A method for direction finding of incoherent distributed sources under strong impulse noise

Abstract

The present invention discloses a method for direction finding of incoherently distributed sources under strong impulse noise. The method comprises the following steps: first, obtaining snapshot sampling data, performing de-impact preprocessing, and constructing a generalized Capon space spectrum function; second, initializing the quantum position of each arrow and setting parameters to construct a fitness function; third, dividing the arrow group into sub-arrow groups, and performing fitness function evaluation on all arrows. The quantum position of the arrow with the best fitness in each sub-arrow group is selected as the optimal quantum position; fourth, updating the quantum position of each arrow according to the shooting mechanism; fifth, mapping the updated quantum position of each arrow to a position, calculating the updated fitness function value, and updating the optimal quantum position of each sub-arrow group; and sixth, returning to step three, looping and iterating until the maximum number of iterations is reached, outputting the optimal quantum position set, and transforming it into the central azimuth and angular spread estimates of the incoherently distributed source through mapping. The method is robust and high-performance under strong impulse noise conditions.

Description

Technical Field

[0001] The invention belongs to the field of array signal processing and relates to a direction finding method for incoherent distributed sources under strong impulse noise. Background Art

[0002] In recent years, high-resolution array signal processing technology, especially array direction finding, has attracted considerable attention. It has been widely applied in fields such as seismic detection, radar, passive sonar, and wireless communications, and has led to the development of numerous high-resolution estimation algorithms. Most of these estimation algorithms assume that the signal source is a point target in the far field. The point target model is an approximation of the actual environment, and these algorithms often assume that the background noise is Gaussian. Using second-order or higher-order cumulants for analysis can yield ideal results. However, since the size of the target depends on the distance from the array receiving antenna, and is affected by multipath effects, scattering and other phenomena, the signal arrival angle in wireless mobile communications is often spread out within a certain range, presenting a distributed signal source. According to the scattering characteristics of the distributed source, it can be divided into two categories: coherent distributed source and incoherent distributed source. The incoherent distributed source model is more suitable for wireless communication scenarios than the coherent distributed source model. In addition, there is impulsive noise in the actual environment, such as sea clutter noise, atmospheric noise, wireless channel noise, etc. The model of these noises can be expressed as SαS random process, which is mismatched with the Gaussian noise model, making the traditional algorithm based on second-order or high-order cumulants invalid. Therefore, it is of great significance and value to study the direction finding method of incoherent distributed source under impulsive noise.

[0003] Using the generalized Capon algorithm for incoherent distributed source direction finding can achieve high-precision direction finding performance. However, it requires a two-dimensional spectral peak search of the spatial spectrum function, which not only produces inevitable quantization errors, but also the computational complexity increases sharply as the scanning interval decreases, greatly limiting the engineering application of the generalized Capon algorithm. Therefore, how to quickly obtain search results without quantization errors is a classic problem in the application of the generalized Capon algorithm. Using an intelligent optimization algorithm to solve it is a potential solution, but it can only solve multi-dimensional joint optimization problems and cannot effectively solve multi-peak optimization problems to obtain multiple optimal solutions. Therefore, it is necessary to design a new multi-peak intelligent optimization algorithm for multi-peak optimization for specific problems.

[0004] Through searching the existing technical literature, it is found that Zhang Gaoyi et al. proposed a decoupling estimation method for DOA and angular spread of incoherent distributed sources based on least mean square fitting in the paper “Decoupling Estimation Method for DOA and Angular Spread of Incoherent Distributed Sources” published in Journal of Electronics and Information Technology (2010, 32(01):98-101). After estimating the covariance matrix, the angle and angular spread information can be estimated from the phase information and amplitude information respectively. However, it is only applicable to the scenario of single incoherent distributed source, and its performance will be degraded or even completely failed under impulse noise. Shahrokh Valaee et al. proposed a direction finding method for incoherent distributed sources based on DSPE algorithm in the paper “Parametric Localization of Distributed Sources” published in IEEE Transactions on Signal Processing (1995, 43(09):2144-2153). It can be applied to the scenario of multiple incoherent distributed sources coexisting and shows certain robustness in Gaussian noise environment, but its performance will be degraded or even fail under impulse noise.

