Two-dimensional MUSIC spectrum peak searching method based on improved Archimedes algorithm

Abstract

The invention discloses a two-dimensional MUSIC spectrum peak searching method based on an improved Archimedes algorithm, and the method comprises the steps: carrying out the one-dimensional MUSIC spatial spectrum function derivation of a signal model, and expanding the one-dimensional MUSIC spatial spectrum function to a two-dimensional MUSIC spatial spectrum function; secondly, taking a spatial spectrum function of the two-dimensional MUSIC as a target function of an Archimedes optimization algorithm; and then, in combination with an objective function, introducing a fusion chaos algorithm strategy to initialize a population, introducing a mutation algorithm, disturbing positions, and improving an Archimedes optimization algorithm. And finally, carrying out two-dimensional MUSIC spectral peak search through an improved Archimedes optimization algorithm, and taking the direction of arrival, namely, a pitch angle and an azimuth angle, obtained in a mode of solving maximum and minimum values through a target function as spectral peak values. The two-dimensional MUSIC spectrum peak searching method has the advantages that the optimization speed is higher, the optimization precision is higher, the robustness is better, and the two-dimensional MUSIC spectrum peak searching can be quickly and accurately carried out.

Description

Technical Field

[0001] The invention belongs to the technical field of sound source localization, and in particular relates to a two-dimensional MUSIC spectrum peak searching method based on an improved Archimedean algorithm. Background Art

[0002] In order to solve the problem of large amount of computation in MUSIC algorithm, some researchers have conducted relevant research and achieved a lot of progress and results. One of the ideas in these results is to introduce swarm intelligence algorithm in spectrum peak search to reduce the amount of computation in the algorithm.

[0003] Based on this, the Archimedean algorithm (AOA) is introduced to accelerate the peak search part. However, the Archimedean algorithm AOA performs poorly in the global exploration process and tends to converge prematurely. Therefore, the AOA has good optimization accuracy, but it is easily trapped in local extreme values ​​and lacks stability. Summary of the invention

[0004] In order to overcome the problem that one of the key steps of the MUSIC algorithm is the spectrum peak search, the grid search method used in the traditional method has the problems of huge computational complexity and poor real-time performance, although the search accuracy is high. Based on this, the improved Archimedes algorithm is introduced to accelerate the spectrum peak search part. An improved Archimedes algorithm based on the fusion chaos algorithm and the Gauss-Cauchy mixed mutation algorithm is proposed. On the one hand, when the population is initialized, the chaos algorithm is used to avoid the problem of poor population diversity. On the other hand, the Gauss-Cauchy mixed mutation algorithm is used to randomly fuse and mutate the individuals in each iteration to prevent the algorithm from falling into the local optimum, so as to improve the stability of the algorithm.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A two-dimensional MUSIC spectrum peak search method based on an improved Archimedean algorithm comprises the following steps:

[0007] S1. The signal model is derived, and then the one-dimensional MUSIC spatial spectrum function is derived, and the one-dimensional MUSIC spatial spectrum function is extended to the two-dimensional MUSIC spatial spectrum function.

[0008] S2. The spatial spectrum function of two-dimensional MUSIC is used as the objective function of the Archimedean optimization algorithm.

[0009] S3. Combined with the objective function, the fusion chaos algorithm strategy is introduced to initialize the population, the mutation algorithm is introduced to perturb the position, and the Archimedean optimization algorithm AOA is improved.

[0010] Improved Archimedean optimization algorithm: To provide the Archimedean algorithm with better traversability for the initial population, a fusion chaos algorithm strategy is introduced to initialize the population, and a hybrid mapping combining circle chaos mapping and Chebyshev chaos mapping is introduced to initialize the population, thereby improving the convergence speed and solution accuracy of the algorithm. In order to prevent the Archimedean algorithm from falling into the local optimal solution, a Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position, so that the population jumps out of the local optimal solution and expands the population search solution space.

