Improved distributed radar jammer location configuration optimization method based on stochastic relaxation

Abstract

The application discloses a random relaxation improved distributed radar jamming source positioning configuration optimization method, relates to the technical field of distributed radar resource scheduling, and effectively balances the sensitivity difference between different optimization indexes, and has stronger optimization ability compared with other algorithms. The method comprises the following steps: a distributed radar jamming source positioning scene is constructed, and a distributed radar jamming source positioning configuration optimization problem is constructed by taking the positioning performance and monitoring performance of the distributed radar jamming source positioning as the guide. Each particle represents an array scheme; a particle swarm is initialized. The fitness value of the particle is calculated according to the objective function of the optimization problem. An external file is used to store the optimal solution set in the iteration process; the individual optimal position and the global optimal position are updated. The speed and position of the particle are updated, the particle swarm optimization algorithm is repeated until the termination condition is reached, and the external file is output as the optimal solution set.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of distributed radar resource scheduling, and particularly relates to a random relaxation improved distributed radar jammer positioning configuration optimization method. BACKGROUND

[0002] The emergence of active jamming seriously inhibits the work efficiency of electronic systems. If the position of the jammer can be accurately located, prior information can be provided for subsequent anti-jamming strategies. Distributed radar can obtain multi-perspective and multi-dimensional observation information such as time of arrival (TOA), angle of arrival (AOA) and time difference of arrival (TDOA) through the deployment of multiple unit radars and signal-level cooperative work, and has great potential in jammer positioning.

[0003] The node deployment of distributed radar has a very high degree of freedom, and the positioning effect of the jammer is affected by the node configuration. Therefore, in recent years, many scholars have carried out research on the node deployment strategy of distributed radar. Related research can be divided into single-target-oriented and multi-target-oriented radar node configuration optimization research. Among them, the single-target-oriented radar configuration optimization constructs an optimization problem with the positioning area Cramer-Rao bound or coverage rate as the target and solves it through traditional optimization methods, which has low computational complexity. However, due to the single optimization target, it is difficult to meet the complex jammer positioning requirements; and the multi-target-oriented radar configuration optimization constructs an optimization problem by integrating multiple jammer positioning task requirements and solves it through a heuristic algorithm to obtain a group of feasible distributed radar node deployment schemes. However, multi-objective optimization problems often have high computational complexity, nonlinearity and non-convexity, and existing heuristic algorithms often fall into local optimum when solving such problems.

[0004] Therefore, when facing multi-objective optimization problems, how to achieve stronger optimization ability is a problem to be solved at present. SUMMARY

[0005] Therefore, the present application provides a random relaxation improved distributed radar jammer positioning configuration optimization method, which can improve the positioning performance and monitoring performance in the distributed radar jammer positioning scenario. The algorithm effectively balances the sensitivity difference between different optimization indicators, has stronger optimization ability than other algorithms, and has strong robustness to changes in jammer transmit power, and has certain practical application potential.

[0006] To achieve the above purpose, the technical scheme of the present application includes the following steps:

[0007] Step 1: Construct a distributed radar jamming source localization scenario, and, guided by the localization and surveillance performance of distributed radar jamming source localization, construct a distributed radar jamming source localization configuration optimization problem.

[0008] Step 2: Each particle represents a formation scheme; initialize the particle swarm, which includes initializing the velocity and position of all particles. The particle velocity is set to zero during initialization, and the particle position is randomly initialized.

[0009] Step 3: Calculate the fitness value of the particle based on the objective function of the optimization problem.

[0010] Step 4: Use an external archive to store the optimal solution set during the iteration process. The external archive is selected based on the dominance relationship between the fitness values ​​of individual optimal particles: In each iteration, traverse all individual optimal particles. When an individual optimal particle is dominated by an external archive particle, select the next individual optimal particle. When an individual optimal particle dominates an external archive particle, delete the external archive particle and add the individual optimal particle to the external archive. When an individual optimal particle and an external archive particle do not have a dominance relationship, if the external archive is not full, add the individual optimal particle to the external archive. If the external archive is full, select the external archive particle with the densest distribution, delete it, and add the individual optimal particle to the external archive.