[0005] The search results of existing literature show that the existing incoherent distributed source direction finding methods mostly use the DSPE algorithm and the least mean square fitting algorithm. The DSPE algorithm has a large amount of computation and has quantization errors. The least mean square fitting algorithm is only applicable to single incoherent distributed source scenarios. Both of these methods are only applicable to Gaussian noise. Their performance will deteriorate or even fail in the environment of impulse noise. Therefore, a method for incoherent distributed source direction finding under impulse noise is proposed. Specifically, a global median filter is designed to perform de-impact preprocessing on the received data under impulse noise, and a generalized Capon direction finding equation based on the preprocessed data is designed to perform incoherent distributed source direction finding. In addition, a multi-peak quantum archery mechanism is designed for fast quantization error-free solution. This solves the technical problem of the performance deterioration of the existing incoherent distributed source direction finding method under strong impulse noise, which will promote its engineering application process. Summary of the Invention

[0006] In view of the above-mentioned existing technologies, the technical problem to be solved by the present invention is to provide a method for direction finding of incoherent distributed sources under strong impact noise, which is robust and has high performance in a strong impact noise environment, and designs a multi-peak quantum archery mechanism to quickly solve the designed multi-peak incoherent distributed source direction finding equation without quantization error, thereby breaking through some application limitations of the existing incoherent distributed source direction finding method.

[0007] To solve the above technical problems, the present invention provides a method for direction finding of incoherent distributed sources under strong impulse noise, comprising:

[0008] Step 1: Obtain snapshot sampling data of the array receiving signal, use a global median filter to perform shock removal preprocessing on the received data, and then construct a generalized Capon spatial spectrum function;

[0009] Step 2: Initialize the quantum position of each arrow and set related parameters to construct the fitness function;

[0010] Step 3: Use K-means clustering to divide the arrow group into O sub-arrow groups, and evaluate all arrows with a fitness function. Select the quantum position of the arrow with the best fitness in each sub-arrow group as the optimal quantum position of the sub-arrow group.

[0011] Step 4: Each arrow in the sub-arrow group updates its quantum position according to the shooting mechanism;

[0012] Step 5: Map the updated quantum position of each arrow in all sub-arrow groups to a position, calculate the fitness function value of each arrow after the update, and update the optimal quantum position of each sub-arrow group;

[0013] Step 6: Determine whether the maximum number of iterations has been reached If not, set g = g + 1 and return to step 3; if reached, terminate the loop iteration and output the optimal quantum position set, which is transformed into the optimal position set after mapping, which is the estimated value of the central azimuth and angular spread of the incoherent distribution source.

[0014] Furthermore, the snapshot sampling data of the array receiving signal in step 1 includes:

[0015] Assume that there are P incoherent distributed sources with wavelength λ incident on a uniform linear array composed of M array elements, and the array spacing is d. Define the maximum number of snapshots as K. Then the k-th snapshot data received by the uniform linear array can be expressed as:

[0016]

[0017] Where k = 1, 2, ..., K, x(k) = [x1(k), x2(k), ..., x M (k)] T Receive snapshot data vector for M×1 dimensional array, s i (k) is the incident signal of the i-th incoherent distribution source, L i is the multipath number of the i-th incoherent distribution source, γ i,l (k) is the complex Gaussian gain factor of the lth path of the i-th incoherent distribution source, i = 1, 2, ..., P, l = 1, 2, ..., L i , is the M×1-dimensional array steering vector of the lth path of the i-th incoherent distribution source, θ i represents the central azimuth of the i-th incoherent distribution source, represents the angular deviation between the arrival angle of the lth path of the i-th incoherent distribution source and the central azimuth, The mean is 0 and the variance is Gaussian distribution, Δ i is the angular spread of the i-th incoherent distribution source, n(k) is the M×1-dimensional complex impulse noise vector obeying the standard SαS distribution with characteristic exponent α, j is the complex unit, and T is the matrix transpose.