[0011] S4. The improved Archimedean optimization algorithm is used to perform a two-dimensional MUSIC spectrum peak search. The two-dimensional MUSIC spectrum peak search obtains the wave direction, that is, the pitch angle and the azimuth angle as the spectrum peak value by finding the maximum value of the objective function. The wave direction estimation results at different azimuths and the spectrum peak search time are compared.

[0012] Furthermore, the step S1 specifically includes:

[0013] S11. Derivation of signal model:

[0014] For two-dimensional DOA estimation, an L-type array or a uniform planar array is generally selected. Here, a uniform planar array is used. Assume that the number of planar array elements is M×P, and the number of signal sources is K. Assume that the direction of arrival of each signal source in space is represented by (θ1, φ1), (θ2, φ2)…, (θ K ,φ K ) where θ k ,φ K are the elevation angle and azimuth angle of the kth signal source respectively. The uniform array can be divided into several sub-arrays according to rows or columns, where each sub-array is a uniform linear array. Taking the row as an example, the mathematical model of the sub-array m can be expressed as:

[0015] A m =A x D m (A y ),m=1,2,…,M

[0016] Where: A x and A y is the L-type array response matrix corresponding to the subarray, D m (.) represents a diagonal matrix consisting of m rows of the matrix in the brackets. Then the uniform plane array receives the signal:

[0017]

[0018] Among them, S is the signal emitted by the signal source, and N is the noise.

[0019] S12. Perform one-dimensional MUSIC derivation and extend it to the spatial spectrum function of two-dimensional MUSIC as the objective function:

[0020] The covariance matrix is ​​obtained according to the uniform planar array receiving signal. The array covariance matrix R can be divided into two spaces, signal subspace and noise subspace, by eigendecomposition, namely:

[0021]

[0022] Where: s is the diagonal matrix consisting of the larger K eigenvalues ​​in the eigendecomposition of R, U s is the signal subspace spanned by the corresponding eigenvector. Similarly, ∑ N is a diagonal matrix consisting of NK eigenvalues, U N is the spanned noise subspace. From the orthogonality of the noise subspace and the signal subspace, we can get:

[0023]

[0024] According to the above formula, we can get:

[0025] A(θ)R s A H (θ)U N =0

[0026] Where: Matrix R s is a full rank matrix, non-singular, so it has an inverse matrix. So equation (5) can be transformed into: A H (θ)U N =0, which shows that the matrix A H Each vector in (θ) is orthogonal to the noise subspace, so:

[0027] U N a(θ i )=0,i=1,2,…,K

[0028] Where: a(θ i ) is A(θ i ), the spatial spectrum function is obtained by the orthogonal relationship between the noise characteristic vector and the signal characteristic vector:

[0029]

[0030] Where a(θ) is the vector of the array response matrix, U N is the noise subspace, a H (θ) is the conjugate transpose of a(θ), For U N The conjugate transpose of .

[0031] Two-dimensional MUSIC is similar to one-dimensional MUSIC, except that the direction matrix is ​​expanded. The spatial spectrum function of two-dimensional MUSIC is:

[0032]

[0033] Where: where a x (θ, φ) and a y (θ, φ) is the quality of the L-type array response matrix corresponding to the subarray, is the tensor product, E N is the noise feature vector, For E N The conjugate transpose of . Then the angle where the spectrum peak of the spectrum function is located is the spatial wave arrival direction, and the spatial spectrum function of the above two-dimensional MUSIC is the target function.

[0034] Furthermore, the step S3 specifically includes:

[0035] S31. In order to provide the Archimedean algorithm with a better ergodicity for the initialization population, a fusion chaos algorithm strategy is introduced to initialize the population, and a hybrid mapping combining circle chaos mapping and Chebyshev chaos mapping is introduced to initialize the population, thereby improving the convergence speed and solution accuracy of the algorithm:

[0036] Furthermore, the step S31 specifically includes:

[0037] The S311.Circle chaotic map is defined as follows:

[0038]

[0039] Among them, x n is the input value at time n;

[0040] S312.Chebyshev chaotic map is defined as follows:

[0041] x n+1 = cos(φcos -1 x n )

[0042] The value of Φ is a constant.

