Distributed radar interference source positioning configuration optimization method based on random relaxation improvement

Abstract

The invention discloses a distributed radar interference source positioning configuration optimization method based on random relaxation improvement, and relates to the technical field of distributed radar resource scheduling, the algorithm effectively balances the sensitivity difference between different optimization indexes, and compared with other algorithms, the algorithm has higher optimization capacity. Comprising the following steps: constructing a distributed radar interference source positioning scene, and constructing a distributed radar interference source positioning configuration optimization problem by taking the positioning performance and monitoring performance of distributed radar interference source positioning as guidance; each particle represents a layout scheme; and initializing a particle swarm. And calculating fitness values of the particles according to an objective function of the optimization problem. An external file is used for storing an optimal solution set in the iteration process; and updating the individual optimal position and the global optimal position. And updating the speed and position of the particles, repeating the particle swarm optimization algorithm until a termination condition is reached, and outputting an external file as an optimal solution set.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed radar resource scheduling, and in particular to a random relaxation improved distributed radar interference source positioning configuration optimization method. Background Art

[0002] The emergence of active interference seriously inhibits the working efficiency of electronic systems. If the location of the interference source can be accurately located, it can provide prior information for subsequent anti-interference 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 collaborative work, which has great potential in locating interference sources.

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

[0004] Therefore, when facing multi-objective optimization problems, how to achieve stronger optimization capabilities is an urgent problem to be solved. Summary of the invention

[0005] In view of this, the present invention provides a distributed radar interference source positioning configuration optimization method improved by random relaxation, which can simultaneously improve the positioning performance and monitoring performance in the distributed radar interference source positioning scenario. The algorithm effectively balances the sensitivity differences between different optimization indicators and has stronger optimization ability than other algorithms. At the same time, the algorithm shows strong robustness to changes in the interference source transmission power and has certain practical application potential.

[0006] To achieve the above object, the technical solution of the present invention comprises the following steps:

[0007] Step 1: Construct a distributed radar interference source positioning scenario, and based on the positioning performance and monitoring performance of the distributed radar interference source positioning, construct a distributed radar interference source positioning configuration optimization problem.

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

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

[0010] Step 4: Use an external archive to store the optimal solution set in the iterative 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, and when the individual optimal particle is dominated by the external archive particle, select the next individual optimal 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 with each other, 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 and 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 speed and position

[0013] Step 7: Determine whether the algorithm meets the termination condition. If so, 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 positioning scenario is constructed, specifically:

[0015] The target area is divided into radar mission area RMA and radar deployment area RDA, RMA is recorded as RDA is denoted as RDA contains 5 radar nodes, RMA contains several areas where the interference sources are located, and the area where the interference sources are located is the key sub-area KS; RMA is discretized and Ψ m and Denote the set of grid points in the RMA and the kth KS, and define the set of all KS as Ψ ks , then m , and ks It is expressed as:

[0016]

[0017] in, Respectively represent the 1st to Nth in RMA m The coordinate set of grid points, ψ n =(x n ,y n ,z n ) T represents the coordinates of the nth grid point in the RMA region, (·) T represents the transpose operation, N m is the number of grid points in RMA; The table shows the 1st to 2nd KS The coordinates of the grid points, is the number of grid points in the kth KS; Represents the coordinates of the nth grid point in KS; K is the number of KS.

[0018] Furthermore, guided by the positioning performance and monitoring performance of distributed radar interference source positioning, the distributed radar interference source positioning configuration optimization problem is constructed, specifically:

[0019] The positioning performance evaluation index is designed based on the geometric dilution GDOP of the maximum positioning accuracy in each KS. Let the GDOP of the grid point in the kth KS be Where Θ represents the array scheme; the maximum value of GDOP in each KS grid point represents the positioning accuracy of the corresponding KS:

[0020]

[0021] The positioning performance objective function is:

[0022]

[0023] in,

[0024]

[0025] in is the expected positioning accuracy of the kth KS, β1 and β2 correspond to the coefficients of the cases where the expected positioning accuracy is not met and is met, respectively.