[0018] Furthermore, the step 1 of performing shock removal preprocessing on the received data using a global median filter includes:

[0019] The k-th snapshot received data is expressed as follows after global median filtering preprocessing:

[0020]

[0021] Among them, if |x m (k)|>G m ,but otherwise G m =median{[x m (1),x m (2),…,x m (K)]} represents the global median of the snapshot data received by the mth array element, median represents the vector median, and m = 1, 2, …, M.

[0022] Furthermore, constructing the generalized Capon space spectrum function includes:

[0023] The generalized Capon space spectrum function is constructed as:

[0024]

[0025] Among them, λ max Indicates finding the maximum eigenvalue of the matrix, R s (θ,Δ)=diag(a(θ))B(θ,Δ)diag(a H (θ)) represents the noise-free covariance matrix, θ and Δ represent the central azimuth and angular spread of the incoherent distribution source, respectively, diag represents the diagonal matrix, a(θ)=[1,e -j2πdsin(θ) / λ ,…,e -j2π(M-1)dsin(θ) / λ ] T , Toeplitz means generating a Toeplitz matrix with the vector in brackets as the first row, the transposed vector in brackets as the first column, and the remaining elements equal to the adjacent elements in the upper left corner. is the sampling covariance matrix of the array element receiving data after global median filtering, which is expressed as: Where K is the maximum number of snapshots and the superscript H represents the conjugate transpose.

[0026] Furthermore, in step 2, the quantum position of each arrow is initialized and related parameters are set, and the fitness function is constructed, including:

[0027] First, assume that there are Q arrows in the arrow group, and the maximum number of iterations is In the g-th iteration, the quantum position of the q-th arrow in the 2-dimensional search space is When g = 1, each dimension of the quantum position of all arrows in the first generation is initialized to a uniform random number between [0, 1], and the quantum position is mapped to the position according to the mapping rule Map each dimension of the quantum position of all arrows into the search space, where u 1,max and u 1,min are the upper and lower limits of the center azimuth search space, u 2,max and u 2,min The upper and lower limits of the angle expansion search space are q=1,2,...,Q, respectively, and the position of the qth arrow in the gth generation is obtained. The fitness function of the qth arrow of the gth generation is

[0028] Furthermore, in step 3, the arrow group is divided into O sub-groups using K-means clustering, and all arrows are evaluated by the fitness function, and the quantum position of the arrow with the best fitness in each sub-group is selected as the optimal quantum position of the sub-group.

[0029] (1) Randomly select the quantum positions of O arrows from all arrows as the initial arrow group center set

[0030] (2) For the qth arrow, calculate its Euclidean distance to all elements in the arrow group center set in, o=1,2,…,O, assign the quantum position of the qth arrow to the closest sub-arrow group according to the calculated Euclidean distance. After all arrows are assigned, for the oth sub-arrow group, calculate the average value of the quantum positions of all arrows in the sub-arrow group as the new sub-arrow group center. If the arrow group center set does not change compared with the last time, evaluate all arrows with the fitness function and select the quantum position of the arrow with the best fitness in the sub-arrow group as the optimal quantum position of the sub-arrow group. o=1,2,…,O, go to step 4; otherwise, return to step (2) to redistribute all arrows.