[0043] S313. Random position parameters fusion of two chaotic maps:

[0044] Each individual in the population generates a random number between (0,1) as the position parameter of the individual. The position parameters of all individuals form the position parameter matrix Pt, where N is the population size and D is the spatial dimension.

[0045] Pt(i,j)=randi=1,2,…,Nj=1,2,…,D.

[0046] Set the selection probability to 0.5 and update the individual positions of the population as follows.

[0047]

[0048] in, is the position of individuals in a population with a population size of i and a spatial dimension of j at time n.

[0049] The generated initial population is subjected to boundary constraint checks, and positions exceeding or falling below the upper and lower bounds are assigned boundary values.

[0050] Perform bounds constraint checks on the generated initial population:

[0051]

[0052] S32. Introduce the number of iterations into the mutation probability Rand, where Rand is a random value between 0 and 1:

[0053]

[0054] Where CurrentGen is the current iteration number and Gen is the maximum iteration number.

[0055] When the above conditions are met, the Gauss-Cauchy mixed mutation algorithm is introduced to perturb the position.

[0056] In order to prevent the Archimedean algorithm from falling into the local optimal solution, the Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position, so that the population can jump out of the local optimal solution and expand the population search solution space:

[0057] Furthermore, the step S32 specifically includes:

[0058] S321. Gaussian mutation algorithm:

[0059] Gaussian mutation was originally used to change the local search performance of the genetic algorithm in the key search area. It replaces the original gene value with a random number that conforms to the normal distribution with a mean of μ and a variance of σ. The following is the Gaussian mutation formula:

[0060]

[0061] Gaussian i (x) = N(x best ,δ)

[0062] x is the position of the individual, x bestis the current global optimal individual, δ is the standard deviation of the Gaussian distribution, and the Gaussian mutation makes the population escape the local optimal solution. The local search ability of Gaussian mutation is good, but the ability to make the population jump out of the local optimal solution is weak, which is not conducive to global convergence.

[0063] S322. Cauchy mutation algorithm:

[0064] The Cauchy mutation has a very strong global perturbation ability and better global search ability. The following is the Cauchy mutation formula:

[0065]

[0066] x is the location of the population.

[0067] S323. Gauss-Cauchy hybrid mutation algorithm:

[0068] Based on the characteristics of Gaussian mutation and Cauchy mutation, a Gaussian-Cauchy mixed mutation mechanism is proposed. The formula is as follows:

[0069] Mutation i (x) = α·Gaussian i (x)+β·Cauthy i (x)

[0070]

[0071] Since in the entire population iteration process, the initial population is usually far away from the actual optimal solution, as the number of iterations increases, the number of individuals close to the actual optimal solution will increase, and the number of individuals that need to mutate will also decrease. In order to prevent more individuals with better fitness from mutating, the number of iterations is introduced into the mutation probability Rand, where Rand is a random value between 0 and 1, CurrentGen is the current number of iterations, Gen is the maximum number of iterations, α is the Gaussian coefficient of variation, and β is the Cauchy coefficient of variation. Since the fixed Cauchy coefficient of variation is not conducive to solving the optimal individual in the entire iteration process, a larger coefficient is required in the early and middle stages of the algorithm to make the algorithm jump out of the local optimum, while a smaller coefficient is required in the later stages of the algorithm so that the algorithm can complete convergence. Therefore, the number of iterations is introduced here with a sine function to limit the Cauchy coefficient of variation to the range of 0 to 1 and decrease with the increase of the number of iterations.