[0026] In addition to accurately locating the detected interference sources, the distributed radar also needs to conduct wide-range monitoring of the airspace where new interference sources may appear; assuming that the interference source is located at the grid point The probability of finding The recorded probability of discovery is higher than the expected probability of discovery The grid points of are effective monitoring points, and the proportion of effective monitoring points to all grid points is counted to describe the monitoring performance of the system. The monitoring performance objective function is:

[0027]

[0028] in,

[0029]

[0030] is the expected discovery probability.

[0031] 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; the radar node uses an omnidirectional antenna to receive and process multiple interference source signals at the same time. The number of receiving radar nodes is N, and the false alarm probability of the interference source signal is:

[0032]

[0033] Among them, γ is the detection threshold, σ 2 is the noise power; The probability of the interference source being discovered is:

[0034]

[0035] Among them, Q N is the Marcum Q function of order N, χ i,n Indicates that the i-th radar node receives The signal-to-noise ratio of the interference source signal at is expressed as:

[0036]

[0037] Among them, P j Indicates the transmission power of the interference source, represents the receiving gain of the antenna of the nth radar node, λ represents the carrier wavelength, and F r represents the pattern propagation factor of the receiving antenna, R i,n Represents the i-th receiving radar and grid point The distance between them, k, F n , T0, B, L s They represent the Boltzmann constant, receiver noise figure, standard temperature, receiver bandwidth and loss factor respectively.

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

[0039]

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

[0041] Furthermore, in step 2, the particle swarm is initialized in the following manner:

[0042] Build a distributed system containing N, N ≥ 4 radars and define the deployable area of ​​radar nodes as The coordinates of the radar node are 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 expressed as:

[0043]

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

[0045] Initializing the particle swarm includes initializing the speed and position of all particles. The particle speed is set to zero during initialization, and the particle position is initialized randomly.

[0046] Furthermore, step five, updating the individual optimal position and the global optimal position, is as follows:

[0047] Set the number of particles to M, and the speed and position of the i-th, i=1,2,...,M-th particle in the population at the t-th iteration to v i (t) and x i (t), and the individual optimal position of 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. For the positioning performance objective function and the monitoring performance objective function, the objective function with weaker optimization sensitivity is taken as f k , meeting a preset expectation

[0049] Add a decay parameter d t =exp(-t / T max ) to control the probability of relaxation, T max is the maximum number of iterations; the above operation uses a logical variable B p (t) to represent:

[0050]

[0051] Among them, 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:

[0052]

[0053] Where f(x i (t)) is the fitness value of particle i, f(p i (t-1)) is the individual optimal position p of particle i in the t-1 iteration i The fitness value of (t-1), the particle in the external archive at the tth iteration is y l (t), l = 1, 2, ..., L, the relative distance d between the rth, r = 2, ..., L-1th particle and the surrounding particles r (t) is:

[0054]

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

[0056]

[0057] Here, |·| means taking the absolute value.

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

[0059]

[0060] Furthermore, in step six, the speed and position of the particle are updated, specifically:

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

[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] 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, both of which obey the uniform distribution U(0,1); v i (t-1), x i (t-1), p i (t-1) represents the velocity, position and individual optimal position of particle i in the t-1th iteration respectively; g(t-1) represents the global optimal particle position in the t-1th iteration.

