Method for Estimating Direction of Arrival of Non-uniform Linear Array Based on Quantum Honey Badger Search Mechanism

Abstract

The present invention discloses a method for estimating the direction of arrival of non-uniform linear arrays based on the quantum honey badger search mechanism. Step 1: Obtain the snapshot sampling data of the received signals of a special non-uniform linear array after infinity norm normalization processing. Step 2: Obtain the direction-of-arrival estimation equation and derive the objective function of the angle estimation value. Step 3: Initialize the quantum positions, positions, and related parameters of the quantum honey. Step 4: Calculate the fitness value of the quantum honey badger and obtain the initial global optimal quantum position. Step 5: Determine the quantum position update strategy and update the quantum positions of the quantum honey badger using the simulated simplified quantum rotation gate. Step 6: Map the quantum positions to the positions of the quantum honey badger, calculate the fitness value, and update the global optimal quantum position. Step 7: If the maximum number of iterations is not reached, return to Step 5; if it is reached, terminate the iteration and output the optimal quantum position of the quantum honey badger population up to the (ε + 1)-th generation. The present invention has the characteristics of robustness, high precision, and a wider application range.

Description

Technical Field

[0001] The present invention belongs to the field of array signal processing, and relates to a method for estimating the direction of arrival (DOA) of non-uniform linear arrays based on a quantum honey badger search mechanism. Background Art

[0002] The research field of array signal processing technology mainly combines multiple sensors into an antenna array according to different arrangement rules in space, and then uses these antenna arrays to receive signals from space to obtain the information carried by the signals. Array signal processing technology processes these data through a series of methods to obtain the characteristic parameters of the signals, so as to obtain information such as the energy distribution and the direction of arrival of the signals in space. Direction of arrival (DOA) estimation, also known as direction finding, is to study the direction of arrival of spatial signals. As a key technology and key research content of array signal processing, it has been widely used in many fields such as seismic exploration, radar, passive sonar, and wireless communication. At present, most DOA estimation methods are based on equidistant uniform linear arrays, mainly because equidistant uniform linear arrays have the form of Vandermonde matrices, which is convenient for mathematical processing.

[0003] However, in many actual application environments, the structural size of the array is often restricted by many factors, and it is impossible to construct an ideal uniform array. Therefore, it is of great significance to study the DOA estimation methods for special arrays. Special non-uniform linear arrays are a type of array used to increase the array aperture. This type of array can achieve the function of expanding the array aperture, and can better reduce the influence caused by mutual coupling between array antennas, thereby further improving the accuracy of DOA estimation of incident signals, and has thus received extensive attention.

[0004] Classical DOA estimation algorithms mainly include subspace decomposition algorithms, maximum likelihood algorithms, compressive sensing algorithms, and subspace fitting algorithms. Among them, subspace decomposition algorithms mainly include noise subspace algorithms represented by MUSIC and signal subspace algorithms represented by Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT). These algorithms are all based on eigenvalue decomposition operations. Although their computational complexity is relatively small, a large number of snapshots are often required to obtain good estimation performance, and they cannot directly estimate coherent sources without losing the array aperture, and preprocessing is also required to estimate coherent signal sources. Moreover, the performance of traditional spatial spectrum estimation methods deteriorates or even fails in the case of impulsive noise, low signal-to-noise ratio, and small number of snapshots. The weighted subspace fitting algorithm obtains the signal subspace and the noise subspace by performing eigenvalue decomposition on the covariance matrix of the received signals, and then obtains the objective function by fitting the subspace composed of the signal subspace and the noise subspace of the received data and the actual signal steering vector. In comparison, the maximum likelihood algorithm and the subspace fitting algorithm have excellent estimation performance, especially in the case of impulsive noise environment, low signal-to-noise ratio, and small number of snapshots, they have superior DOA estimation performance.

