Phased array radar network node selection and power allocation joint optimization method and system

Abstract

The application belongs to the technical field of radar signal processing, and discloses a phased array radar network node selection and power distribution joint optimization method and system, derives target tracking performance and system radio frequency stealth performance of the phased array radar network, and total interference energy of the phased array radar network to a communication electronic system area; a node selection and power distribution optimization model of the phased array radar network is established by taking minimization of the total interference energy of the phased array radar network to the communication electronic system area as an objective function; a heuristic algorithm is used to determine a target set that needs to be tracked at a current time, and then a particle swarm algorithm with a compression factor is used to solve the node selection and power distribution optimization model. The application can effectively solve the deficiencies of the traditional phased array radar network in node selection and power distribution, improve the anti-interference ability, stealth performance and target tracking precision of the radar system, and has important practical application value.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal processing, and particularly relates to a phased array radar network node selection and power distribution joint optimization method and system. BACKGROUND

[0002] At present, phased array radar technology has realized the transformation from analog to digital, and modern phased array radars mostly adopt digital beam forming technology, can form multiple beams at the same time, and realize real-time tracking of multiple targets. In recent years, the application of phased array radars has been expanded from the traditional military defense field to the civil field, such as weather monitoring, aerospace, traffic monitoring, etc. Since radars need wider bandwidth to improve the range resolution and anti-jamming performance, it is inevitable to conflict with communication systems, and the strategy of allowing radars and communication systems to share the spectrum under controllable mutual interference can encourage coexistence. Networked radars connect multiple radars through a network to realize the sharing of data and information, and such a radar system has significant advantages in complex electromagnetic environments and dense target scenarios. Radar resource management technology can realize the closed-loop regulation and control of networked radar system resources, such as beam management, power control, etc., to maximize the performance of the system under limited resources. The two main goals of the common radar resource management algorithm are to minimize the tracking error under limited radiation resources and to minimize the transmission resource consumption while maintaining a given tracking accuracy. However, in recent years, most of the research on spectrum coexistence of radars and communication systems is about spectrum sensing or transmit beam forming, and few researches consider spectrum coexistence from the aspect of radar resource scheduling. In addition, modern radars also face complex operational environments, and in order to improve the survivability and anti-jamming capability of radars, radio frequency stealth technology has developed rapidly. Radar resource scheduling plays a crucial role in radar radio frequency stealth technology, and effective resource scheduling can significantly improve the performance and stealth of the radar system. Therefore, in the complex situation of communication and radar spectrum coexistence, a comprehensive resource allocation strategy is needed to improve the radio frequency stealth performance of the system. Most of the existing research results have studied the spectrum sharing problem of radar network and communication electronic system region and the resource scheduling problem of radar network facing radio frequency stealth, but the actual problem of comprehensively considering the three aspects still needs to be solved. There is no public report on the joint optimization of phased array radar network node selection and power distribution based on low interception characteristics and spectrum compatibility for multi-target tracking.

[0003] Through the above analysis, the problems and defects of the prior art are:

[0004] (1) Spectrum conflict: In order to improve the range resolution and anti-jamming performance, radar systems need wider bandwidth, which inevitably conflicts with communication systems. At present, a large number of studies focus on the coexistence of radar and communication through spectrum sensing or beamforming technology, and few consider the spectrum conflict problem from the aspect of resource scheduling.

[0005] (2) Radio frequency stealth: The existing research rarely comprehensively considers the integrated problem of spectrum sharing and radio frequency stealth.

[0006] (3) Resource management: The existing radar resource management algorithm mainly focuses on minimizing tracking error and transmission resource consumption, and the resource allocation strategy in complex environment is relatively insufficient.

[0007] (4) Node selection and power allocation: The existing technology fails to comprehensively consider the actual needs of multi-target tracking, spectrum sharing and radio frequency stealth performance. SUMMARY

[0008] In view of the problems in the prior art, the application provides a phased array radar network node selection and power allocation joint optimization method and system.

[0009] The application is implemented in the following manner: a phased array radar network node selection and power allocation joint optimization method, comprising:

[0010] Deriving the target tracking performance and system radio frequency stealth performance of the phased array radar network, and the total interference energy of the phased array radar network to the communication electronic system region;

[0011] Taking the minimization of the total interference energy of the phased array radar network to the communication electronic system region as an objective function, a phased array radar network node selection and power allocation optimization model is established;

[0012] A heuristic algorithm is used to determine the target set that needs to be tracked at the current time, and then a particle swarm algorithm with a compression factor is used to solve the node selection and power allocation optimization model.

[0013] Further, the method comprises the following steps:

[0014] Establishing a radar system model: considering a phased array radar network composed of multiple widely distributed radar nodes, each phased array radar node is a uniform linear array, and each radar transmits mutually non-interfering orthogonal signals. The phased array radar system needs to track a known number of moving targets, in addition, there are a known number of communication electronic system regions in the detection region of the radar network, which can be regarded as a cyclically symmetric band-limited complex Gaussian sequence occupying a certain bandwidth in the frequency domain, and they and the frequency bands occupied by each radar node are mutually overlapped;

[0015] The scenario of spectrum compatibility between the phased array radar network and the communication electronic system region is constructed, and the overall energy distribution of the radar in the space-frequency domain is considered to describe the interference influence on the communication electronic system region.

[0016] The scenario of multi-target tracking of the constructed phased array radar network is constructed, and the posterior Cramer-Rao lower bound of the position term of target estimation is used as the measurement index of the multi-target tracking performance.

[0017] The scenario of reducing the interception of the constructed phased array radar network by the enemy passive detection system is constructed, and the total power of the radar network is used as the measurement index of the radio frequency stealth performance.

[0018] In the case of meeting the pre-given tracking performance of each target and the system radio frequency stealth performance constraint, the radar node selection and power allocation variables are taken as the optimization objects, the total interference energy of the phased array radar network on the communication electronic system region is taken as the objective function, and a phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility is established for multi-target tracking.

[0019] A two-stage solving method is used to solve the problem. First, a heuristic algorithm is used to determine the target set that needs to be tracked at the current time. Then, a particle swarm algorithm with a compression factor is used to solve the optimization problem containing the target tracking performance, low interception performance and system performance constraints, and the phased array radar node selection and power allocation are jointly optimized.

[0020] Further, the scenario of spectrum compatibility between the phased array radar network and the communication electronic system region is constructed, and the overall energy distribution of the radar in the space-frequency domain is considered to describe the interference influence on the communication electronic system region, specifically:

[0021] There are Q widely distributed point targets and M communication electronic system regions in the detection region of the phased array radar network composed of N widely distributed radar nodes. The coordinates of the nth radar node are x n =[x n ,y n ] T ,n=1,...,N,(·) T The transpose of the matrix is represented, the position and velocity of the qth target are x q,k =[x q,k ,y q,k ] T ,q=1,...,Q and The coordinates of the mth communication electronic system region are x m =[x m ,y m ] T, m = 1,..., M. The overall jamming energy level of the phased array radar network to the M communication electronic system regions can be written as follows:

[0022]

[0023] where E m (x k ) represents the jamming energy received by the mth communication electronic system region from the phased array radar network that is focusing on tracking multiple targets:

[0024]

[0025] where u q,n,k represents the selection and normalized power allocation of the radar nodes at time k, 0 < u q,n,k ≤ 1 represents that the qth target is tracked by the nth radar at time k with normalized power u q,n,k , u q,n,k = 1 represents that the nth radar operates at full power to track the qth target, and u q,n,k = 0 represents that the radar n does not track the qth target at time k. E q,n (x m ) is the jamming energy caused by the nth radar to the communication electronic system region with coordinates x m = [x m , y m ] T in the frequency band [f m,n,L , f m,n,U ] that is mutually covered by the mth communication electronic system region and the nth radar node:

[0026]

[0027] where the superscript (·) H represents the conjugate transpose of a matrix, f m,n,L and f m,n,U are the lower and upper bounds of the mutually covered frequency band of the mth communication electronic system region and the nth radar node, s q,n (x, l) represents the lth sampling point in the signal sequence s q,n (x), and s q,n (x m ) is the transmitted signal sequence of the radar n that is tracking the target with azimuth angle at the communication electronic system region with coordinates x m :

[0028]

[0029] where θ n (x m) is the coordinate of the communication electronic system region with coordinates x m = [x m , y m ] T -jπsin(θ-π2) -j(V-1)πsin(θ-π2) T represents the transmit steering vector, V is the number of phased array radar elements. s n = [s n (T s ),...,s n (lT s )] T , s n (lT s ), l = 1,..., L is the transmit waveform sequence of the nth radar node, and the energy has been normalized, i.e. is the sampling time, T s is the sampling period. Considering that the time delay of the signal does not affect the energy distribution in the spatial and frequency domains, it is ignored here.