[0065] Beneficial effects:

[0066] The present invention provides a distributed radar interference source positioning configuration optimization method improved by random relaxation. The method effectively balances the differences in optimization sensitivity between different objective functions by designing a new individual optimal particle update rule, and can simultaneously improve the positioning performance and monitoring performance in the distributed radar interference source positioning scenario. It also overcomes the defect that the existing algorithms are prone to fall into local optimality when dealing with multi-objective optimization problems with high computational complexity, nonlinearity, and non-convexity to a certain extent. At the same time, the algorithm is insensitive to the changes in the transmission power of non-cooperative targets (interference sources) and exhibits strong robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 Locate the interference source for distributed radar scenarios;

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

[0069] Figure 3 Comparison of solution sets of 2R-MOPSO, T-MOPSO, and SC-MOPSO;

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

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

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

[0073] Figure 7 Comparison of 2R-MOPSO solution sets under different interference source transmission powers;

[0074] Figure 8 This is the scene graph in Example 1 of the present invention. DETAILED DESCRIPTION

[0075] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0076] The present invention constructs a distributed radar interference source positioning scenario (such as Figure 1 The interference source location scenario is divided into the radar mission area (RMA) and the radar deployment area (RDA). RMA is denoted as RDA is denoted as RDA contains N radar nodes, and RMA contains several areas where the interference sources are located. For the convenience of description, the area where the interference sources are located is called the key subarea (KS). RMA is discretized and represented by Ψ m and Denote the set of grid points in the RMA and the kth KS, and define the set of all KS as Ψ ks , then m , and ks It can be expressed as:

[0077]

[0078] Among them, ψ n =(x n ,y n ,z n ) T represents the coordinates of the nth grid point in the region, (·) T represents the transpose operation, N m is the number of grid points in 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. The GDOP of the grid point in the kth KS is Where Θ represents the array scheme. The maximum value of GDOP in each KS grid point represents the positioning accuracy of the corresponding KS:

[0080]

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

[0082]

[0083] in,

[0084]

[0085] is the expected positioning accuracy of the kth KS, β1 = 0.8, β2 = 0.2, corresponding to the cases where the expected positioning accuracy is not met and is met, respectively.

[0086] In addition to accurately locating the detected interference sources, distributed radars also need to conduct wide-area monitoring of the airspace where new interference sources may appear. Assume that the interference source is located at the grid point The probability of finding The recorded probability of discovery is higher than the expected probability of discovery The grid points are effective monitoring points, and the proportion of effective monitoring points to all grid points is counted to describe the monitoring performance of the system. The monitoring performance objective function is defined as:

[0087]

[0088] in,

[0089]

[0090] Assume 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; assume 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] Among them, γ is the detection threshold, σ 2 is the noise power. The probability of the interference source being discovered is:

[0093]

[0094] Among them, Q N is the Marcum Q function of order N, χ i,n Indicates that the i-th radar node receives The signal-to-noise ratio of the interference source signal at is expressed as:

[0095]

[0096] Among them, P j Indicates the transmission power of the interference source, represents the receiving gain of the antenna of the nth radar node, λ represents the carrier wavelength, and F r represents the pattern propagation factor of the receiving antenna, R i,n Represents the i-th receiving radar and grid point The distance between them, k, F n , T0, B, Ls They represent the Boltzmann constant, receiver noise figure, standard temperature, receiver bandwidth and loss factor respectively.

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

[0098]

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

[0100] A random relaxation improved multi-objective particle swarm optimization algorithm process is as follows Figure 2 As shown, the specific steps include:

[0101] Step 1: Initialize the particle swarm

[0102] When using the particle swarm optimization algorithm to solve the radar node formation optimization problem, each particle represents a formation solution. Construct a distributed system containing N (N ≥ 4) radars and define the deployable area of ​​the radar node as The coordinates of the radar node are s i =(x i ,y i ,z i ) T (i=1,2,...,N), the position of a single particle in the optimization space can be expressed as:

[0103]

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

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

[0106] Step 2: Calculate 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, let us assume that the optimization problem is a minimization problem. Suppose there are I objective functions in the optimization problem, which are denoted as f1,...,f I (In the present invention, I = 2), then the fitness value of particle i on each objective function is calculated as f1(x i ),...,f I (xi ), the fitness value of particle i can be expressed by the vector f(x i ) to simplify the representation. 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 3: Determine the dominance relationship and update external files

[0109] 2R-MOPSO uses an external archive to store the optimal solution set in the iterative process. The external archive is selected based on the dominance relationship between the fitness values ​​of individual optimal particles: in each iteration, all individual optimal particles are traversed. When the individual optimal particle is dominated by the external archive particle, the next individual optimal particle is selected; 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; if the external archive is full, the external archive particle with the densest distribution is selected and deleted, and the individual optimal particle is added to the external archive.