[0011] Step 5: Update the individual optimal position and the global optimal position.

[0012] Step 6: Update the particle velocity and position

[0013] Step 7: Determine if the algorithm meets the termination condition. If the termination condition is met, stop the iteration and output the external file as the optimal solution set; otherwise, repeat steps 3 to 6 until the algorithm meets the termination condition.

[0014] Furthermore, a distributed radar interference source localization scenario is constructed, specifically as follows:

[0015] The target area is divided into the Radar Mission Area (RMA) and the Radar Deployment Area (RDA), denoted as RMA. RDA is denoted as The RDA contains 5 radar nodes, and the RMA contains several preliminarily identified interference source areas, with the interference source areas being the key sub-regions KS. The RMA is discretized, and each is represented by Ψ. m and Let Ψ represent the set of grid points within the RMA and the k-th KS, and define the set of all KS as Ψ. ks , then Ψ m , and Ψ ks Represented as:

[0016]

[0017] where, denote the coordinate set of the 1st~Nth grid point in RMA, respectively, m n n n n T denote the coordinate of the nth grid point in RMA region, (·) T denote the transpose operation, N m is the number of grid points in RMA; denote the coordinate of the 1st~Nth grid point in KS, respectively, is the number of grid points in the kth KS; denote the coordinate of the nth grid point in KS; K is the number of KSs.

[0018] Further, the positioning performance and monitoring performance of the distributed radar jammer positioning are oriented to construct the distributed radar jammer positioning configuration optimization problem, specifically:

[0019] The positioning performance evaluation index is designed based on the maximum positioning accuracy GDOP in each KS, and the GDOP of the grid point in the kth KS is denoted as where Θ denotes the array scheme; the maximum value of the GDOP of each KS grid point is taken to represent that the positioning accuracy of the corresponding KS is:

[0020]

[0021] The positioning performance objective function is:

[0022]

[0023] where,

[0024]

[0025] where is the expected positioning accuracy of the kth KS, β1and β2correspond to the coefficients of the cases where the expected positioning accuracy is not satisfied and is satisfied, respectively.

[0026] In addition to accurately positioning the proven jammer, the distributed radar also needs to perform wide-range monitoring on the airspace where new jammer may appear; it is assumed that the discovery probability of the jammer located at the grid point is The discovery probability higher than the expected discovery probability ​​​​​​The grid points that are effective monitoring points are counted, and the proportion of effective monitoring points in all grid points is calculated to describe the monitoring performance of the system. The monitoring performance objective function is:

[0027]

[0028] wherein,

[0029]

[0030] is the expected discovery probability.

[0031] In the distributed radar, the signals in each receiving channel are independent of each other, and the background noise of each channel is Gaussian white noise with the same power. The radar nodes use omnidirectional antennas to simultaneously receive and process multiple interference source signals. The number of receiving radar nodes is N, and the false alarm probability of the interference source signal is:

[0032]

[0033] wherein, γ is a detection threshold, σ 2 is the noise power; the probability that the interference source located at is discovered is:

[0034]

[0035] wherein, Q N is the Marcum Q function of order N, χ i,n represents the signal-to-noise ratio of the interference source signal received by the i th radar node at , and is expressed as:

[0036]

[0037] wherein, P j represents the interference source transmission power, represents the receiving gain of the n th radar node antenna, λ represents the carrier wavelength, F r represents the directional diagram propagation factor of the receiving antenna, R i,n represents the distance between the i th receiving radar and the grid point , k, F n , T0, B, L s respectively represent the Boltzmann constant, the receiver noise coefficient, the standard temperature, the receiver bandwidth and the loss factor.

[0038] The positioning performance and monitoring performance objectives are unified into a minimization problem, the objective function vector is defined as f(Λ(Θ,Ψ ks ),1-Γ(Θ,Ψ m )), and the optimization problem is expressed as:

[0039]

[0040] Let f1=Λ(Θ,Ψ ks ), f2=1-Γ(Θ,Ψ m ).