[0030] Further, the position term posterior Cramer-Rao lower bound of target estimation is used as a performance measurement of multi-target tracking, which is specifically

[0031]

[0032] wherein, represents the position term extraction matrix, J q (u k ) represents the Bayesian Fisher information matrix of the target state at the kth time, which can be expressed as

[0033]

[0034] In the above formula, J P,q,k (u k-1 ) and J Z,q,n (u k ) represent the prior information matrix derived from the target tracking related to the previous time and the information matrix related to the target measurement at the current time, respectively. The specific formula is as follows:

[0035]

[0036] wherein, Q q is the covariance matrix of zero-mean Gaussian noise variables, represents the Jacobian matrix of the target predicted state, R q,n,k is the covariance matrix of the measurement error with zero mean at the kth time; the superscript (·) -1 ​​​denotes the inverse of the matrix, F is the state transition matrix of the qth target. Assume that the expected tracking accuracy of the qth target at time k is η q,k,des , which is the upper bound of the root mean square error of the target tracking, i.e., the square root of the sum of the posteriori Cramer-Rao lower bound of the position of each target at each time cannot exceed its expected value:

[0037]

[0038] where tr(·) denotes the trace of a matrix.

[0039] Further, the scenario of reducing the interception of the phased array radar network by the enemy passive detection system is constructed, and the total power of the radar network is used as the measurement index of the radio frequency stealth performance, specifically

[0040]

[0041] In the above formula, the 1 on the left side is an all-1 column vector of dimension N×1, and the 1 on the right side is an all-1 column vector of Q×1, is the upper limit of the total power of the phased array radar system. u n,k =[u 1,n,k ,...,u q,n,k ,...,u Q,n,k ] T , where u q,n,k represents the normalized transmit power of the radar node n for tracking the qth target at time k.

[0042] Further, the phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility for multi-target tracking is:

[0043]

[0044] where E(u k ) is the overall interference energy of the phased array radar network to the M communication electronic system regions, u k represents the radar node selection and normalized power allocation variable, u q,k =[u q,1,k ,...,u q,n,k ,...,u q,N,k ] T denotes the tracking of the qth target by each radar at time k, u n,k =[u 1,n,k ,...,u q,n,k ,...,u Q,n,k ] T denotes the tracking of each target by the nth radar node at time k, where u q,n,kdenotes the tracking situation of the qth target at time k by radar node n; · 0 denotes the l0 norm, N max is the maximum number of radar nodes used for tracking the qth target at time k; is the square root of the sum of the posterior Cramer-Rao lower bounds of the position terms of the qth target at time k, tr(·) denotes the trace of a matrix, η q,k,des denotes the expected tracking accuracy of the qth target at time k, is the total power upper limit of the phased array radar system.

[0045] Further, the two sub-optimization models of decomposition are

[0046]

[0047] and

[0048] where ΔT q denotes the time interval between the adjacent two tracking frames of target q, J P,q,k (ΔT q ) is related to the prior information matrix J P,q,k (u k-1 ), denotes the position term extraction matrix, η q,k,des denotes the expected tracking accuracy of the qth target at time k.

[0049] E(u k ) is the overall interference energy of the phased array radar network to the M communication electronic system regions, u k denotes the radar node selection and normalized power allocation variable, u q,k = [u q,1,k ,..., u q,n,k ,..., u q,N,k ] T denotes the tracking situation of each radar to the qth target at time k, u n,k = [u 1,n,k ,..., u q,n,k ,..., u Q,n,k ] T denotes the tracking situation of each target by the nth radar node at time k, where u q,n,k denotes the tracking situation of the qth target at time k by radar node n; · 0 denotes the l0 norm, Q k,up denotes the set of targets to be updated at time k, N max is the maximum number of radar nodes used for tracking the qth target at time k; is the square root of the sum of the posterior Cramer-Rao lower bounds of the position terms of the qth target at time k, tr(·) denotes the trace of a matrix, η q,k,desThis represents the expected tracking accuracy of the q-th target at time k. This represents the upper limit of the total power of a phased array radar system.

[0050] Furthermore, the method for solving the two sub-optimization models using heuristic algorithms and particle swarm optimization with compression factors is as follows:

[0051] (1) Determine the set of targets to be updated at each time step:

[0052] (a) Initialize the revisit time interval ΔT for each target q =ΔT,q=1,...,Q, where ΔT represents the time interval between two adjacent tracking frames of the phased array radar;

[0053] (b) The Fischer information matrix J of the target at the previous moment q (u k-1 ) and formula Calculate the prior information matrix J of target q. P,q,k (u k-1 );

[0054] (c) For q = 1, ..., Q, determine respectively Whether it is valid, among which Represents the position term extraction matrix, η q,k,des Let represent the expected tracking accuracy of the q-th target at time k. If true, then determine ΔT. q =ΔT; if not, then ΔT q =ΔT q +ΔT and J q (u k-1 ) = J P,q,k (u k-1 ), and use the newly calculated J q (u k-1 Repeat steps (b) and (c) to obtain the revisit time interval ΔT for each target. q ,q=1,...,Q;

[0055] (d) ΔT based on each target q q To determine whether the state of target k needs to be updated at the current time, if it does, i.e., ΔT q If ΔT = 0, then the target belongs to the set of targets to be updated Q at the current time k. k,up This will give us the current set of targets to be updated, Q. k,up ;

[0056] (2) Joint radar node selection and power allocation optimization:

[0057] (a) Determine the set of targets to be updated Q at the current time k. k,upAfter that, the sub-optimization model is solved by using the PSO with compression factor:

[0058]

[0059] (b) The position pop and velocity of each particle ρ (ρ = 1, 2,..., N pop ) are initialized based on chaotic sequences Let the evolution iteration number g = 1, and judge the position of each particle to ensure that all particles meet the four constraints in the optimization problem, otherwise re-initialize;

[0060] (c) In the gth evolution iteration, judge whether the position of each particle meets the constraints in the optimization problem and where and When the particle meets the above constraints, the fitness value of the particle, i.e. the objective function of the optimization problem, is calculated; when the particle does not meet the constraints, the fitness value will be added to a very large normal number penalty factor;

[0061] (d) Update the particle optimal solution of each particle and the population optimal solution s g,best of the entire particle population based on the fitness value of each particle in the current iteration and the particle optimal solution and population optimal solution in the last iteration, where the smaller the fitness value of the particle, the better the solution in the solution space;

[0062] (e) Update the velocity and position of each particle, and the update formula is as follows

[0063]

[0064] where, and represent the position and velocity of particle ρ (ρ = 1, 2,..., N pop ) in the gth generation, respectively. represents the compression factor, where C = c1 + c2 and C > 4, c1 and c2 are positive learning factors. In addition, r1 and r2 represent random quantities obeying uniform distribution in the interval [0, 1], and s g,bestRespectively represent the optimal solution of the particles in the gth generation and the optimal solution of the population. Determine whether the iteration number is less than the maximum number of iterations. When the iteration number is less than the maximum number of iterations, the iteration number g=g+1, and the solution of the optimization problem is continued; otherwise, the algorithm stops, and the optimization result u is output k,opt = s G,best That is, the radar node selection and power allocation results at the kth moment are obtained.