[0031] Furthermore, in step 4, each arrow in all sub-arrow groups updates its quantum position according to the shooting mechanism, including:

[0032] Among the o-th arrow group of the g-th generation, there are Arrows, o=1,2,…,O, For the o-th arrow group of the g-th generation, calculate the cumulative probability vector in, is the cumulative probability of the ωth arrow in the oth sub-arrow group of the gth generation, cumsum means finding the cumulative probability of a vector, represents the selection probability vector of the o-th sub-arrow group of the g-th generation, represents the probability of selecting the ωth arrow in the oth sub-arrow group of the gth generation, min represents the minimum value of the vector, is the fitness function set of all arrows in the o-th sub-arrow group of the g-th generation, is the fitness function value of the ω-th arrow in the o-th sub-arrow group of the g-th generation,

[0033] For the b-th dimension quantum position of the ω-th arrow in the o-th sub-arrow group of the g-th generation, generate a random number uniformly distributed between [0,1] b=1,2,if for An integer between ; otherwise is the selection coefficient of the b-th dimension quantum position of the ω-th arrow in the o-th sub-arrow group of the g-th generation; if Then the b-dimensional quantum rotation angle of the ω-th arrow in the o-th sub-arrow group of the g+1th generation is otherwise, in, is the b-th dimensional quantum position of the ω-th arrow in the o-th sub-arrow group of the g-th generation, and is a random number uniformly distributed between [0,1], and round represents the rounding function; then the simulated quantum rotating gate is used to update the b-dimensional quantum position of the ω-th arrow in the o-th sub-arrow group: represents the bth dimension of the optimal quantum position in the oth sub-arrow group of the gth generation.

[0034] Furthermore, in step 5, the updated quantum position of each arrow in all sub-arrow groups is mapped to a position, the fitness function value of each arrow after the update is calculated, and the optimal quantum position of each sub-arrow group is updated, including:

[0035] For the ω-th arrow in the o-th sub-arrow group of the g+1-th generation, its updated quantum position is mapped to position Then, the fitness function is evaluated for each arrow in the sub-arrow group, and the optimal quantum position of the o-th sub-arrow group is updated until the g+1th generation. Update the optimal quantum positions of all sub-arrow groups to obtain the optimal quantum position set

[0036] Beneficial effects of the present invention:

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] (1) To address the problems of high computational complexity and performance degradation of existing incoherent distributed source direction finding methods in an impulsive noise environment, a more robust incoherent distributed source direction finding method based on a multi-peak quantum arrow mechanism was designed. A global median filter was designed under impulsive noise, and a generalized Capon direction finding method based on a multi-peak quantum arrow mechanism was used to achieve fast and high-precision direction finding of incoherent distributed sources.

[0039] (2) The incoherent distributed source direction-finding method designed in the present invention designs a global median filter to perform de-impact preprocessing on the received data, thereby achieving effective direction-finding of the target under impact noise. The designed multi-peak quantum archery mechanism can solve the generalized Capon direction-finding equation based on the covariance matrix of the preprocessed data with high precision, and obtain the direction-finding results quickly and accurately.

[0040] (3) Simulation experiments have demonstrated the effectiveness of the incoherent distributed source direction finding method based on the multi-peak quantum archery mechanism under strong impact noise, breaking through the application limitation of the traditional method that its performance deteriorates under impact noise, and realizing the fast non-quantization error solution of the generalized Capon algorithm, which will greatly promote its engineering application process. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Schematic diagram of the incoherent distributed source direction finding method under strong impulse noise designed by the present invention;

[0042] Figure 2 The relationship curve between the central azimuth root mean square error and the generalized signal-to-noise ratio when α = 0.8;

[0043] Figure 3 The relationship curve between the angle expansion root mean square error and the generalized signal-to-noise ratio when α=0.8. DETAILED DESCRIPTION

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] Combine Figure 1 , the present invention comprises the following steps:

[0046] Step 1: Obtain snapshot sampling data of the array receiving signal, use a global median filter to perform shock removal preprocessing on the received data, and then construct a generalized Capon spatial spectrum function.