[0041] Further, in step two, the particle swarm is initialized in the following way:

[0042] A distributed system containing N, N≥4 radars is constructed, and the deployable area of the radar nodes is defined as Let the coordinates of the radar nodes be s i =(x i ,y i ,z i ) T , i=1,2,...,N, then the position of a single particle in the optimization space is represented as:

[0043]

[0044] where M is the number of particles in the population.

[0045] Initializing the particle swarm involves initializing the velocities and positions of all particles, with the particle velocities being set to zero at initialization and the particle positions being randomly initialized.

[0046] Further, in step five, the individual optimal position and the global optimal position are updated, specifically:

[0047] Set the number of particles to M, and the velocity and position of the i, i=1,2,...,M particle in the population at the tth iteration are v i (t) and x i (t), while the individual optimal position of the particle i in the iteration process is p i (t) and the global optimal particle position g(t).

[0048] Under the same disturbance of the independent variable, the change in the function value is the optimization sensitivity, and for the positioning performance objective function and the monitoring performance objective function, the objective function with weaker optimization sensitivity is taken as f k , which satisfies a preset expected value

[0049] An attenuation parameter d t =exp(-t / T max ) is added to control the probability of relaxation occurring, and T max is the maximum number of iterations; the above operation is represented by a logical variable B p (t):

[0050]

[0051] where r t Under uniform distribution U(0,1), define ∧ as an "and" operator and ∨ as an "or" operator, the update rule of the individual optimal particle is:

[0052]

[0053] where f(x i (t)) is the fitness value of particle i, f(p i (t-1)) is the fitness value of the individual optimal position p i (t-1) of particle i at the t-1 iteration, and the particles in the external archive at the t iteration are denoted as y l (t), l = 1, 2,..., L, and the relative distance d r (t) of the r, r = 2,..., L-1 particle to the surrounding particles is:

[0054]

[0055] where f i,r (t) is expressed as:

[0056]

[0057] where |·| represents taking an absolute value.

[0058] The particle with the largest relative distance to the surrounding particles is selected as the global optimal particle:

[0059]

[0060] Further, step six, updating the speed and position of the particle, is specifically:

[0061] The displacement-velocity model is used to describe the optimization process of the particle in the optimization space, and the speed and position update rule of particle i, i = 1,..., N at the t iteration is:

[0062] v i (t) = wv i (t-1) + c1r1(p i (t-1) - x i (t-1)) + c2r2(g(t-1) - x i (t-1))(19)

[0063] x i (t) = x i (t-1) + v i (t)(20)

[0064] wherein w is an inertia weight, c1 and c2 represent individual learning factor and population learning factor respectively; r1 and r2 are random numbers, both of which are subject to uniform distribution U(0, 1); v i (t-1), x i (t-1), p i (t-1) respectively represent the velocity, position and individual optimal position of the particle i in the t-1th iteration; g(t-1) represents the global optimal particle position in the t-1th iteration.

[0065] Advantages:

[0066] The application provides a random relaxation improved distributed radar jammer positioning configuration optimization method, which effectively balances the difference in optimization sensitivity between different objective functions by designing a new individual optimal particle update rule, can simultaneously improve the positioning performance and monitoring performance in the distributed radar jammer positioning scene, and to some extent, overcomes the defect that the existing algorithm is easy to fall into local optimum when dealing with high computational complexity, nonlinearity and non-convex multi-objective optimization problems; at the same time, the algorithm is not sensitive to the change of the transmission power of the non-cooperative target (jammer), and shows strong robustness. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 for the distributed radar jammer positioning scene;

[0068] Figure 2 for the flowchart of the random relaxation improved multi-objective particle swarm optimization algorithm;

[0069] Figure 3 for the 2R-MOPSO, T-MOPSO and SC-MOPSO solution set comparison;

[0070] Figure 4 for the 2R-MOPSO optimization array situation;

[0071] Figure 5 for the T-MOPSO optimization array situation;

[0072] Figure 6 for the SC-MOPSO optimization array situation;

[0073] Figure 7 for the 2R-MOPSO solution set comparison under different jammer transmission powers;

[0074] Figure 8 for the scene diagram in the embodiment 1 of the application. DETAILED DESCRIPTION

[0075] The application will be described in detail below with reference to the drawings and embodiments.