[0110] Step 4: Update individual optimal and global optimal

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

[0112] When 2R-MOPSO updates the individual optimal particle, the new individual optimal particle does not need to perform better in all indicators. Under the disturbance of the same independent variable, the change in the function value 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 , meeting a preset expectation In addition, 2R-MOPSO adds a decay parameter d t =exp(-t / T max ) to control the probability of relaxation, T max is the maximum number of iterations. The above operation can be represented by a logical variable:

[0113]

[0114] Among them, 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:

[0115]

[0116] Let the particle in the external archive at the tth iteration be y l (t), l=1,2,...,L, define the relative distance between the rth, r=2,...,L-1th particle and the surrounding particles as:

[0117]

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

[0119]

[0120] Here, |·| means taking the absolute value.

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

[0122]

[0123] Step 5: Update the particle speed and position

[0124] 2R-MOPSO uses a simple displacement-velocity model to describe the optimization process of particles in the optimization space. The speed and position update rules of particle i, i = 1, ..., N in the tth 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] Among them, 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 obey the uniform distribution U(0,1).

[0128] Step 6: Determine whether the algorithm meets the termination condition

[0129] When the algorithm reaches the maximum number of iterations, stop iterating and output the external archive as the optimal solution set; otherwise, repeat steps 2 to 5 until the algorithm meets the termination condition.

[0130] Example 1

[0131] The distributed radar adopted in the present invention is a passive receiving system. Considering that the area of ​​RDA is smaller than that of RMA in the interference source positioning scenario, the optimization sensitivity of the system monitoring performance is significantly 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 implemented using MATLAB R2021a software. The relevant parameter settings are shown in Tables 1 and 2, and the interference source transmission power P is set j =1500W, false alarm probability P fa =1×10 -6 , expected detection probability The present invention sets 5 interference sources, and the ranges of KS where they are located are shown in Table 3.

[0133] In order to verify the performance of 2R-MOPSO, the present invention compares two other MOPSO-based optimization algorithms, namely T-MOPSO and SC-MOPSO. SC-MOPSO is a variant MOPSO that imposes optimization direction constraints, which is used to solve problems with complex constraints, non-convexity and high computational complexity. In the simulation, the present invention adjusts the implementation details of SC-MOPSO 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, L=15.

[0134] Table 1 for Figure 8 Scene parameters of the scene graph shown

[0135] Number of radar nodes 5 TDOA measurement error standard deviation 10ns Site error 1m Interference source height 10km RMA resolution unit size 2km×2km KS quantity 5

[0136] Table 2 Radar parameters

[0137] Table 3 KS distribution range

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

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

[0140] The best positioning performance is selected from the solution sets generated by 2R-MOPSO, T-MOPSO and SC-MOPSO, respectively. The fitness values ​​of the three deployment schemes calculated in formula (5) are 0.15, 0.17, and 0.18 respectively. The deployment scheme with the best monitoring performance is selected and recorded as Their effective monitoring coverage on RMA is 83.9%, 83.1%, and 82.4%, respectively. From the above data, we can see 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 indicator is also better than the other two algorithms.