[0005] After searching the existing literature, it is found that a direction-of-arrival (DoA) estimation method based on Toeplitz covariance matrix reconstruction proposed by Sun Bing et al. in the paper "DoA Estimation Method for Coprime Array Based on Toeplitz Covariance Matrix Reconstruction" published in the Journal of Electronics & Information Technology (1009 - 5896(2019)08 - 1924 - 07) improves the utilization rate of virtual array elements, increases the virtual aperture and the number of signals that can be estimated. However, it cannot perform robust direction finding in an impulsive noise environment, nor can it measure the incoming wave directions of coherent sources. In addition, the retrieval results of existing literature show that most existing direction finding methods are proposed on the premise that the array element noise is assumed to be independent Gaussian white noise when it is empty. However, in the actual application environment, in many cases, the noise has impulsive characteristics and is non-Gaussian noise, such as underwater noise, low-frequency atmospheric noise, and several artificial noises, etc., which can be described by the SαS process with different characteristic exponents α. However, non-Gaussian SαS noise does not have higher-order moments of the second order and above, so the model applied to the Gaussian model is mismatched with it, making the traditional algorithms based on second-order or higher-order cumulants fail. Therefore, it has great research significance and value to study a high-precision estimation method with high robustness, few snapshots, low signal-to-noise ratio, and no quantization error for the DoA estimation method based on maximum likelihood and weighted subspace fitting of a special non-uniform linear array in an impulsive noise environment. Since the objective function of the designed DoA estimation method based on a special non-uniform linear array is a multi-dimensional non-linear function, the solution process is complex and the amount of calculation is large, and it is difficult for traditional methods to effectively solve it. The honey badger algorithm is a new method inspired by the foraging behavior of honey badgers. However, it is easy to fall into local convergence for complex engineering problems. Therefore, it is necessary to improve the behavior criteria of honey badgers by combining the quantum evolution mechanism to make it have the advantages of fast convergence speed and high search accuracy. Summary of the Invention

[0006] Aiming at the above-mentioned existing technologies, the technical problem to be solved by the present invention is to provide a non-uniform linear array DoA estimation method based on a quantum honey badger search mechanism, which can quickly achieve high-precision DoA estimation under the conditions of few snapshots, strong impulse, and the existence of coherent sources.

[0007] To solve the above technical problem, a non-uniform linear array DoA estimation method based on a quantum honey badger search mechanism of the present invention includes:

[0008] Step 1: Establish a receiving data model of a special non-uniform linear array in an impulsive noise environment, obtain the snapshot sampling data of the signals received by the special non-uniform linear array, and perform infinity norm normalization processing;

[0009] Step 2: Use the data received by the array to construct a sine transform exponential kernel low-order matrix based on the infinity-norm normalized signal, and then obtain the direction-of-arrival estimation equation based on the sine transform exponential kernel low-order matrix, thereby obtaining the objective function of the angle estimation value;

[0010] Step 3: Initialize the quantum positions, positions, and related parameters of each quantum honey badger in the quantum honey badger group;

[0011] Step 4: Calculate the fitness value of each quantum honey badger to obtain the initial global optimal quantum position;

[0012] Step 5: For each quantum honey badger, determine the quantum position update strategy according to the probability selection constant, generate the corresponding quantum rotation angle according to the quantum evolution rule, and update the quantum position of the quantum honey badger using the simulated simplified quantum rotation gate;

[0013] Step 6: Map the newly generated quantum position of each quantum honey badger to the position of the quantum honey badger, calculate the fitness value of the corresponding position, and update its current global optimal quantum position;

[0014] Step 7: Determine whether the maximum number of iterations T max is reached. If not, let ε = ε + 1, and return to Step 5 to continue the iteration; if the maximum number of iterations is reached, terminate the iteration, and output the optimal quantum position of the quantum honey badger group until the (ε + 1)-th generation, which is the global optimal quantum position. The global optimal position obtained after mapping is the direction-of-arrival estimation value.

[0015] Furthermore, the establishment of the special non-uniform linear array reception data model in Step 1, the acquisition of the snapshot sampling data of the special non-uniform linear array reception signal, and the infinity-norm normalization processing include:

[0016] Define a special non-uniform linear array element position vector p = [p1, p2,..., p M , p1 < p2 <... < p M , p m represents the position of the m-th element from the first element, m = 1, 2,..., M; the position of the first element is expressed as p1 = 0, then H = [h1, h2,..., h M and p = Hd = [h1d, h2d,..., h M d], where d is the minimum element spacing of the uniform linear array that can be virtualized by the formed special uniform linear array, and satisfies λ is the wavelength of the incident signal; form a set The elements in are consecutive natural numbers from 1 to , and the maximum difference of the virtualized uniform linear array is And the relative position difference set The natural numbers in it are consecutive;