[0047] Assume that the array has P incoherent distributed sources with wavelength λ incident on a uniform linear array composed of M array elements, and the array spacing is d. Define the maximum number of snapshots as K, then the k-th snapshot data received by the uniform linear array can be expressed as Where k = 1, 2, ... Δ, K, x(k) = [x1(k), x2(k), ..., x M (k)] T Receive snapshot data vector for M×1 dimensional array, s i (k) is the incident signal of the i-th incoherent distribution source, L i is the multipath number of the i-th incoherent distribution source, γ i,l (k) is the complex Gaussian gain factor of the lth path of the i-th incoherent distribution source, i = 1, 2, ..., P, l = 1, 2, ..., L i , is the M×1-dimensional array steering vector of the lth path of the i-th incoherent distribution source, θ i represents the central azimuth of the i-th incoherent distribution source, represents the angular deviation between the arrival angle of the lth path of the i-th incoherent distribution source and the central azimuth, The mean is 0 and the variance is Gaussian distribution, Δ i is the angular spread of the i-th incoherent distribution source, n(k) is the M×1-dimensional complex impulse noise vector obeying the standard SΔS distribution with characteristic exponent Δ, j is the complex unit, and T is the matrix transpose.

[0048] The k-th snapshot received data can be expressed as follows after global median filtering preprocessing: Among them, if |x m (k)|>G m ,but otherwise G m =median{[x m (1),x m (2),…,x m (K)]} represents the global median of the snapshot data received by the mth array element, median represents the vector median, m = 1, 2, ..., M. Then the sampling covariance matrix of the array element receiving data after global median filtering can be expressed as Where K is the maximum number of snapshots, and the superscript H represents the conjugate transpose. The generalized Capon space spectrum function is further constructed as Among them, λ max Indicates finding the maximum eigenvalue of the matrix, R s (θ,Δ)=diag(a(θ))B(θ,Δ)diag(a H(θ)) represents the noise-free covariance matrix, θ and Δ represent the central azimuth and angular spread of the incoherent distribution source, respectively, diag represents the diagonal matrix, a(θ)=[1,e -j2πdsin(θ) / λ ,…,e -j2π(M-1)dsin(θ) / λ ] T , Toeplitz means generating a Toeplitz matrix with the vector in brackets as the first row, the transposed vector in brackets as the first column, and the remaining elements equal to the adjacent elements in the upper left corner.

[0049] Step 2: Initialize the quantum position of each arrow and set related parameters to construct the fitness function.

[0050] First, assume that there are Q arrows in the arrow group, and the maximum number of iterations is In the g-th iteration, the quantum position of the q-th arrow in the 2-dimensional search space is When g = 1, each dimension of the quantum position of all arrows in the first generation is initialized to a uniform random number between [0, 1], and the quantum position is mapped to the position according to the mapping rule Map each dimension of the quantum position of all arrows into the search space, where u 1,max and u 1,min are the upper and lower limits of the center azimuth search space, u 2,max and u 2,min The upper and lower limits of the angle expansion search space are q=1,2,…,Q, respectively, and the position of the qth arrow in the gth generation is obtained. The fitness function of the qth arrow of the gth generation is

[0051] Step 3: Use K-means clustering to divide the arrow group into O sub-arrow groups, and evaluate the fitness function of all arrows. Select the quantum position of the arrow with the best fitness in each sub-arrow group as the optimal quantum position of the sub-arrow group. The specific steps are as follows:

[0052] (1) Randomly select the quantum positions of O arrows from all arrows as the initial arrow group center set

[0053] (2) For the qth arrow, calculate its Euclidean distance to all elements in the arrow group center set in, o=1,2,…,O, assign the quantum position of the qth arrow to the closest sub-arrow group according to the calculated Euclidean distance. After all arrows are assigned, for the oth sub-arrow group, calculate the average value of the quantum positions of all arrows in the sub-arrow group as the new sub-arrow group center. If the arrow group center set does not change compared with the last time, evaluate all arrows with the fitness function and select the quantum position of the arrow with the best fitness in the sub-arrow group as the optimal quantum position of the sub-arrow group. o=1,2,…,O, go to the next step; otherwise, return to step 3 (2) to redistribute all arrows.