[0065] Another object of the present application is to provide a phased array radar network node selection and power allocation optimization system, comprising:

[0066] A system modeling module is configured to establish a radar system composed of a plurality of wide-area distributed time-synchronized phased array radar networks, wherein each phased array radar node is a uniform linear array, and each radar transmits mutually non-interfering orthogonal signals. The phased array radar system needs to track a known number of moving targets under the condition that a known number of communication electronic system regions exist in the detection region;

[0067] A measurement index calculation module is configured to calculate the overall energy distribution of the phased array radar network in the space-frequency domain as the interference energy measurement index of the communication electronic system region based on the spectrum compatibility scenario of the phased array radar network and the communication electronic system region; calculate the posterior Cramer-Rao lower bound of the target estimated position term as the measurement index of the multi-target tracking performance based on the tracking scenario of the phased array radar network to multiple targets; and calculate the total power of the radar network as the measurement index of the radio frequency stealth performance based on the scenario of reducing the interception of the phased array radar network by the enemy passive detection system;

[0068] An optimization model construction module is configured to, under the condition of satisfying the pre-specified tracking performance and system radio frequency stealth performance constraints of each target, take the radar node selection and power allocation variables as the optimization object, take the minimization of the total interference energy of the phased array radar network to the communication electronic system region as the objective function, and establish a phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility for multi-target tracking;

[0069] An optimization model solving module is configured to decompose the phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility for multi-target tracking into two sub-optimization models, and solve the two sub-optimization models by using a heuristic algorithm and a particle swarm algorithm with a compression factor.

[0070] Another object of the present application is to provide a device apparatus comprising a memory and a processor, wherein the memory is configured to store a computer program capable of running on the processor;

[0071] A processor configured to execute the steps of the method for multi-target tracking based on low-interception characteristic and spectrum compatibility phased array radar network node selection and power allocation joint optimization when running the computer program.

[0072] In combination with the above technical solutions and the technical problems solved, the technical solutions to be protected by the present application have the following advantages and positive effects:

[0073] Firstly, compared with the prior art, the present application has the following significant technical effect: by optimizing the radar node selection and power allocation parameters when tracking multiple targets under the condition of radar and communication electronic system regional spectrum sharing, the interference energy of the phased array radar network to the communication electronic system region is maximally reduced under the condition of meeting the expected target tracking performance, and the total transmit power of the phased array radar network is controlled, thereby improving the radio frequency stealth performance. The reason for producing this advantage is that the present application derives the posterior Cramer-Rao lower bound based on the radar node selection and power allocation variables and the total power of the radar network, and takes them as the indicators of the target tracking performance and the system radio frequency stealth performance, respectively. In addition, the present application derives the total interference energy of the phased array radar network to the communication electronic system region related to the radar node selection and power allocation variables. Under the condition of meeting the given tracking performance of each target and the system radio frequency stealth performance constraint, the total interference energy of the phased array radar network to the communication electronic system region is minimized as the optimization target, and the radar node selection and power allocation parameters are jointly optimized. This method can realize lower interference energy and good radio frequency stealth performance under the requirement of ensuring the target tracking accuracy.

[0074] Secondly, the present application solves the following technical problems:

[0075] Low multi-target tracking accuracy: In the prior art, the tracking accuracy of the phased array radar network to multiple targets is insufficient, and it cannot effectively cope with the multi-target tracking task in a complex environment.

[0076] Large interference of the radar network to the communication electronic system: The radar network may cause large interference to the communication electronic system during operation, thereby affecting the normal operation thereof.

[0077] Poor radio frequency stealth performance: The radar system is easily intercepted by the enemy passive detection system, and the radio frequency stealth performance cannot be guaranteed, thereby increasing the risk of system exposure.

[0078] Large difficulty in node selection and power allocation optimization: In the optimization process of node selection and power allocation in the traditional method, the calculation complexity is high, and it is difficult to quickly obtain the optimal solution.

[0079] The present application has the following significant technical progress:

[0080] The multi-target tracking accuracy is improved: By introducing the posteriori Cramer-Rao lower bound (PCRLB) as a measure of multi-target tracking performance, the radar network can track multiple targets more accurately, improving the target tracking accuracy.

[0081] The interference on communication electronic systems is reduced: An optimization model of spectrum compatibility is established to minimize the total interference energy of the radar network on the communication electronic system area, effectively reducing the interference on the communication electronic systems.

[0082] The radio frequency stealth performance is enhanced: By constructing a scenario to reduce the interception of the radar network by enemy passive detection systems, and taking the total power as a measure of radio frequency stealth performance, the radio frequency stealth capability of the system is improved, reducing the risk of being detected.

[0083] The node selection and power allocation are optimized: A heuristic algorithm is used to determine the target set that needs to be tracked, and a particle swarm algorithm with compression factor is used to solve the node selection and power allocation optimization model, significantly improving the calculation efficiency and optimization effect.

[0084] The overall performance of the system is improved: Through the joint optimization method, the target tracking performance, radio frequency stealth performance and spectrum compatibility are comprehensively considered, and the overall performance of the system is improved.

[0085] Third, as the creative evidence of the invention claims, it is also reflected in the following important aspects:

[0086] (1) The expected income and commercial value of the technical solution of the invention after transformation are:

[0087] The technical solution of the invention can significantly reduce the interference of the radar system on communication equipment, improve the radio frequency stealth performance, reduce the spectrum conflict with commercial communication systems, and increase the operational flexibility and tactical effectiveness of the radar system. This optimization strategy can be widely applied in military and civilian fields, such as unmanned aerial vehicle navigation, air traffic monitoring and other security sensitive fields, and is expected to bring significant economic benefits and market potential.

[0088] (2) The technical solution of the invention fills the technical gap in the industry at home and abroad:

[0089] The invention fills the technical gap in the optimization problem of simultaneously considering low interception probability and spectrum coexistence in phased array radar systems. Previous researches often only focus on the performance optimization of radar systems, ignoring the compatibility with other radio spectrum users, or only focus on the spectrum coexistence of radar and communication, ignoring the radio frequency stealth performance of radar. The algorithm of the invention combines the low interception and spectrum coexistence capabilities of radar for the first time, providing a new solution for resource management of phased array radar networks.

[0090] Fourth, the prior art problem: the traditional phased array radar network usually adopts fixed node selection and power allocation strategy, which is difficult to adapt to complex electromagnetic environment and task requirements. This may lead to excessive interference of radar system to communication electronic system, while itself is also easy to be intercepted by enemy detection system, affecting the overall combat effectiveness.

[0091] Technical progress one: the present application realizes the comprehensive evaluation of the multi-aspect performance of radar system by establishing the mathematical model of the target tracking performance, radio frequency stealth performance and interference energy of communication electronic system of phased array radar network.

[0092] Technical progress two: the present application proposes a model of joint optimization of node selection and power allocation, aiming to minimize the interference energy to communication electronic system, while taking into account the target tracking performance and radio frequency stealth performance, realizing the optimal configuration of radar system resources.

[0093] Technical progress three: the present application adopts a two-stage solution method combining heuristic algorithm and particle swarm algorithm with compression factor, which can efficiently solve the joint optimization problem of node selection and power allocation, improving the intelligent level and adaptability of radar system.

[0094] Through the above technical progress, the present application can effectively solve the deficiencies of traditional phased array radar network in node selection and power allocation, improve the anti-interference ability, stealth performance and target tracking precision of radar system, and has important practical application value. BRIEF DESCRIPTION OF DRAWINGS

[0095] Figure 1 is the flow chart of the joint optimization method of phased array radar network node selection and power allocation provided by the embodiment of the present application.