[0141] In order to more intuitively compare the array layouts given by the three algorithms, Figure 4 , 5 , 6 respectively show The three deployment schemes all meet the expected positioning accuracy, but Effective detection coverage ratio for RMA and 3.7% and 5% higher respectively; in addition, Under this condition, the worst GDOP of each KS is less than and Under the condition of meeting the expected positioning accuracy, if the positioning effect of the array scheme is described by the sum of the worst GDOP of each KS, then The positioning effect is better than 18.2% better than 13.5% better.

[0142] In the actual interference source location scenario, since the enemy interference source is a non-cooperative target, its transmission power cannot be accurately estimated. Therefore, the algorithm must be able to adapt to different interference source transmission powers to ensure the robustness of the generated solution set. The present invention sets different interference source transmission powers [1200W, 1300W, 1400W, 1600W] to generate a set of solution sets, and brings the array scheme in the solution set into P j =1500W After correction, Figure 3 For comparison, the solution set of 2R-MOPSO is Figure 7 shown.

[0143] Figure 7Among different solution sets, the solutions focusing on positioning performance are almost on the same Pareto frontier, indicating that 2R-MOPSO is insensitive to the interference source transmission power when optimizing the positioning performance index; the average coverage rate difference of the solutions focusing on monitoring performance is less than 1%, indicating that 2R-MOPSO is weakly sensitive to the interference source transmission power when optimizing the positioning performance index. Under the experimental conditions in this section, 2R-MOPSO has good robustness to the interference source transmission power indicator.

[0144] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A random relaxation improved distributed radar interference source positioning configuration optimization method, characterized in that: The steps include: Step 1: Construct a distributed radar interference source positioning scenario, and construct a distributed radar interference source positioning configuration optimization problem based on the positioning performance and monitoring performance of the distributed radar interference source positioning; Step 2: Each particle represents a deployment scheme; initialize the particle swarm, including initializing the speed and position of all particles. The particle speed is set to zero during initialization, and the particle position is randomly initialized. Step 3: Calculate the fitness value of the particle according to the objective function of the optimization problem; Step 4: Use an external archive to store the optimal solution set in the iterative 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, and when the individual optimal particle is dominated by the external archive particle, select the next individual optimal 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 with each other, 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 and delete it, and add the individual optimal particle to the external archive; Step 5: Update the individual optimal position and the global optimal position; Step 6: Update the particle speed and position Step 7: Determine whether the algorithm meets the termination condition. If so, 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.

2. The random relaxation improved distributed radar interference source positioning configuration optimization method according to claim 1, characterized in that: The construction of the distributed radar interference source positioning scenario is specifically as follows: The target area is divided into radar mission area RMA and radar deployment area RDA, RMA is recorded as RDA is denoted as RDA contains 5 radar nodes, RMA contains several areas where the interference sources are located, and the area where the interference sources are located is the key sub-area KS; RMA is discretized and Ψ m and Denote the set of grid points in the RMA and the kth KS, and define the set of all KS as Ψ ks , then m , and ks It is expressed as: in, Respectively represent the 1st to Nth in RMA m The coordinate set of grid points, ψ n =(x n ,y n ,z n ) T represents the coordinates of the nth grid point in the RMA region, (·) T represents the transpose operation, N m is the number of grid points in RMA; The table shows the 1st to 2nd KS The coordinates of the grid points, is the number of grid points in the kth KS; Represents the coordinates of the nth grid point in KS; K is the number of KS.