[0054] Step 4: Each arrow in the sub-arrow group updates its quantum position according to the shooting mechanism. The specific steps are as follows:

[0055] Among the o-th arrow group of the g-th generation, there are Arrows, o=1,2,…,O, For the o-th arrow group of the g-th generation, calculate the cumulative probability vector in, is the cumulative probability of the ωth arrow in the oth sub-arrow group of the gth generation, cumsum means finding the cumulative probability of a vector, represents the selection probability vector of the o-th sub-arrow group of the g-th generation, represents the probability of selecting the ωth arrow in the oth sub-arrow group of the gth generation, min represents the minimum value of the vector, is the fitness function set of all arrows in the o-th sub-arrow group of the g-th generation, is the fitness function value of the ω-th arrow in the o-th sub-arrow group of the g-th generation,

[0056] For the b-th dimension quantum position of the ω-th arrow in the o-th sub-arrow group of the g-th generation, generate a random number uniformly distributed between [0,1] b=1,2,if for An integer between ; otherwise is the selection coefficient of the b-th dimension quantum position of the ω-th arrow in the o-th sub-arrow group of the g-th generation. If Then the b-dimensional quantum rotation angle of the ω-th arrow in the o-th sub-arrow group of the g+1th generation is otherwise, in, is the b-th dimensional quantum position of the ω-th arrow in the o-th sub-arrow group of the g-th generation, and is a random number uniformly distributed between [0,1], and round represents the rounding function. Then, a simulated quantum rotating gate is used to update the b-dimensional quantum position of the ω-th arrow in the o-th sub-arrow group: represents the bth dimension of the optimal quantum position in the oth sub-arrow group of the gth generation.

[0057] Step 5: Map the updated quantum position of each arrow in all sub-arrow groups to a position, calculate the fitness function value of each arrow after the update, and update the optimal quantum position of each sub-arrow group.

[0058] For the ω-th arrow in the o-th sub-arrow group of the g+1-th generation, its updated quantum position is mapped to position Then, the fitness function is evaluated for each arrow in the sub-arrow group, and the optimal quantum position of the o-th sub-arrow group is updated until the g+1th generation. Update the optimal quantum positions of all sub-arrow groups to obtain the optimal quantum position set

[0059] Step 6: Determine whether the maximum number of iterations has been reached If not, set g = g + 1 and return to step 3; if reached, terminate the loop iteration and output the optimal quantum position set, which is transformed into the optimal position set after mapping, which is the estimated value of the central azimuth and angular spread of the incoherent distribution source.

[0060] The incoherent distributed source direction finding method based on the multi-peak quantum archery mechanism designed in the present invention is recorded as MQAA-GMF-GC; the DSPE direction finding method based on two-dimensional spectrum peak search is recorded as 2D-DSPE.

[0061] In the simulation experiment, the number of targets P = 2, the multipath number of the targets L1 = L2 = 50, the central azimuth angles are θ1 = -10.25° and θ2 = 20.55°, the angular spread Δ1 = Δ2 = 5.35°, K = 100, M = 16, the array element spacing is half a wavelength, the scanning interval of the 2D-DSPE algorithm is 0.1°, and the number of Monte Carlo experiments is 100.

[0062] The parameters of the multi-peak quantum archery mechanism are set as follows: Q = 30, O=2,[u 1,min ,u 1,max ]=[-90,90],[u 2,min ,u 2,max ]=[0,10]. Combined Figure 2 、 Figure 3 Under strong impulse noise with characteristic index α=0.8, the comparison of the central azimuth angle and angular spread root mean square error curves with the generalized signal-to-noise ratio shows the advantages of the method designed in the present invention over the traditional method in a strong impulse noise environment, realizes the fast non-quantization error solution of the traditional method, and breaks through some application limitations of the traditional incoherent distributed source direction finding method.