[0096] Figure 2 is the comparison result of the total interference energy of communication electronic system region of phased array radar network of the optimization method proposed by the present application and the fixed target revisit time interval algorithm and joint system resource and tracking precision management algorithm.

[0097] Figure 3 is the comparison result of the total transmit power of phased array radar network of the optimization method proposed by the present application and the fixed target revisit time interval algorithm and joint system resource and tracking precision management algorithm. DETAILED DESCRIPTION

[0098] In order to make the purpose, technical scheme and advantages of the present application more clear and explicit, the present application will be further described in detail below in combination with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0099] Example 1: Phased array radar network node selection and power allocation in maritime surveillance

[0100] In maritime surveillance tasks, phased array radar networks are used to track maritime targets while avoiding interference with communication electronic systems, such as ship communication systems. This task involves multiple radar nodes distributed in different locations.

[0101] 1) Establish a radar system model:

[0102] The radar network consists of multiple radar nodes distributed in different locations on the sea; each radar node is a uniform linear array that transmits orthogonal signals without interfering with each other; the radar system needs to track multiple moving ships.

[0103] 2) Construct a spectrum compatibility scenario:

[0104] Establish the overlap between the frequency bands of the radar network and the ship communication system; use the energy distribution of radar transmission in the space-frequency domain to describe the interference with the communication system.

[0105] 3) Multi-target tracking scenario:

[0106] Use the posterior Cramer-Rao lower bound of target position estimation as a measure of tracking performance.

[0107] 4) Radio frequency stealth performance:

[0108] Use the total transmit power of the radar network as a measure of radio frequency stealth performance.

[0109] 5) Optimization model establishment:

[0110] Under the constraints of predetermined tracking performance and radio frequency stealth performance, minimize the total interference energy of the radar on the ship communication system; establish an optimization model for node selection and power allocation.

[0111] 6) Solution method:

[0112] Use a heuristic algorithm to determine the set of ship targets that need to be tracked at the current time; use a particle swarm algorithm with compression factor to solve the optimization model, jointly optimizing node selection and power allocation.

[0113] Through the above method, effective tracking of multiple ships is achieved, and the interference with their communication systems is minimized, ensuring the radio frequency stealth performance of the radar network.

[0114] Example 2: Phased array radar network node selection and power allocation in urban airspace monitoring

[0115] In the urban airspace surveillance task, phased array radar network is used to track unmanned aerial vehicles (UAVs) while avoiding interference with ground communication electronic systems (such as mobile communication base stations). The task involves multiple radar nodes distributed in different areas of the city.

[0116] 1) Establish a radar system model:

[0117] The radar network consists of multiple radar nodes distributed in different areas of the city; each radar node is a uniform linear array that transmits orthogonal signals without mutual interference; the radar system needs to track multiple UAVs.

[0118] 2) Build a spectrum compatibility scenario:

[0119] Establish the overlap of the radar network and the frequency band of the ground communication base station; use the energy distribution of the radar transmission in the space-frequency domain to describe the interference with the communication base station.

[0120] 3) Multi-target tracking scenario:

[0121] Use the posteriori Cramer-Rao lower bound of target position estimation as the tracking performance measurement index.

[0122] 4) Radio frequency stealth performance:

[0123] Use the total transmit power of the radar network as the measurement index of radio frequency stealth performance.

[0124] 5) Optimization model establishment:

[0125] Under the constraint conditions of meeting the predetermined tracking performance and radio frequency stealth performance, the target is to minimize the total interference energy of the radar with the ground communication base station; establish an optimization model for node selection and power allocation.

[0126] 6) Solution method:

[0127] Use a heuristic algorithm to determine the set of UAV targets that need to be tracked at the current time.

[0128] Use a particle swarm algorithm with a compression factor to solve the optimization model, jointly optimizing node selection and power allocation.

[0129] Through the above method, the effective tracking of multiple UAVs is successfully achieved, and the interference with the ground communication base station is minimized, ensuring the radio frequency stealth performance of the radar network.

[0130] The present application is directed to a phased array radar network composed of multiple widely distributed time-synchronized radar nodes, each of which is a uniform linear array, and each radar transmits mutually non-interfering orthogonal signals, in addition, there are a known number of communication electronic system regions and a constant number of moving targets to be tracked in the detection region of the radar network, under the condition of meeting the pre-defined target tracking accuracy and radar network radio frequency stealth performance constraints, the radar target node selection and power allocation parameters are adaptively jointly optimized to minimize the total interference energy of the phased array radar network on the communication electronic system region. First, a spectrum compatible scenario of the phased array radar network and the communication electronic system region is constructed, and the interference energy of the phased array radar network on the communication electronic system region is derived as the objective function of the optimization model; a multi-target tracking scenario of the phased array radar network is constructed, and the posteriori Cramer-Rao lower bound of the target estimation position term is used as a measurement index of the multi-target tracking performance; a scenario of reducing the interception of the phased array radar network by the enemy passive detection system is constructed, and the total power of the radar network is used as a measurement index of the radio frequency stealth performance. Then, under the condition of meeting the pre-defined tracking performance of each target and the system radio frequency stealth performance constraints, the radar node selection and power allocation variables are taken as the optimization objects, the total interference energy of the phased array radar network on the communication electronic system region is taken as the objective function, and a phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility for multi-target tracking is established. Finally, a two-stage solving method is used to solve the problem, a heuristic algorithm is used to determine the target set that needs to be tracked at the current time, and a particle swarm algorithm with a compression factor is used to solve the optimization problem containing the target tracking performance, low interception performance and system performance constraints, and the optimization results of the phased array radar node selection and power allocation variables are obtained.

[0131] As Figure 1 shown, the multi-target tracking oriented phased array radar network node selection and power allocation joint optimization method based on low interception characteristics and spectrum compatibility of the present application comprises the following steps:

[0132] 1. Establish a radar system model:

[0133] Consider a phased array radar network composed of multiple widely distributed time-synchronized radar nodes, each of which is a uniform linear array, and each radar transmits mutually non-interfering orthogonal signals. The phased array radar system needs to track a known number of moving targets, in addition, there are a known number of communication electronic system regions in the detection region of the radar network, which can be regarded as a cyclically symmetric band-limited complex Gaussian sequence occupying a certain bandwidth in the frequency domain, and they and the frequency bands occupied by each radar node have mutual coverage.

[0134] 2. Construct a scenario for the regional spectrum compatibility of phased array radar networks and communication electronic systems, considering the overall energy distribution of the radar in the spatial frequency domain to describe the interference impact on the communication electronic system region:

[0135] Within the detection area of ​​a phased array radar network consisting of N widely distributed radar nodes, there are Q widely distributed point targets and M communication and electronic system areas. The coordinates of the nth radar node are x. n =[x n ,y n ] T ,n=1,...,N,(·) T Let x represent the transpose of the matrix, where x is the position and velocity of the q-th target. q,k =[x q,k ,y q,k ] T ,q=1,...,Q and The coordinates of the m-th communication electronic system region are x m =[x m ,y m ] T The overall interference energy level of a phased array radar network on M communication electronic system areas, where m = 1, ..., M, can be expressed in the following form:

[0136]

[0137] Among them, E m (u k () represents the interference energy received by the m-th communication electronic system area from the phased array radar network that is focusing and tracking multiple targets:

[0138]

[0139] Where u q,n,k This represents the selection of radar nodes and normalized power allocation at time k, where 0 < u q,n,k ≤1 indicates that at time k, the q-th target is detected by the n-th radar with normalized power u. q,n,k Tracking, where u q,n,k =1 indicates that the nth radar operates at full power to track the qth target, while u q,n,k =0 indicates that radar n does not track the q-th target at time k. E q,n (x m ) represents the frequency band mutually covered by the nth radar and the mth communication electronic system area [f m,n,L ,f m,n,U The coordinates above are x m =[x m ,y m ] TInterference energy caused by the communication electronic system area:

[0140]

[0141]

[0142] Among them, the superscript (·) H f represents the conjugate transpose of a matrix. m,n,L and f m,n,U These represent the lower and upper bounds of the frequency bands mutually covered by the m-th communication electronic system region and the n-th radar node, respectively. q,n (x,l) represents the signal sequence s. q,n The l-th sampling point in (x), s q,n (x m (x) is the coordinate of m The communication electronic system area received the signal originating from the direction of the azimuth. The transmitted signal sequence of radar n for tracking the target

[0143]

[0144] Where θ n (x m (x) is the coordinate of m =[x m ,y m ] T The azimuth angle of the communication electronic system area relative to radar n, v(θ)=[1,e -jπsin(θ-π2) ,...,e -j(V-1)πsin(θ-π2) ] T This represents the launch steering vector, where V is the number of elements in the phased array radar. n =[s n (T s ),...,s n (lT s )] T s n (lT s ), l=1,...,L is the transmitted waveform sequence of the nth radar node, and the energy has been normalized. For the sampling time, T s The sampling period is denoted as . Considering that signal delay does not affect the distribution of its energy in the spatial and frequency domains, it is ignored here.

[0145] 3. Construct a phased array radar network for multi-target tracking scenarios, and use the posterior Cramer-Rao lower bound of the target estimation position term as a metric for multi-target tracking performance:

[0146] Define the state variable of target q at the k-th tracking time as: Consider each target moves at a constant velocity, i.e., the constant velocity (CV) model, the state equation of target q can be expressed as

[0147] X q,k = FX q,k-1 + V q,k-1 , q = 1,..., Q (17)

[0148] wherein is the state transition matrix of target q, and ΔT represents the time interval between two adjacent tracking frames of the phased array radar, and I2 represents a 2x2 unit matrix. V q,k-1 in equation (17) represents the process noise, which is modeled as a zero-mean Gaussian noise variable with a covariance matrix Q q , and the covariance matrix Q q can be expressed as

[0149]

[0150] wherein κ q is a constant corresponding to the target maneuvering level.

[0151] After target detection and parameter estimation and other processing are performed on the received target echo, the measurement result of the target can be obtained. Let the measurement set of target q at time k be wherein Z q,n,k is the measurement value obtained by the nth radar node:

[0152] Z q,n,k = h n (X q,k ) + n q,n,k (19)

[0153] wherein h n (·) is a nonlinear transformation from the target state vector of the target position and velocity in the Cartesian coordinate to the observation vector of the time delay, Doppler frequency shift and direction angle:

[0154]

[0155] In the above equation, τ q,n,k , f q,n,k and θ q,n,k represent the time delay, Doppler frequency shift and azimuth angle of target q measured at the nth radar node, respectively, f c is the carrier frequency of the transmitted signal, and c is the speed of light. In equation (19), the measurement error n q,n,k is a multi-dimensional Gaussian variable with a zero mean and a covariance matrix R q,n,k .

[0156] Define the unknown parameter vector χ q,n,k = [τq,n,k ,f q,n,k ,θ q,n,k ] T , whose unbiased estimation has a mean square error lower bounded by the Cramer-Rao bound:

[0157]

[0158] where denotes the expectation sign, is the Fisher information matrix of the unknown parameters:

[0159]

[0160] s q,n,k = [s n (T s -τ q,n,k ),...,s n (lT s -τ q,n,k ),...,s n (LT s -τ q,n,k )] T (25)

[0161] where ζ q,n is the complex reflection coefficient related to the RCS of the target q, P q,n,k denotes the transmit power of the nth radar node.

[0162] a q,n,k denotes the phase change caused by the Doppler shift f q,n,k of the signal at L sampling times, s q,n,k denotes the L sampling values of the signal after a delay τ q,n,k . D n is the receive noise and interference covariance matrix of radar n.

[0163]

[0164] where f m,n,L and f m,n,U are the lower and upper bounds of the mutual coverage frequency range of the mth communication electronic system area and the nth radar node, respectively, N m,n denotes the signal power spectral density intensity.

[0165] V(θ m,n ) = v(θ m,n ) v(θ m,n ) H , N n is the noise covariance matrix of the nth radar receiver, αm,n This represents the strength coefficient of the transmission channel.

[0166] It is known that at a high signal-to-noise ratio, the mean square error of radar node n with respect to target q in terms of time delay, Doppler shift, and azimuth estimation asymptotically follows a zero-mean Gaussian distribution with the Cramer-Rao lower bound as the covariance. Therefore, R can be approximated as... q,n,k =J -1 (χ q,n,k ).

[0167] The posterior Cramer-Rao lower bound of the target estimation position term is used as a metric for multi-target tracking performance:

[0168]

[0169] in, J represents the position term extraction matrix. q (u k ) represents the Bayesian Fischer information matrix of the target state at time k, which can be expressed as:

[0170]

[0171] In the above formula, J P,q,k (u k-1 ) and J Z,q,n (u k These represent the prior information matrix related to target tracking from previous moments and the information matrix related to target measurement at the current moment, respectively. The specific formulas are as follows:

[0172]

[0173] Among them, Q q The covariance matrix of the zero-mean Gaussian noise variable. R represents the Jacobian matrix of the target predicted state. q,n,k It is the covariance matrix of the measurement error with zero mean at time k; superscript (·) -1 Let F denote the inverse of the matrix, and let F be the state transition matrix for the target q.

[0174] Assume the expected tracking accuracy of the q-th target at time k is η. q,k,des This is used as the upper limit of the root mean square error of target tracking, meaning that the square root of the sum of the posterior Cramer-Rao lower bounds of the position terms of each target at each time step must not exceed its expected value:

[0175]

[0176] 4. Construct scenarios to reduce the chances of phased array radar networks being intercepted by enemy passive detection systems, and use the total power of the radar network as a metric for radio frequency stealth performance:

[0177]

[0178] In the formula, 1 on the left is a full 1 column vector of dimension N x 1, and 1 on the right is a full 1 column vector of Q x 1, is the total power upper limit of the phased array radar system. u n,k = [u 1,n,k ,...,u q,n,k ,...,u Q,n,k ] T , where u q,n,k represents the normalized transmit power of radar node n at time k for tracking the qth target.

[0179] 5. In the case of meeting the pre-defined tracking performance of each target and the system radio frequency stealth performance constraint, the radar node selection and power allocation variables are taken as the optimization objects, the total interference energy of the phased array radar network to the communication electronic system area is taken as the objective function, and a phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility for multi-target tracking is established:

[0180]

[0181] where E(u k ) is the overall interference energy of the phased array radar network to the M communication electronic system areas, u k represents the radar node selection and normalized power allocation variable, u q,k = [u q,1,k ,...,u q,n,k ,...,u q,N,k ] T represents the tracking of each radar to the qth target at time k, u n,k = [u 1,n,k ,...,u q,n,k ,...,u Q,n,k ] T represents the tracking of each target by the nth radar node at time k, where u q,n,k represents the tracking of the qth target by radar node n at time k; 0 represents the l0 norm, N max is the maximum value of the number of radar nodes for tracking the qth target at time k; is the square root of the sum of the posteriori Cramer-Rao lower bounds of the position terms of the qth target at time k, tr(·) represents the trace of a matrix, η q,k,des represents the expected tracking accuracy of the qth target at time k, is the total power upper limit of the phased array radar system.

[0182] 6. A two-stage solution method is used to solve the above optimization model, which can decompose the multi-objective tracking-oriented phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility into two sub-optimization models

[0183]

[0184] and

[0185]

[0186] where ΔT q represents the time interval between the adjacent two tracking frames of the target q, J P,q,k (ΔT q ) is related to the prior information matrix J P,q,k (u k-1 ), represents the position item extraction matrix, η q,k,des represents the expected tracking accuracy of the qth target at the kth moment.