3. The random relaxation improved distributed radar interference source positioning configuration optimization method according to claim 1, characterized in that: The distributed radar interference source positioning configuration optimization problem is constructed based on the positioning performance and monitoring performance of the distributed radar interference source positioning, which is specifically: The positioning performance evaluation index is designed based on the geometric dilution GDOP of the maximum positioning accuracy in each KS. Let the GDOP of the grid point in the kth KS be Where Θ represents the array scheme; the maximum value of GDOP in each KS grid point represents the positioning accuracy of the corresponding KS: The positioning performance objective function is: in, in is the expected positioning accuracy of the kth KS, β1 and β2 correspond to the coefficients of the cases where the expected positioning accuracy is not met and is met, respectively; In addition to accurately locating the detected interference sources, the distributed radar also needs to conduct wide-range monitoring of the airspace where new interference sources may appear; assuming that the interference source is located at the grid point The probability of finding The recorded probability of discovery is higher than the expected probability of discovery The grid points of are effective monitoring points, and the proportion of effective monitoring points to all grid points is counted to describe the monitoring performance of the system. The monitoring performance objective function is: in, is the expected 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 Gaussian white noise with the same power; the radar node uses an omnidirectional antenna to receive and process multiple interference source signals at the same time. The number of receiving radar nodes is N, and the false alarm probability of the interference source signal is: Among them, γ is the detection threshold, σ 2 is the noise power; The probability of the interference source being discovered is: Among them, Q N is the Marcum Q function of order N, χ i,n Indicates that the i-th radar node receives The signal-to-noise ratio of the interference source signal at is expressed as: Among them, P j Indicates the transmission power of the interference source, represents the receiving gain of the antenna of the nth radar node, λ represents the carrier wavelength, and F r represents the pattern propagation factor of the receiving antenna, R i,n Represents the i-th receiving radar and grid point The distance between them, k, F n , T0, B, L s represent the Boltzmann constant, receiver noise figure, standard temperature, receiver bandwidth and loss factor respectively; The positioning performance and monitoring performance objectives are unified into a minimization problem, and the objective function vector is defined as f(Λ(Θ,Ψ ks ),1-Γ(Θ,Ψ m ), then the optimization problem is expressed as: And denote \(f1 = \Lambda(\Theta,\Psi ks ), f2 = 1 - \Gamma(\Theta,\Psi m ).

4. The random relaxation improved distributed radar interference source positioning configuration optimization method according to claim 1, characterized in that: In step 2, the particle swarm is initialized in the following manner: Build a distributed system containing N, N ≥ 4 radars and define the deployable area of ​​radar nodes as The coordinates of the radar node are 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 expressed as: Where M is the number of particles in the population; Initializing the particle swarm includes initializing the speed and position of all particles. The particle speed is set to zero during initialization, and the particle position is initialized randomly.

5. The random relaxation improved distributed radar interference source positioning configuration optimization method according to claim 4, characterized in that: The step 5, updating the individual optimal position and the global optimal position, is specifically as follows: Set the number of particles to M, and the speed and position of the i-th, i=1,2,...,M-th particle in the population at the t-th iteration to v i (t) and x i (t), and the individual optimal position of particle i in the iteration process is p i (t) and the global optimal particle position g(t); Under the same disturbance of the independent variable, the change in the function value 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 , meeting a preset expectation Add a decay parameter d t =exp(-t / T max ) to control the probability of relaxation, T max is the maximum number of iterations; the above operation uses a logical variable B p (t) to represent: Among them, 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 individual optimal position p of particle i in the t-1 iteration i The fitness value of (t-1), the particle in the external archive at the tth iteration is y l (t), l = 1, 2, ..., L, the relative distance d between the rth, r = 2, ..., L-1th particle and the surrounding particles r (t) is: Among them, f i,r (t) is expressed as: Among them, |·| means taking the absolute value; Select the particle with the largest relative distance to the surrounding particles as the global optimal particle:

6. The random relaxation improved distributed radar interference source positioning configuration optimization method according to claim 1, characterized in that: Step 6: Update the particle's speed and position, specifically: The displacement-velocity model is used to describe the optimization process of particles in the optimization space. The speed 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 and c2 represent the individual learning factor and the population learning factor respectively; r1 and r2 are random numbers, both of which obey the uniform distribution U(0,1); v i (t-1), x i (t-1), p i (t-1) represents the velocity, position and individual optimal position of particle i in the t-1th iteration respectively; g(t-1) represents the global optimal particle position in the t-1th iteration.

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