[0072]

[0073] Beneficial effects of the present invention:

[0074] The two-dimensional MUSIC spectrum peak search based on the improved Archimedean algorithm of the present invention takes the two-dimensional MUSIC spectrum peak function as the objective function, has a faster optimization speed, higher optimization accuracy and better robustness than the original Archimedean optimization algorithm, improves the optimization accuracy and speed, and can quickly and accurately perform two-dimensional MUSIC spectrum peak search. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a two-dimensional MUSIC spectrum peak search flow chart based on the improved Archimedean algorithm of the present invention;

[0076] Figure 2 It is a two-dimensional MUSIC spectrum peak diagram with azimuth and elevation angles of [25,15];

[0077] Figure 3 It is a two-dimensional MUSIC spectrum peak diagram with azimuth and elevation angles of [85,35];

[0078] Figure 4 It is a two-dimensional MUSIC spectrum peak diagram with azimuth and elevation angles of [-45,-30]. DETAILED DESCRIPTION

[0079] The technical idea of ​​the present invention is as follows: firstly, a two-dimensional MIUSIC space spectrum function is derived as the objective function; then a fusion chaos algorithm strategy is introduced to initialize the population, and a circle and Chebyshev mixed mapping is introduced to initialize the population, thereby expanding the search range of the algorithm, thereby improving the convergence speed and solution accuracy of the algorithm; finally, a Gaussian-Cauchy mixed mutation algorithm is introduced to enable the population to jump out of the local optimum and expand the population's search solution space.

[0080] This embodiment provides a two-dimensional MUSIC spectrum peak search method based on an improved Archimedean algorithm. Figure 1 As shown, the following steps are included:

[0081] S1. The signal model is derived, and then the one-dimensional MUSIC spatial spectrum function is derived, and then extended to the two-dimensional MUSIC spatial spectrum function.

[0082] S2. The spatial spectrum function of two-dimensional MUSIC is used as the objective function of the Archimedean optimization algorithm.

[0083] Furthermore, the step S2 specifically includes:

[0084] S21. Original algorithm flow of Archimedes optimization algorithm:

[0085] The Archimedean optimization algorithm is a population-based optimization algorithm inspired by Archimedean principle. The algorithm regards all objects immersed in liquid as populations. Objects continuously adjust their density, volume and acceleration through collision or buoyancy to achieve equilibrium. It includes three stages: initialization stage, global exploration stage (collision between objects) and local development stage (no collision between objects).

[0086] Furthermore, the step S21 specifically includes:

[0087] S211. Initialization phase:

[0088] In the initialization phase, AOA initializes the population position by the following formula

[0089] X i =lb i +rand×(ub i -lb i )

[0090] Where [lb i ,ub i ] represents the search space, rand∈(0,1) is a random number.

[0091] The density (den), volume (vol) and acceleration (acc) of each individual are randomly initialized by the following formula:

[0092] den i =rand

[0093] vol i =rand

[0094] acc i =lb i +rand×(ub i -lb i )

[0095] At this stage, AOA will evaluate the population and select the current best individual (x best ), the density of the optimal individuals (den best )、Volume best ) and the acceleration of the optimal individual (acc best ). And update the volume and density of other individuals with the density and volume of the optimal individual:

[0096]

[0097] Next, set the transfer algorithm TF and density factor d according to the following two formulas:

[0098]

[0099] Among them, t represents the current iteration number, t max Represents the maximum number of iterations.

[0100] S212. Global exploration phase (collision between objects):

[0101] If TF < 0.5, AOA performs global exploration and updates the individual acceleration according to the following formula:

[0102]

[0103] in, Indicates that in generation t+1, i th The acceleration of an individual, den mr and vol mr is the density and volume of the randomly selected individual in the current iteration. AOA normalizes the acceleration of each individual according to the following formula for updating the individual position:

[0104]

[0105] in is i in generation t+1 th The normalized acceleration of the individual. u and l are used to adjust the normalization range.