[0187] E(u k ) is the overall interference energy of the phased array radar network to the M communication electronic system regions, u k represents the radar node selection and normalized power allocation variable, u q,k =[u q,1,k ,...,u q,n,k ,...,u q,N,k ] T represents the tracking situation of each radar to the qth target at the kth moment, u n,k =[u 1,n,k ,...,u q,n,k ,...,u Q,n,k ] T represents the tracking situation of the nth radar node to each target at the kth moment, where u q,n,k represents the tracking situation of the radar node n to the qth target at the kth moment; ·0 represents the l0 norm, Q k,up represents the set of targets to be updated at the kth moment, N max is the maximum value of the number of radar nodes used to track the qth target at the kth moment; is the square root of the sum of the posterior Cramer-Rao lower bounds of the position items of the qth target at the kth moment, tr(·) represents the trace of the matrix, η q,k,des represents the expected tracking accuracy of the qth target at the kth moment, is the total power upper limit of the phased array radar system.

[0188] Firstly, a heuristic algorithm is used to determine the target set to be tracked at current time, and then a particle swarm optimization algorithm with compression factor is used to solve the optimization problem with the constraints of target tracking performance, low interception performance and system performance, and the node selection and power allocation of phased array radar are jointly optimized. The specific solving steps are as follows:

[0189] (1) Determine the target set to be updated at each time:

[0190] (a) Initialize the revisit time interval ΔT of each target q = ΔT, q = 1, …, Q, where ΔT represents the time interval between adjacent tracking frames of the phased array radar;

[0191] (b) Calculate the prior information matrix J P,q,k (u k-1 ) of target q from the Fisher information matrix J q (u k-1 ) of the target at the last time and the formula

[0192] (c) For q = 1, …, Q, respectively judge whether is established, where denotes the position item extraction matrix, and η q,k,des denotes the expected tracking accuracy of the qth target at k time. If it is established, ΔT q = ΔT; if it is not established, ΔT q = ΔT q + ΔT and J q (u k-1 ) = J P,q,k (u k-1 ), and repeat steps (b) and (c) with the newly calculated J q (u k-1 ) to obtain the revisit time interval ΔT q of each target, q = 1, …, Q;

[0193] (d) Based on ΔT q of each target q, judge whether the state of the target needs to be updated at current time k, if it needs to be updated, i.e. ΔT q = ΔT, then the target belongs to the target set to be updated Q k,up at current time k, and the target set to be updated at current time Q k,up is obtained;

[0194] (2) Joint optimization of radar node selection and power allocation:

[0195] (a) Determine the target set to be updated Q k,up ​Then, the sub-optimization model is solved using a particle swarm optimization algorithm with a compression factor:

[0196]

[0197] (b) Initialize each particle ρ (ρ = 1, 2, ..., N) based on a chaotic sequence. pop ) position and speed Let the number of evolutionary iterations g = 1, and judge the position of each particle to ensure that all particles meet the four constraints in the optimization problem; otherwise, reinitialize.

[0198] (c) In the g-th evolutionary iteration, determine the position of each particle. Do the constraints in the optimization problem satisfy? and in and When a particle satisfies the above constraints, its fitness value is calculated, which is the objective function of the optimization problem. When a particle does not satisfy the constraints, its fitness value will be penalized by a very large positive constant.

[0199] (d) Update the optimal solution for each particle up to the current iteration. And the population-optimal solution s of the entire particle population g,best Based on the fitness values ​​of each particle in the current iteration and the optimal solutions of the particles and the population in the previous iteration, the optimal solutions of the particles and the population in the current iteration are updated. The particles with smaller fitness values ​​correspond to higher quality solutions in the solution space.

[0200] (e) Update the velocity of each particle and location The updated formula is as follows

[0201]

[0202] in, and Let ρ represent particles ρ (ρ = 1, 2, ..., N). pop The position and velocity in the g-th generation. Indicates the compression factor. Where C = c1 + c2 and C > 4, and c1 and c2 are positive learning factors. Furthermore, r1 and r2 both represent random quantities that follow a uniform distribution on the interval [0,1]. and s g,bestRespectively represent the optimal solution of the particles in the gth generation and the optimal solution of the population. Determine whether the iteration number is less than the maximum number of iterations. When the iteration number is less than the maximum number of iterations, the iteration number g=g+1, and the solution of the optimization problem is continued; otherwise, the algorithm stops, and the optimization result u is output k,opt G,best That is, the radar node selection and power allocation results at the kth moment are obtained.

[0203] The multi-target tracking-oriented phased array radar network node selection and power allocation optimization system based on low interception characteristics and spectrum compatibility of the application comprises:

[0204] A system modeling module is configured to establish a radar system composed of a plurality of wide-area distributed time-synchronized phased array radar networks, wherein each phased array radar node is a uniform linear array, and each radar transmits mutually non-interfering orthogonal signals. The phased array radar system needs to track a known number of moving targets in the presence of a known number of communication electronic system regions in the detection region;

[0205] A measurement index calculation module is configured to calculate the overall energy distribution of the phased array radar network in the space-frequency domain as the interference energy measurement index for the communication electronic system region based on the spectrum compatibility scenario of the phased array radar network and the communication electronic system region; calculate the posterior Cramer-Rao lower bound of the target estimated position term as the measurement index of the multi-target tracking performance based on the tracking scenario of the phased array radar network for multiple targets; and calculate the total power of the radar network as the measurement index of the radio frequency stealth performance based on the scenario of reducing the interception of the phased array radar network by the enemy passive detection system;

[0206] An optimization model construction module is configured to, under the condition of satisfying the pre-specified tracking performance and system radio frequency stealth performance constraints of each target, take the radar node selection and power allocation variables as the optimization object, take the minimization of the total interference energy of the phased array radar network for the communication electronic system region as the objective function, and establish a multi-target tracking-oriented phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility.

[0207] An optimization model solving module is configured to decompose the multi-target tracking-oriented phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility into two sub-optimization models, and solve the two sub-optimization models by using a heuristic algorithm and a particle swarm algorithm with a compression factor.

[0208] The device of the application comprises a memory and a processor, wherein:

[0209] The memory is configured to store a computer program capable of running on the processor;

[0210] ​A processor is configured to execute the steps of the method for multi-target tracking based on low probability of intercept and spectrum compatibility phased array radar network node selection and power allocation joint optimization method, and achieve the technical effects of the method.

[0211] A storage medium stores a computer program, which, when executed by at least one processor, implements the steps of the method for multi-target tracking based on low probability of intercept and spectrum compatibility phased array radar network node selection and power allocation joint optimization method, and achieves the technical effects of the method.

[0212] The present application is based on the actual engineering application requirements, considering the phased array radar network composed of multiple widely distributed radar nodes, each phased array radar node is a uniform linear array, and each radar transmits orthogonal signals without interference. The phased array radar system tracks a known number of moving targets, and there are a known number of communication electronic system regions in its detection area, which overlap with the frequency bands occupied by each radar node, and can be regarded as a cyclically symmetric band-limited complex Gaussian sequence occupying a certain bandwidth in the frequency domain. The interference energy of the phased array radar network on the communication electronic system region, the posterior Cramer-Rao lower bound of target tracking, and the total transmit power of the radar network are used as indicators of the interference of the radar network on the communication electronic system region, target tracking performance, and system radio frequency stealth performance, respectively. Then, the pre-specified tracking performance and system radio frequency stealth performance of each target are used as constraints, the radar node selection and power allocation variables are used as optimization objects, and the total interference energy of the phased array radar network on the communication electronic system region is used as the objective function to minimize. An optimization model for multi-target tracking based on low probability of intercept and spectrum compatibility phased array radar network node selection and power allocation is established. A two-stage solution method is used to solve the optimization problem, a heuristic algorithm is used to determine the target set that needs to be tracked at the current time, and then a particle swarm algorithm with a compression factor is used to solve the optimization problem with target tracking performance, low probability of intercept performance, and system performance constraints. The optimized radar node selection and power allocation variables are obtained, and the low interference energy and good radio frequency stealth performance are achieved under the requirement of target tracking accuracy.