[0076] The present application constructs a distributed radar jammer positioning scene (as shown in the figure) and is oriented to the positioning performance and monitoring performance of the distributed radar jammer positioning. Figure 1 The jammer positioning scene is divided into a radar mission area (RMA) and a radar deployment area (RDA), the RMA is denoted as The RDA is denoted as The RDA contains N radar nodes, and the RMA contains several initially ascertained jammer regions, for convenience of description, the jammer region is hereinafter referred to as a key subarea (KS). The RMA is discretized, and the set of grid points in the RMA and the kth KS are denoted as Ψ m and respectively, and the set of all KSs is denoted as Ψ ks Ψ m , and Ψ ks can be represented as:

[0077]

[0078] wherein ψ n =(x n ,y n ,z n ) T represents the coordinates of the nth grid point in the region, (·) T represents a transposition operation, N m is the number of grid points in the RMA, is the number of grid points in the kth KS, and K is the number of KSs.

[0079] The positioning performance evaluation index is designed based on the geometric dilution of precision (GDOP) of the maximum positioning accuracy in each KS, and the GDOP of the grid point in the kth KS is denoted as wherein Θ represents the arrangement scheme. The maximum value of the GDOP of each KS grid point represents the positioning accuracy of the corresponding KS:

[0080]

[0081] The positioning performance target function is defined as:

[0082]

[0083] wherein,

[0084]

[0085] is the expected positioning accuracy of the kth KS, β1=0.8, β2=0.2, corresponding to the situation that the expected positioning accuracy is not satisfied and is satisfied, respectively.

[0086] In addition to accurately positioning the proven interference sources, the distributed radar also needs to monitor the airspace where new interference sources may appear. Assuming that the discovery probability of the interference source located at the grid point is The grid points with discovery probability higher than the expected discovery probability are recorded as effective monitoring points, and the proportion of effective monitoring points in all grid points is counted to describe the monitoring performance of the system. The monitoring performance target function is defined as:

[0087]

[0088] wherein,

[0089]

[0090] Assuming that the signals in each receiving channel of the distributed radar are independent of each other, and the background noise of each channel is Gaussian white noise with the same power; assuming that the radar node uses an omnidirectional antenna and can simultaneously receive and process multiple interference source signals. The number of receiving radar nodes is N, and the false alarm probability of the interference source signal is:

[0091]

[0092] wherein, γ is the detection threshold, σ 2 is the noise power. The discovery probability of the interference source located at is:

[0093]

[0094] wherein, Q N is the Marcum Q function with order N, χ i,n represents the signal-to-noise ratio of the interference source signal received by the i th radar node at , and is expressed as:

[0095]

[0096] wherein, P j represents the transmission power of the interference source, represents the receiving gain of the n th radar node antenna, λ represents the carrier wavelength, F r represents the directional diagram propagation factor of the receiving antenna, R i,n represents the distance between the i th receiving radar and the grid point , k, F n , T0, B, Ls respectively denote the Boltzmann constant, the receiver noise figure, the standard temperature, the receiver bandwidth and the loss factor.

[0097] In combination with the above discussion, the positioning performance and the monitoring performance objectives are unified into a minimization problem, and the objective function vector is defined as f(A(Θ,Ψ ks ),1-Γ(Θ,Ψ m )), and the optimization problem can be expressed as:

[0098]

[0099] And let f1=A(Θ,Ψ ks ), f2=1-Γ(Θ,Ψ m ).