[0106] At this stage, the individual positions are updated by:

[0107]

[0108] Where C1 is a fixed constant and rand∈(0,1) is a random number.

[0109] S213. Local development stage (no collision between objects):

[0110] If TF>0.5, AOA performs local synchronization, updates the individual acceleration according to formula (9), and normalizes the acceleration according to formula (7):

[0111]

[0112] At this stage, the individual positions are updated by:

[0113]

[0114] Where C2 is a fixed constant; T = C3×TF, and T∈[C3×03,1]; F is a direction factor used to determine the iterative position update direction, defined as follows:

[0115]

[0116] Among them, P = 2×rand-C4, C4 is a fixed constant.

[0117] S3. Improved Archimedean optimization algorithm: To provide the Archimedean algorithm with better traversability for the initial population, the fusion chaos algorithm strategy is introduced to initialize the population, and the hybrid mapping combining the circle chaos mapping and the Chebyshev chaos mapping is introduced to initialize the population, thereby improving the convergence speed and solution accuracy of the algorithm. In order to prevent the Archimedean algorithm from falling into the local optimal solution, the Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position, so that the population jumps out of the local optimal solution and expands the population search solution space.

[0118] S4. The two-dimensional MUSIC spectrum peak search effect of the improved Archimedean optimization algorithm is verified. The two-dimensional MUSIC spectrum peak search obtains the wave direction, namely the pitch angle and the azimuth angle, as the spectrum peak value by finding the maximum value of the objective function. The wave direction estimation results at different azimuths and the spectrum peak search time are compared respectively.

[0119] In step S1, a signal model is derived, and then a one-dimensional MUSIC spatial spectrum function is derived, and then expanded to a two-dimensional MUSIC spatial spectrum function as a target function.

[0120] S11. Derive a signal model of a uniform planar array to obtain a received signal model.

[0121] S12. The one-dimensional MUSIC spatial spectrum function is derived and extended to the two-dimensional MUSIC spatial spectrum function as the target function.

[0122] In step S2, the spatial spectrum function of the two-dimensional MUSIC in step S12 is used as the objective function of the Archimedean optimization algorithm.

[0123] S21. Initialization of the original Archimedean algorithm, randomly initialize the density (den), volume (vol) and acceleration (acc) of each individual and update the transfer algorithm TF and density factor d, and use TF to determine whether to proceed to the global exploration stage (conflicts and collisions between objects) or the local development stage (no conflicts and collisions between objects).

[0124] S22. When TF < 0.5, the global exploration phase is carried out (collisions occur between objects).

[0125] S23. When TF>0.5, proceed to the local development phase (no collision between objects).

[0126] In step S3, the improved Archimedean optimization algorithm is used. In order to provide the Archimedean algorithm with a better traversal of the initial population, the fusion chaos algorithm strategy is introduced to initialize the population, and the hybrid mapping combining the circle chaos mapping and the Chebyshev chaos mapping is introduced to initialize the population, thereby improving the convergence speed and solution accuracy of the algorithm. In order to prevent the Archimedean algorithm from falling into the local optimal solution, the Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position, so that the population jumps out of the local optimal solution and expands the population search solution space.

[0127] S31. In order to provide the Archimedean algorithm with a better initialization population, a fusion chaos algorithm strategy is introduced to initialize the population.

[0128] S32. In order to prevent the Archimedean algorithm from falling into the local optimal solution, the Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position, so that the population can jump out of the local optimal solution and expand the population search solution space:

[0129] Step S31 specifically includes:

[0130] S311.Circle chaos map definition.

[0131] S312. Chebyshev chaotic map definition, where the experimental effect is best when the Φ value is 4.5.

[0132] S313. The Archimedean initialization in S21 fuses the two chaotic maps, and determines which chaotic map to use by judging the random position parameter Pt.

[0133] Step S32 specifically includes:

[0134] S321. List the expression of Gaussian mutation algorithm.