[0213] In this embodiment, a radar network consisting of 12 phased array radar nodes is considered to track 4 targets in the airspace, each radar node is fixed and known, and the system parameters are all the same. In addition, there are 2 communication electronic system regions in the detection region of the phased array radar network. Each phased array radar node occupies a bandwidth of 1 MHz, each communication electronic system region has a frequency band width of 6 MHz, and the frequency bands occupied by each radar and each communication electronic system region do not overlap, but the communication electronic system region and the working frequency band of each node in the phased array radar network partially overlap. The time interval ΔT between the adjacent two tracking frames of the phased array radar network is considered to be 4 seconds, and the tracking duration is 400 seconds, that is, 100 frames of tracking sequences are observed. The maximum value N of the phased array radar nodes used to track the same target in the same tracking frame max = 3, and the upper limit of the total normalized power of the phased array radar network The expected tracking accuracy of each target is η 1,des = η 2,des = η 3,des = η 4,des = 25 m.

[0214] In order to verify the effectiveness and superiority of the algorithm, the algorithm is compared with the following two existing algorithms under the conditions that the expected tracking accuracy of each target is η 1,des = η 2,des = η 3,des = η 4,des = 25 m, and the upper limit of the total normalized power of the phased array radar network

[0215] (1) Fixed target revisit time interval algorithm: in this algorithm, all targets are tracked by the phased array radar network in each tracking frame, that is, the particle swarm algorithm with compression factor is used to solve the radar and power allocation for tracking each target at each time.

[0216] (2) Joint system resource and tracking accuracy management algorithm: in this algorithm, only the system total resource constraint and the tracking accuracy constraint are considered, the limit of the total power of the phased array radar network is cancelled, and the same solving steps are still used for solving.

[0217] Figure 2 And Figure 3 The performance of the algorithm and the two comparison algorithms in terms of interference to the communication system and radio frequency stealth is given, which is measured by the total interference energy of the phased array radar network to multiple communication electronic system regions and the total normalized transmit power of the radar network. It can be seen from Figure 2 that the interference energy of the proposed algorithm to the communication region is reduced by about half compared with the fixed target revisit time interval algorithm and the joint system resource and tracking accuracy management algorithm, which reflects the rationality and effectiveness of the heuristic algorithm used.​Figure 3 It can be concluded that, since the proposed algorithm considers the constraint of total system power, the total transmit power of the phased array radar network is reduced by about half compared with the fixed target revisit time interval algorithm, and by about one third compared with the joint system resource and tracking accuracy management algorithm. Therefore, the proposed algorithm has great advantages in terms of interference to communication equipment and radio frequency stealth, and the overall performance is greatly improved.

[0218] It should be noted that the embodiments of the present application can be realized by hardware, software or a combination of software and hardware. The hardware part can be realized by special logic; the software part can be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or a specially designed hardware. Those skilled in the art can understand that the above-mentioned devices and methods can be realized by computer executable instructions and / or included in processor control code, such as provided on a carrier medium, such as a magnetic disk, CD or DVD-ROM, a programmable memory, such as a read-only memory (firmware), or a data carrier, such as an optical or electronic signal carrier. The device and its modules of the present application can be realized by hardware circuit, such as ultra-large scale integrated circuit or gate array, semiconductor, such as logic chip, transistor, etc., or programmable hardware device, such as field programmable gate array, programmable logic device, etc., or by software executed by various types of processors, or by a combination of the above-mentioned hardware circuit and software, such as firmware.

[0219] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any modification, equivalent replacement and improvement within the technical range disclosed by the present application, which is within the spirit and principle of the present application, should be covered within the protection scope of the present application.

Claims

1. A joint optimization method for node selection and power allocation in a phased array radar network, characterized in that, The steps of the method are: Step one, establishing a radar system model: a phased array radar network composed of multiple widely distributed time-synchronized radar nodes, each phased array radar node being a uniform linear array, and each radar transmitting mutually non-interfering orthogonal signals; the phased array radar system tracks a known number of moving targets, in addition, there are a known number of communication electronic system regions in the detection region of the radar network, which are regarded as cyclically symmetric band-limited complex Gaussian sequences occupying a certain bandwidth in the frequency domain, and there is mutual coverage between the frequency bands occupied by each radar node; Step two, constructing a frequency spectrum compatible scene of the phased array radar network and the communication electronic system region, and using the overall energy distribution of the radar in the space-frequency domain to describe the interference influence on the communication electronic system region; Step three, constructing a multi-target tracking scene of the phased array radar network, and using the posteriori Cramer-Rao lower bound of the position term of target estimation as a measurement index of the multi-target tracking performance; Step four, constructing a scene of reducing the interception of the phased array radar network by an enemy passive detection system, and using the total power of the radar network as a measurement index of the radio frequency stealth performance; Step five, under the condition of meeting the pre-defined tracking performance of each target and the system radio frequency stealth performance constraint, taking the radar node selection and power allocation variables as optimization objects, taking the minimization of the total interference energy of the phased array radar network on the communication electronic system region as an objective function, and establishing a phased array radar network node selection and power allocation optimization model based on low interception characteristics and frequency spectrum compatibility for multi-target tracking; Step six, decomposing the phased array radar network node selection and power allocation optimization model based on low interception characteristics and frequency spectrum compatibility for multi-target tracking into two sub-optimization models, and solving the two sub-optimization models by using a two-stage solving method, first determining the target set that needs to be tracked at the current time by using a heuristic algorithm, and then solving the optimization problem containing the target tracking performance, low interception performance and system performance constraint by using a particle swarm algorithm with a compression factor, and jointly optimizing the phased array radar node selection and power allocation. 2.The method of claim 1, wherein, The step of constructing a frequency spectrum compatible scene of the phased array radar network and the communication electronic system region, and using the overall energy distribution of the radar in the space-frequency domain to describe the interference influence on the communication electronic system region, comprises: The overall interference energy level of the phased array radar network on M communication electronic system regions is as follows: where E m (u k ) represents the interference energy received by the mth communication electronic system region from the phased array radar network that is performing the focused tracking of the multiple targets: Where u q,n,k This represents the selection of radar nodes and normalized power allocation at time k, where 0 < u q,n,k ≤1 indicates that at time k, the q-th target is detected by the n-th radar with normalized power u. q,n,k Tracking, where u q,n,k =1 indicates that the nth radar operates at full power to track the qth target, while u q,n,k =0 indicates that radar n does not track the q-th target at time k, E q,n (x m () represents the frequency band mutually covered by the nth radar and the mth communication electronic system. The upper coordinate is x m =[x m ,y m ] T Interference energy caused by the communication electronic system area. 3.The method of claim 1, wherein, The step of using the posteriori Cramer-Rao lower bound of the position term of target estimation as a measurement index of the multi-target tracking performance, specifically comprises: wherein denotes the position item extraction matrix, J q (u k ) denotes the Bayesian Fisher information matrix of the target state at the kth time instant, denoted as: In the above equation, J P,q,k (u k-1 ) and J Z,q,n (u k ) represent the prior information matrix related to target tracking from previous time and the information matrix related to target measurement at current time, respectively, and u q,n,k represents the tracking result of the qth target by the radar node n at time k.

4. The method of claim 1, wherein, The step of constructing a scene of reducing the interception of the phased array radar network by an enemy passive detection system, and using the total power of the radar network as a measurement index of the radio frequency stealth performance, specifically comprises: In the above equation, the left 1 is an all-one column vector of dimension N x 1, the right 1 is an all-one column vector of dimension Q x 1, u k denotes the radar node selection and normalized power allocation variables, is the total power cap for the phased array radar system.