[0100] A flow of a multi-objective particle swarm optimization algorithm improved by random relaxation is shown in Fig. 1, and specifically includes the following steps: Figure 2

[0101] Step one, initializing the particle swarm

[0102] When using the particle swarm optimization algorithm to solve the radar node array optimization problem, each particle represents a kind of array scheme. A distributed system containing N (N≥4) radars is constructed, and the deployable area of the radar node is defined as Let the coordinates of the radar node be s i =(x i ,y i ,z i ) T (i=1,2,...,N), then the position of a single particle in the optimization space can be expressed as:

[0103]

[0104] Wherein, M is the number of particles in the population.

[0105] Initializing the particle swarm includes initializing the velocity and position of all particles. The particle velocity is set to zero in the initialization, and the particle position is randomly initialized.

[0106] Step two, calculating the fitness value of the particle

[0107] The fitness value of the particle will be calculated according to the objective function of the optimization problem. For the convenience of discussion, it is assumed that the optimization problem is a minimization problem. Let there be I objective functions in the optimization problem, respectively denoted as f1,...,f I (in the present application I=2), then the fitness value of particle i on each objective function is calculated as f1(x i ),...,f I (x​i ), the fitness value of particle i can be simplified as a vector f(x i ). If it is the first iteration, the fitness value of the particle is taken as the fitness value of its initial individual optimal particle.

[0108] Step three, judge the dominance relationship, update the external archive

[0109] 2R-MOPSO uses an external archive to store the optimal solution set in the iteration process. The external archive is selected according to the dominance relationship between the fitness values of the individual optimal particles: in each iteration, all individual optimal particles are traversed, and the next individual optimal particle is selected when the individual optimal particle is dominated by the external archive particle; when the individual optimal particle dominates the external archive particle, the external archive particle is deleted, and the individual optimal particle is added to the external archive; when the individual optimal particle and the external archive particle do not have a dominance relationship with each other, if the external archive is not full, the individual optimal particle is added to the external archive, and if the external archive is full, the external archive particle with the most dense distribution is selected to delete, and the individual optimal particle is added to the external archive.

[0110] Step four, update the individual optimal and global optimal

[0111] The number of particles is set to M, the velocity and position of the i-th, i = 1, 2,..., M particle in the population at the t-th iteration are v i (t) and x i (t), and the particle also knows its individual optimal position p i (t) and the global optimal particle position g(t) in the iteration process.

[0112] When updating the individual optimal particle, the new individual optimal particle does not need to perform better in all indicators, and the change in function value under the same disturbance of the independent variable is the optimization sensitivity. For the positioning performance objective function and the monitoring performance objective function, the objective function with weaker optimization sensitivity is taken as f k , which satisfies a preset expected value In addition, 2R-MOPSO adds a decay parameter d t = exp(-t / T max ) to control the probability of relaxation occurring, and T max is the maximum number of iterations. The above operation can be represented by a logical variable:

[0113]

[0114] Where r t obeys uniform distribution U(0, 1), and ∧ is defined as the "and" operator and ∨ is the "or" operator, then the update rule of the individual optimal particle is:

[0115]

[0116] The particles in the external archive at the t-th iteration are denoted as y l (t), l = 1, 2,..., L, and the relative distance of the r-th, r = 2,..., L-1 particle to the surrounding particles is defined as:

[0117]

[0118] where f i,r (t) is expressed as:

[0119]

[0120] where |·| represents taking the absolute value.

[0121] The particle with the largest relative distance to the surrounding particles is selected as the global optimal particle:

[0122]

[0123] Step five, update the velocity and position of the particle

[0124] 2R-MOPSO uses a simple displacement-velocity model to describe the optimization process of particles in the optimization space, and the velocity and position update rules of particle i, i = 1,..., N at the t-th iteration are:

[0125] v i (t) = wv i (t-1) + c1r1(p i (t-1) - x i (t-1)) + c2r2(g(t-1) - x i (t-1)) (19)

[0126] x i (t) = x i (t-1) + v i (t) (20)

[0127] where w is the inertia weight, c1 and c2 represent the individual learning factor and the population learning factor, respectively; r1 and r2 are random numbers, which follow a uniform distribution U(0, 1).