Claims

1. A method for direction finding of incoherent distributed sources under strong impulse noise, characterized in that: include: Step 1: Obtain snapshot sampling data of the array receiving signal, use a global median filter to perform shock removal preprocessing on the received data, and then construct a generalized Capon spatial spectrum function; Step 2: Initialize the quantum position of each arrow and set related parameters to construct the fitness function; First, assume that there are Q arrows in the arrow group, and the maximum number of iterations is In the g-th iteration, the quantum position of the q-th arrow in the 2-dimensional search space is When g = 1, each dimension of the quantum position of all arrows in the first generation is initialized to a uniform random number between [0, 1], and the quantum position is mapped to the position according to the mapping rule Map each dimension of the quantum position of all arrows into the search space, where u 1,max and u 1,min are the upper and lower limits of the center azimuth search space, u 2,max and u 2,min The upper and lower limits of the angle expansion search space are q=1,2,…,Q, respectively, and the position of the qth arrow in the gth generation is obtained. The fitness function of the qth arrow of the gth generation is Among them, λ max Indicates finding the maximum eigenvalue of a matrix; R s () represents the noise-free covariance matrix; is the sampling covariance matrix of the array element receiving data after global median filtering, which is expressed as: Where K is the maximum number of snapshots, the superscript H represents the conjugate transpose, and the k-th snapshot received data is preprocessed by the global median filter and is expressed as Step 3: Use K-means clustering to divide the arrow group into O sub-arrow groups, and evaluate all arrows with a fitness function. Select the quantum position of the arrow with the best fitness in each sub-arrow group as the optimal quantum position of the sub-arrow group. Step 4: Each arrow in the sub-arrow group updates its quantum position according to the shooting mechanism; Among the o-th arrow group of the g-th generation, there are Arrows, o=1,2,…,O, For the o-th arrow group of the g-th generation, calculate the cumulative probability vector in, is the cumulative probability of the ωth arrow in the oth sub-arrow group of the gth generation, cumsum means finding the cumulative probability of a vector, represents the selection probability vector of the o-th sub-arrow group of the g-th generation, represents the probability of selecting the ωth arrow in the oth sub-arrow group of the gth generation, min represents the minimum value of the vector, is the fitness function set of all arrows in the o-th sub-arrow group of the g-th generation, is the fitness function value of the ω-th arrow in the o-th sub-arrow group of the g-th generation, For the b-th dimension quantum position of the ω-th arrow in the o-th sub-arrow group of the g-th generation, generate a random number uniformly distributed between [0,1] b=1,2,if for An integer between ; otherwise is the selection coefficient of the b-th dimension quantum position of the ω-th arrow in the o-th sub-arrow group of the g-th generation; if Then the b-dimensional quantum rotation angle of the ω-th arrow in the o-th sub-arrow group of the g+1th generation is otherwise, in, is the b-th dimensional quantum position of the ω-th arrow in the o-th sub-arrow group of the g-th generation, and is a random number uniformly distributed between [0,1], and round represents the rounding function; then the simulated quantum rotating gate is used to update the b-dimensional quantum position of the ω-th arrow in the o-th sub-arrow group: represents the bth dimension of the optimal quantum position in the oth sub-arrow group of the gth generation; Step 5: Map the updated quantum position of each arrow in all sub-arrow groups to a position, calculate the fitness function value of each arrow after the update, and update the optimal quantum position of each sub-arrow group; Step 6: Determine whether the maximum number of iterations has been reached If not, set g = g + 1 and return to step 3; if reached, terminate the loop iteration and output the optimal quantum position set, which is transformed into the optimal position set after mapping, which is the estimated value of the central azimuth and angular spread of the incoherent distribution source.

