust power allocation method according to any one of claims 1-7.

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