[0128] Step six, judge whether the algorithm meets the termination condition

[0129] When the algorithm reaches the maximum number of iterations, stop iteration and output the external archive as the optimal solution set; otherwise, repeat steps two to five until the algorithm meets the termination condition.

[0130] Example 1

[0131] The distributed radar adopted by the application is a passive receiving system, considering that the area of RDA is smaller than that of RMA in the interference source positioning scene, which leads to the optimization sensitivity of the system monitoring performance being obviously weaker than the positioning performance, therefore, the random relaxation operation will be performed on the monitoring performance, and the expected detection coverage is set to 0.82.

[0132] The simulation is realized by using MATLAB R2021a software. The related parameter settings are shown in Table 1 and Table 2, and the interference source transmission power P j = 1500 W, the false alarm probability P fa = 1x10 -6 , and the expected detection probability The application sets five interference sources, and the range of KS where the interference sources are located is shown in Table 3.

[0133] In order to verify the performance of 2R-MOPSO, the application compares two other optimization algorithms based on MOPSO, which are T-MOPSO and SC-MOPSO, wherein SC-MOPSO is a variant MOPSO with optimization direction constraint, which is used to solve problems with complex constraints, non-convex and high computational complexity; in the simulation, the implementation details of SC-MOPSO are adjusted to make it more focused on the optimization of monitoring performance indicators. The above three algorithms use the same parameters, M = 100, T max = 200, w = 0.8, c1 = c2 = 1.4, and L = 15.

[0134] Table 1 shows the scene parameters of the scene graph Figure 8

[0135] Number of radar nodes 5 TDOA measurement error standard deviation 10 ns Station error 1m Interferer altitude 10 km RMA resolution cell size 2 km x 2 km Number of KSs 5

[0136] Table 2 shows the radar parameters

[0137] Table 3 shows the KS distribution range

[0138] Area name Horizontal coordinate distribution range Vertical coordinate distribution range Area 1 -150 to -109 km 98 to 138 km Area 2 -81 to -45 km 235 to 280 km Area 3 -14 to 16 km 280 to 320 km Area 4 34 to 96 km 264 to 308 km Area 5 101 to 141 km 101 to 141 km

[0139] The expected positioning accuracy of the five KSs is set to [350, 600, 750, 750, 400] m, and the performance of the solution set given by the three algorithms on the two objective functions is shown in Table 3. From the figure, it can be directly seen that the fitness value of the solution set generated by 2R-MOPSO on the objective function is smaller than that of the other two algorithms as a whole, and the solution set performance is better. Figure 3

[0140] ​​The array scheme with the best positioning performance is selected from the solutions generated by 2R-MOPSO, T-MOPSO and SC-MOPSO, and is denoted as The fitness values calculated by formula (5) of the three array schemes are 0.15, 0.17 and 0.18 respectively; the array scheme with the best monitoring performance is selected, and is denoted as Their effective monitoring coverage rates on RMA are 83.9%, 83.1% and 82.4% respectively. From the above data, it can be seen that, due to the use of the new individual optimal particle update rule, the search ability of 2R-MOPSO is greatly enhanced, and the performance of a single index is also better than that of the other two algorithms.

[0141] In order to more intuitively compare the array schemes given by the three algorithms, Figure 4 , 5 , 6 respectively show the positioning performance and monitoring performance of The three array schemes all meet the expected positioning accuracy, but the effective detection coverage rate on RMA is 3.7% and 5% higher than that of and respectively; in addition, under the array scheme , the worst GDOP of each KS is less than and Under the condition of meeting the expected positioning accuracy, if the sum of the worst GDOP of each KS is used to describe the positioning effect of the array scheme, then the positioning effect is 18.2% better than that of and 13.5% better than that of .