2. The method for direction finding of incoherent distributed sources under strong impulse noise according to claim 1, characterized in that: The snapshot sampling data of the array receiving signal in step 1 includes: Assume that there are P incoherent distributed sources with wavelength λ incident on a uniform linear array composed of M array elements, and the array spacing is d. Define the maximum number of snapshots as K. Then the k-th snapshot data received by the uniform linear array can be expressed as: Where k = 1, 2, ..., K, x(k) = [x1(k), x2(k), ..., x M (k)] T Receive snapshot data vector for M×1 dimensional array, s i (k) is the incident signal of the i-th incoherent distribution source, L i is the multipath number of the i-th incoherent distribution source, γ i,l (k) is the complex Gaussian gain factor of the lth path of the i-th incoherent distribution source, i = 1, 2, ..., P, l = 1, 2, ..., L i , is the M×1-dimensional array steering vector of the lth path of the i-th incoherent distribution source, θ i represents the central azimuth of the i-th incoherent distribution source, represents the angular deviation between the arrival angle of the lth path of the i-th incoherent distribution source and the central azimuth, The mean is 0 and the variance is Gaussian distribution, Δ i is the angular spread of the i-th incoherent distribution source, n(k) is the M×1-dimensional complex impulse noise vector obeying the standard SαS distribution with characteristic exponent α, j is the complex unit, and T is the matrix transpose.

3. The method for direction finding of incoherent distributed sources under strong impulse noise according to claim 2, characterized in that: The step 1 of using a global median filter to perform shock removal preprocessing on the received data includes: The k-th snapshot received data is expressed as follows after global median filtering preprocessing: Among them, if |x m (k)|>G m ,but otherwise G m =median{[x m (1),x m (2),…,x m (K)]} represents the global median of the snapshot data received by the mth array element, median represents the vector median, and m = 1, 2, …, M.

4. The method for direction finding of incoherent distributed sources under strong impulse noise according to claim 3, characterized in that: The constructing of the generalized Capon space spectrum function includes: The generalized Capon space spectrum function is constructed as: Among them, λ max Indicates finding the maximum eigenvalue of the matrix, R s (θ,Δ)=diag(a(θ))B(θ,Δ)diag(a H (θ)) represents the noise-free covariance matrix, θ and Δ represent the central azimuth and angular spread of the incoherent distribution source, respectively, diag represents the diagonal matrix, a(θ)=[1,e -j2πdsin(θ) / λ ,…,e -j2π(Μ-1)dsin(θ) / λ ] T , Toeplitz means generating a Toeplitz matrix with the vector in brackets as the first row, the transposed vector in brackets as the first column, and the remaining elements equal to the adjacent elements in the upper left corner; is the sampling covariance matrix of the array element receiving data after global median filtering, which is expressed as: Where K is the maximum number of snapshots and the superscript H represents the conjugate transpose.

5. The method for direction finding of incoherent distributed sources under strong impulse noise according to claim 1, characterized in that: In step 3, the arrow group is divided into O sub-groups using K-means clustering, and all arrows are evaluated by the fitness function. The quantum position of the arrow with the best fitness in each sub-group is selected as the optimal quantum position of the sub-group. (1) Randomly select the quantum positions of O arrows from all arrows as the initial arrow group center set (2) For the qth arrow, calculate its Euclidean distance to all elements in the arrow group center set in, o=1,2,…,O, assign the quantum position of the qth arrow to the closest sub-arrow group according to the calculated Euclidean distance. After all arrows are assigned, for the oth sub-arrow group, calculate the average value of the quantum positions of all arrows in the sub-arrow group as the new sub-arrow group center. If the arrow group center set does not change compared with the last time, evaluate all arrows with the fitness function and select the quantum position of the arrow with the best fitness in the sub-arrow group as the optimal quantum position of the sub-arrow group. o=1,2,…,O, go to step 4; otherwise, return to step (2) to redistribute all arrows.

6. The method for direction finding of incoherent distributed sources under strong impulse noise according to claim 1, characterized in that: In step 5, the updated quantum position of each arrow in all sub-arrow groups is mapped to a position, and the fitness function value of each arrow after the update is calculated. The optimal quantum position of each sub-arrow group is updated, including: For the ω-th arrow in the o-th sub-arrow group of the g+1-th generation, its updated quantum position is mapped to position Then, the fitness function is evaluated for each arrow in the sub-arrow group, and the optimal quantum position of the o-th sub-arrow group is updated until the g+1th generation. Update the optimal quantum positions of all sub-arrow groups to obtain the optimal quantum position set

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