[0135] S322. List the expression of the Cauchy mutation algorithm.

[0136] S323. Through the mixed expression, the Gauss-Cauchy mixed mutation algorithm is obtained, and considering the specific change process, a smaller coefficient is required in the later stage of the algorithm in order for the algorithm to converge. Therefore, the number of iterations is introduced here with a sine function to limit the Cauchy variation coefficient to the range of 0 to 1, and it decreases with the increase of the number of iterations.

[0137] In step S4, the two-dimensional MUSIC spectrum peak search effect of the improved Archimedean optimization algorithm is verified. The two-dimensional MUSIC spectrum peak search obtains the wave direction, that is, the pitch angle and the azimuth angle as the spectrum peak value by finding the maximum value of the objective function. The wave direction estimation results of different azimuths and the spectrum peak search time are compared respectively.

[0138] The following is an experiment and effect of two-dimensional MUSIC spectrum peak search by improving the Archimedean algorithm in a specific embodiment.

[0139] In order to verify the performance of the hybrid strategy to improve the Archimedean optimization algorithm in this example, the two-dimensional MUSIC spectrum peak search based on the improved Archimedean algorithm was tested. The experimental results are shown in Figure 2. Figure 2 , Figure 3 and Figure 4 The search results of the traditional MUSIC algorithm and the improved algorithm in this paper are shown in and The measurement errors of the two algorithms are expressed as and Table 1 is a comparison of the DOA estimation results of the improved algorithm and the traditional MUSIC algorithm at different azimuths. Table 2 is a comparison of the time taken by the improved algorithm and the traditional MUSIC algorithm for spectrum peak search.

[0140] The number of array elements is M=N=8, which is a 8×8 uniform array, the array element spacing is half wavelength, the number of snapshots is SNAP=500, the noise is Gaussian white noise, the signal-to-noise ratio is 10dB, and the number of signal sources is M=1. The angle search range is (-90°, 90°), and the improved algorithm and the traditional grid search method are used for spectrum peak search, and the maximum number of iterations is iter max =100, the population size is 50, and the step size of the traditional grid search method is Δ=0.1.

[0141] Table 1 Comparison of DOA estimation results at different azimuths

[0142]

[0143] Table 2 Comparison of peak search time

[0144]

Claims

1. A two-dimensional MUSIC spectrum peak search method based on an improved Archimedean algorithm, characterized in that: The following steps are involved: S1. derive the signal model, then derive the one-dimensional MUSIC spatial spectrum function, and expand the one-dimensional MUSIC spatial spectrum function to the two-dimensional MUSIC spatial spectrum function; S2. The spatial spectrum function of two-dimensional MUSIC is used as the objective function of the Archimedean optimization algorithm; S3. Combined with the objective function, the fusion chaos algorithm strategy is introduced to initialize the population, the mutation algorithm is introduced to disturb the position, and the Archimedean optimization algorithm AOA is improved; S4. A two-dimensional MUSIC spectrum peak search is performed using an improved Archimedean optimization algorithm. The two-dimensional MUSIC spectrum peak search obtains the wave arrival direction, namely the pitch angle and the azimuth angle, as the spectrum peak value by finding the maximum value of the objective function.