[0142] In the actual interference source positioning scene, since the enemy interference source is a non-cooperative target, its transmission power cannot be accurately estimated, therefore, the algorithm should be able to adapt to different interference source transmission powers, and ensure the robustness of the generated solution set. The present application sets different interference source transmission powers [1200W, 1300W, 1400W, 1600W] to generate a group of solution sets, and brings the array scheme in the solution set into P j = 1500W after correction, and compares it with the solution set of 2R-MOPSO in Figure 3 , as shown in Figure 7 .

[0143] Figure 7The solutions focusing on positioning performance are almost on the same Pareto front, which shows that 2R-MOPSO is not sensitive to the transmission power of the interference source when optimizing the positioning performance index. The average coverage rate difference of the solutions focusing on monitoring performance is less than 1%, which shows that the sensitivity of 2R-MOPSO to the transmission power of the interference source is weak when optimizing the positioning performance index. Under the experimental conditions in this section, 2R-MOPSO has good robustness to the transmission power of the interference source.

[0144] To sum up, the above is only a preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for configuration optimization of improved distributed radar emitter location with random relaxation, characterized in that, Comprising the following steps: Step one: build a distributed radar jammer positioning scene, and take the positioning performance and monitoring performance of the distributed radar jammer positioning as the guide to build a distributed radar jammer positioning configuration optimization problem; Specifically: The target area is divided into a radar mission area RMA and a radar deployment area RDA, the RMA is denoted as The RDA is denoted as The RDA contains 5 radar nodes, and the RMA contains a number of initially explored interference source regions, and the interference source region is a key sub-area KS; the RMA is discretized, and the set of grid points in the RMA and the kth KS is denoted as Ψ m and The set of all KSs is denoted as Ψ ks Ψ m , and Ψ ks are represented as: in, These represent the first to Nth terms in the RMA. m The set of coordinates of grid points, ψ n =(x n ,y n ,z n ) T Represents the coordinates of the nth grid point within the RMA region, (·) T Indicates the transpose operation, N m This represents the number of grid points in the RMA. The sub-tables represent the first to the last entries within KS. The coordinates of each grid point This represents the number of grid points within the k-th KS. This represents the coordinates of the nth grid point within KS; K is the number of KS. The positioning performance evaluation index is designed based on the geometric dilution of precision (GDOP) of the maximum positioning accuracy in each KS. The GDOP of the grid point in the kth KS is denoted as where Θ represents the arrangement scheme; the maximum value of the GDOP of each KS grid point is taken to represent the positioning accuracy of the corresponding KS as follows: The positioning performance objective function is: Wherein, wherein is the expected positioning accuracy of the kth KS, β1, β2correspond to coefficients for the cases where the expected positioning accuracy is not met and is met, respectively; In addition to accurately locating the identified sources of interference, distributed radar also needs to conduct wide-range surveillance of the airspace where new sources of interference may emerge; assuming the interference source is located at a grid point. The probability of finding it at is The recorded discovery probability is higher than the expected discovery probability. The grid points are considered as effective monitoring points. The proportion of effective monitoring points to all grid points is statistically analyzed, and this proportion is used to describe the system's monitoring performance. Therefore, the objective function for monitoring performance is: Wherein, Desired discovery probability; The signals in each receiving channel of the distributed radar are independent of each other, and the background noise of each channel is a Gaussian white noise with the same power; the radar node uses an omnidirectional antenna to simultaneously receive and process multiple jammer signals; the number of receiving radar nodes is N, and the false alarm probability of the jammer signal is: where γ is the detection threshold, σ 2 is the noise power; the probability that an interferer is found at is where Q N is the Marcum Q function of order N, χ i,n denotes the signal-to-noise ratio of the i-th radar node receiving the interfering source signal, denoted as: where P j represents the transmit power of the interference source, represents the receive gain of the nth radar node antenna, λ represents the carrier wavelength, F r represents the directional pattern propagation factor of the receive antenna, R i,n represents the distance between the ith receive radar and the grid point k, F n , T0, B, L s represent the Boltzmann constant, the receiver noise