5. The method of claim 1, wherein, The phased array radar network node selection and power allocation optimization model based on low interception characteristics and frequency spectrum compatibility for multi-target tracking is: s.t.1≤||u q,k ||0≤N max q = 1,..., Q ||u n,k ||0≤1,0≤u q,n,k ≤1,q=1,...,Q,n=1,...,N Γ q (u k )≤η q,k,des ,q=1,...,Q where E(u k ) is the overall interference energy of the phased array radar network to M communication electronic system regions, u k represents the radar node selection and normalized power allocation variable, u q,k = [u q,1,k ,...,u q,n,k ,...,u q,N,k ] T represents the tracking situation of each radar to the qth target at time k, u n,k = [u 1,n,k ,...,u q,n,k ,...,u Q,n,k ] T represents the tracking situation of each target by the nth radar node at time k, where u q,n,k represents the tracking situation of the qth target by the radar node n at time k; ||·||0represents the l0norm, N max is the maximum value of the number of radar nodes used to track the qth target at time k; is the square root of the sum of the posteriori Cramer-Rao lower bound of the position term of the qth target at time k, tr(·) represents the trace of the matrix, η q,k,des represents the expected tracking accuracy of the qth target at time k, is the total power upper limit of the phased array radar system.

6. The method of claim 1, wherein, The two sub-optimization models decomposed are And s.t.1≤||u q,k ||0≤N max q∈Q k,up ||u n,k ||0≤1,0≤u q,n,k ≤1,q∈Q k,up ,n=1,...,N Γ q (u k )≤η q,k,des ,q=1,...,Q where ΔT q denotes the time interval between the adjacent two tracking frames of the target q, J P,q,k (ΔT q ) is related to the prior information matrix J P,q,k (u k-1 ), denotes the position term extraction matrix, η q,k,des denotes the expected tracking accuracy of the qth target at the kth moment; E(u k ) is the overall interference energy of the phased array radar network to M communication electronic system regions, u k represents the radar node selection and normalized power allocation variable, u q,k = [u q,1,k ,...,u q,n,k ,...,u q,N,k ] T represents the tracking situation of each radar to the qth target at k moment, u n,k = [u 1,n,k ,...,u q,n,k ,...,u Q,n,k ] T represents the tracking situation of each target by the nth radar node at k moment, wherein u q,n,k represents the tracking situation of the qth target by the radar node n at k moment; ||·||0 represents the l0 norm, Q k,up represents the set of targets to be updated at k moment, N max is the maximum value of the number of radar nodes used to track the qth target at k moment; is the square root of the sum of the posteriori Cramer-Rao lower bound of the position term of the qth target at k moment, tr(·) represents the trace of a matrix, η q,k,des represents the expected tracking accuracy of the qth target at k moment, is the total power upper limit of the phased array radar system.

7. The method of claim 6, wherein, The method for solving the two sub-optimization models by using a heuristic algorithm and a particle swarm algorithm with a compression factor is: (1) determining the target set to be updated at each time: (a) initializing a revisit time interval ΔT for each target q = ΔT, q = 1,..., Q, where ΔT denotes a time interval between two adjacent tracking frames of the phased array radar; (b) the Fisher information matrix J q (u k-1 ) of the target at the previous time and the formula P,q,k (u k-1 ) for calculating the prior information matrix J (c) for q = 1,...,Q, respectively, judge whether holds, where denotes the position item extraction matrix, η q,k,des denotes the expected tracking accuracy of the qth target at the kth time. If true, then determine ΔT q = ΔT; If not, then there is ΔT q = ΔT q + ΔT and J q (u k-1 ) = J P,q,k (u k-1 ), and repeat steps (b), (c) with the newly computed J q (u k-1 ) to obtain the revisit time interval ΔT q for each target, q = 1,..., Q. (d) ΔT based on each target q q to determine whether the state of the target needs to be updated at the current time k, if it needs to be updated, i.e. ΔT q = ΔT, the target belongs to the set of targets to be updated Q k,up at the current time k, i.e. the set of targets to be updated Q k,up at the current time k can be obtained (2) jointly optimizing the radar node selection and power allocation: (a) determining a target set Q to be updated at the current time k k,up After that, the sub-optimization model is solved by using the particle swarm algorithm with compression factor: s.t.1≤||u q,k ||0≤N max ,q∈Q k,up ||u n,k ||0≤1,0≤u q,n,k ≤1,q∈Q k,up ,n=1,...,N Γ q (u k )≤η q,k,des ,q=1,...,Q (b) initializing the position of each particle p based on a chaotic sequence and velocity p = 1,2,..., N pop Let the evolution iteration number g = 1, and judge the position of each particle, ensure that all particles meet the four constraint conditions in the optimization problem, otherwise re-initialize; (c) in the gth evolutionary iteration, judging whether the position of each particle satisfies the constraint condition in the optimization problem wherein When the particle satisfies the above constraint condition, the fitness value of the particle, i.e. the objective function of the optimization problem, is calculated; when the particle does not satisfy the constraint condition, the fitness value will be added with a very large normal number of penalty factor;​​​ (d) updating the individual particle best solution of the current iteration and the population best solution s of the entire particle population g,best based on the fitness values of the individual particles in the current iteration and the individual particle best solution and the population best solution in the last iteration, wherein the smaller the fitness value of a particle corresponds to the better solution in the solution space; (e) update the velocity of each particle and position The update formula is as follows: wherein, and denote the position and velocity of particle p at the gth generation, p = 1, 2,..., N pop ; denotes the compression factor, where C = c1 + c2 and C > 4, c1 and c2 are positive learning factors; r1 and r2 both denote random quantities obeying uniform distribution on the interval [0, 1], and s g,best denote the optimal solution of the particle and the optimal solution of the population in the gth generation; it is judged whether the iteration number is less than the maximum number, when the iteration number is less than the maximum number, the iteration number g = g + 1, and the solution of the optimization problem is continued; otherwise, the algorithm stops, and the optimization result u k,opt = s G,best , that is, the radar node selection and power allocation result at the kth moment is obtained. 8.A phased array radar network node selection and power allocation joint optimization method system according to any one of claims 1-7, characterized in that, including: A system modeling module is configured to establish a radar system composed of a plurality of wide-area distributed time-synchronized phased array radar networks, wherein each phased array radar node is a uniform linear array, and each radar transmits mutually non-interfering orthogonal signals; the phased array radar system needs to track a known number of moving targets in the presence of a known number of communication electronic system regions in a detection region; A measurement index calculation module is configured to calculate the overall energy distribution of the phased array radar network in the space-frequency domain as an interference energy measurement index for the communication electronic system region based on the spectrum compatibility scenario of the phased array radar network and the communication electronic system region; calculate the posterior Cramer-Rao lower bound of the estimated position term of the target as a measurement index for the multi-target tracking performance based on the multi-target tracking scenario of the phased array radar network; and calculate the total power of the radar network as a measurement index for the radio frequency stealth performance based on the scenario of reducing the interception of the phased array radar network by an enemy passive detection system. An optimization model construction module is configured to, under the condition of satisfying the pre-defined tracking performance and system radio frequency stealth performance constraints of each target, take radar node selection and power allocation variables as optimization objects, and take minimizing the total interference energy of the phased array radar network for the communication electronic system region as an objective function, to establish a phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility for multi-target tracking. An optimization model solving module is configured to decompose the phased array radar network node selection and power allocation optimization model based on low interception characteristics and spectrum compatibility for multi-target tracking into two sub-optimization models, and solve the two sub-optimization models by using a heuristic algorithm and a particle swarm algorithm with a compression factor.

9. An apparatus device comprising: A computer device comprises a memory and a processor, wherein: The memory is configured to store a computer program capable of running on the processor; The processor is configured to, when running the computer program, execute the steps of the phased array radar network node selection and power allocation joint optimization method according to any one of claims 1-7.

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