2. The two-dimensional MUSIC spectrum peak search method based on the improved Archimedean algorithm according to claim 1, characterized in that: The specific implementation process of step S1 is as follows: S11. Derivation of signal model: A uniform planar array is used for two-dimensional DOA estimation. Assume that the number of planar array elements is M×P and the number of signal sources is K. Assume that the direction of arrival of each signal source in space is represented by (θ1, φ1), (θ2, φ2)…, (θ K ,φ K ) where θ k ,φ K are the elevation angle and azimuth angle of the kth signal source respectively; the uniform array is divided into several sub-arrays according to rows or columns, where each sub-array is a uniform linear array, and the mathematical model of sub-array m is expressed as: A m =A x D m (A y ),m=1,2,…,M Where: A x and A y is the L-type array response matrix corresponding to the subarray, D m (.) represents a diagonal matrix consisting of m rows of the matrix in the brackets; then the uniform plane array receives the signal: Among them, S is the signal emitted by the signal source, and N is the noise; S12. Derivation of one-dimensional MUSIC is performed and extended to the spatial spectrum function of two-dimensional MUSIC: The covariance matrix is ​​obtained according to the uniform planar array receiving signal. The array covariance matrix R is divided into signal subspace and noise subspace by eigendecomposition. The spatial spectrum function is obtained by the orthogonal relationship between the noise eigenvector and the signal eigenvector of the noise subspace and the signal subspace: Where a(θ) is the vector of the array response matrix, U N is the noise subspace, a H (θ) is the conjugate transpose of a(θ), For U N The conjugate transpose of ; Then the spatial spectrum function of two-dimensional MUSIC is: Where: where a x (θ, φ) and a y (θ, φ) is the quality of the L-type array response matrix corresponding to the subarray, is the tensor product, E N is the noise feature vector, For E N The conjugate transpose of , then the angle where the peak of the spectrum function is located is the spatial wave arrival direction.

3. The two-dimensional MUSIC spectrum peak search method based on the improved Archimedean algorithm according to claim 2, characterized in that: The specific implementation process of step S3 is as follows: S31. A hybrid mapping combining the chaotic mapping circle and the chaotic mapping chebyshev is introduced to initialize the population; S32. Introduce the number of iterations into the mutation probability Rand, where Rand is a random value between 0 and 1. Where CurrentGen is the current number of iterations, and Gen is the maximum number of iterations; When the above conditions are met, the Gauss-Cauchy mixed mutation algorithm is introduced to perturb the position.

4. The two-dimensional MUSIC spectrum peak search method based on the improved Archimedean algorithm according to claim 3, characterized in that: The specific implementation process of step S31 is as follows: The S311.Circle chaotic map is defined as follows: Among them, x n is the input value at time n; S312.Chebyshev chaotic map is defined as follows: x n+1 =cos(Φcos -1 x n ) Where Φ is a constant; S313. Random position parameters fusion of two chaotic maps: Each individual in the population generates a random number between (0,1) as the location parameter of the individual. The location parameters of all individuals form the location parameter matrix Pt, where N is the population size and D is the spatial dimension. Pt(i,j)=rand i=1,2,…,N j=1,2,…,D. Set the selection probability to 0.5 and update the individual positions of the population as follows: in, is the position of individuals in a population with a population size of i and a spatial dimension of j at time n; The generated initial population is subjected to boundary constraint checks, and positions exceeding or falling below the upper and lower bounds are assigned boundary values.

5. The two-dimensional MUSIC spectrum peak search method based on the improved Archimedean algorithm according to claim 4, characterized in that: The specific implementation process of step S32 is as follows: S321. Gaussian mutation algorithm: Replace the original gene value with a random number that conforms to the normal distribution with a mean of μ and a variance of σ. The following is the Gaussian mutation formula: Gaussian i (x)=N(x best ,δ) x is the position of the individual, x best is the current global optimal individual, δ is the standard deviation of the Gaussian distribution, and the Gaussian mutation limits the population from escaping the local optimal solution; S322. Cauchy mutation algorithm: The following is the Cauchy variation formula: S323. Gauss-Cauchy hybrid mutation algorithm: Based on the characteristics of Gaussian mutation and Cauchy mutation, a Gaussian-Cauchy mixed mutation mechanism is proposed. The formula is as follows: Mutation i (x)=α·Gaussian i (x)+β·Cauthy i (x) Among them, α is the Gaussian coefficient of variation, and β is the Cauchy coefficient of variation. The number of iterations is combined with a sine function to limit the Cauchy coefficient of variation to the range of 0 to 1, and decreases as the number of iterations increases.

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