figure, the standard temperature, the receiver bandwidth and the loss factor, respectively; The positioning performance and monitoring performance objectives are unified into a minimization problem, the objective function vector is defined as f(A(Θ, Ψ ks ), 1 - Γ(Θ, Ψ m )), and the optimization problem is expressed as: and note that f1= Λ(Θ,Ψ ks ), f2= 1- Γ(Θ,Ψ m ). Step two: each particle represents a deployment scheme; initialize the particle swarm, including the initialization of the speed and position of all particles, the particle speed is set to zero at initialization, and the particle position is randomly initialized; initialize the particle swarm in the following way: A distributed system comprising N, N≥4, radars is constructed, defining a deployable area of radar nodes as Let the coordinates of the radar nodes be s i =(x i ,y i ,z i ) T , i = 1, 2,..., N, then the position of a single particle in the optimization space is represented as: Wherein, M is the number of particles in the population; Initialize the particle swarm, including the initialization of the speed and position of all particles, the particle speed is set to zero at initialization, and the particle position is randomly initialized; Step three: calculate the fitness value of the particle according to the objective function of the optimization problem; Step four: use an external archive to store the optimal solution set in the iteration process; the external archive is selected according to the dominance relationship between the individual optimal particle fitness values: in each iteration, traverse all individual optimal particles, and select the next individual optimal particle when the individual optimal particle is dominated by the external archive particle; when the individual optimal particle dominates the external archive particle, delete the external archive particle and add the individual optimal particle to the external archive; when the individual optimal particle and the external archive particle do not have a dominance relationship, if the external archive is not full, add the individual optimal particle to the external archive, if the external archive is full, select the external archive particle with the most dense distribution to delete, and add the individual optimal particle to the external archive; Step five, update the individual optimal position and global optimal position; specifically: Let the number of particles be M, and the velocity and position of the i-th, i = 1, 2,..., M particle in the population at the t-th iteration be v i (t) and x i (t), while the individual best position of particle i during the iteration process is p i (t) and the global best particle position g(t). Under the perturbation of the same independent variable, the change of the function value is the optimization sensitivity, and the optimization sensitivity of the positioning performance objective function and the monitoring performance objective function is weaker k , and a preset expected value is met Add a decay parameter d t = exp(-t / T max ) to control the probability of relaxation occurring, T max is the maximum number of iterations; the above operation is denoted by a logical variable B p (t). where r t Subject to uniform distribution U(0,1), define ∧ as the "and" operator and ∨ as the "or" operator, then the update rule of the individual optimal particle is: where f(x i (t)) is the fitness value of particle i, f(p i (t - 1)) is the fitness value of the individual optimal position p i (t - 1) of particle i at the (t - 1)th iteration, and y l (t), l = 1, 2,..., L, is the rth, r = 2,..., L - 1, particle and the relative distance d r (t) of the surrounding particles is: wherein f i,r (t) is represented as: Wherein, |·| represents taking the absolute value; Select the particle with the largest relative distance from the surrounding as the global optimal particle: Step six, update the speed and position of the particle; Step seven, judge whether the algorithm meets the termination condition, if the termination condition is reached, stop iteration and output the external archive as the optimal solution set; otherwise, repeat steps three to six until the algorithm meets the termination condition.

2. The method of claim 1, wherein the method is a method of improved distributed radar emitter location configuration optimization by random relaxation. Step six, update the speed and position of the particle, specifically: The displacement-velocity model is used to describe the optimization process of the particle in the optimization space, and the velocity and position update rules of particle i, i = 1,..., N in the tth iteration are: v i (t) = wv i (t-1) + c1r1(p i (t-1) - x i (t-1)) + c2r2(g(t-1) - x i (t-1)) (19) x i (t) = x i (t-1) + v i (t)(20) where w is the inertia weight, c1, c2 represent the individual and population learning factors respectively; r1, r2 are random numbers both of which follow uniform distribution U(0, 1); v i (t-1), x i (t-1), p i (t-1) represent the velocity, position and individual optimal position of particle i at the t-1th iteration respectively; g(t-1) represents the global optimal particle position at the t-1th iteration.

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