[0017] There are N narrowband point sources at the far field of the array incident from directions θ = [θ1, θ2,..., θ N onto a special non-uniform array, with the incident wavelength being λ. Then the k-th snapshot sampling data received by the array is z(k) = A(θ)s(k) + n(k), where k = 1, 2,..., K, and K is the maximum number of snapshots. In the formula, z(k) = [z1(k), z2(k),..., z M (k)] T is the k-th snapshot data vector received by the M×1-dimensional array; s(k) = [s1(k), s2(k),..., s N (k)] T is the N×1-dimensional signal vector; n(k) = [n1(k), n2(k),..., n M (k)] T is the M×1-dimensional noise vector, and the noise is complex impulsive noise that is independent in both space and time and follows the SαS distribution; A(θ) = [a(θ1), a(θ2),..., a(θ N )] is the M×N-dimensional array manifold matrix, where θ = [θ1, θ2,..., θ N is the direction vector of the signal source, and a(θ i ) is the i-th steering vector of the array manifold matrix, i = 1, 2,..., N; for the non-uniform linear array, the array steering vector for the incident angle θ i is where j is the imaginary unit; the infinity-norm normalized signal of the k-th snapshot sampling data received is constructed as where max{·} is the maximum value function.

[0018] Furthermore, the objective function for obtaining the angle estimation value, which uses the data received by the array to construct a sine transform exponential kernel low-order matrix based on the infinity-norm normalized signal in step two, and then obtains the direction-of-arrival estimation equation based on the sine transform exponential kernel low-order matrix, includes:

[0019] Define the sine transform exponential kernel low-order matrix of the infinity-norm normalized signal of the array element received data as In the formula, represents the element in the matrix at the -th row and the -th column, is the weight constant, and respectively represent the in the k-th snapshot signal data vector received peacekeeping first dimensional signal, and satisfy |·| represents the absolute value operation, (·) * represents the conjugate operation, is the kernel length of the kernel function; the low-order matrix of the sine transform exponential kernel can be further expressed as Then, according to the virtual uniform array, the low-order matrix of the sine transform exponential kernel of the normalized signal is is the matrix the maximum dimension after expansion, E is the mathematical expectation, r - m = h l -h f , h l -h f ∈H; the steering matrix after the non-uniform linear array is virtually extended into a virtual uniform linear array is B(θ)=[b(θ1),b(θ2),...,b(θ N )], where the extended steering vector corresponding to the i-th angle is i = 1,2,...,N;

[0020] Then, the maximum likelihood equation based on the low-order matrix of the sine transform exponential kernel can be written as In the formula, tr(·) is the function to find the trace of the matrix, P B(θ) = Β(θ)·(B H (θ)B(θ)) -1 ·B H (θ) is the projection matrix of B(θ);

[0021] Perform eigen-decomposition on the low-order matrix of the sine transform exponential kernel to obtain its signal subspace and noise subspace, that is where, U s is the signal subspace spanned by the eigenvectors corresponding to the large eigenvalues, and the corresponding U n is the noise subspace spanned by the eigenvectors corresponding to the small eigenvalues; Σ s is the diagonal matrix composed of large eigenvalues, and Σ n is the diagonal matrix composed of small eigenvalues;

[0022] Construct a weighted subspace fitting relationship and find an auxiliary matrix T that satisfies: In the formula, represents the angle vector of the estimated signal source, W represents the weighted matrix, is an auxiliary parameter, and fixing B can find the least squares solution of Then, the weighted signal subspace fitting equation based on the low-order matrix of the sine transform exponential kernel for the parameter θ is where, ||·|| F represents the Frobenius norm, tr(·) is a function for calculating the trace of a matrix, and P B(θ) = Β(θ)·(B H (θ)B(θ)) -1 ·B H (θ) is the projection matrix of B(θ), W represents the signal weight matrix. When the weight matrix satisfies it is the optimal signal weight matrix, where σ 2 represents the noise variance, that is the average value of the s small eigenvalues, and I

[0023] According to the relationship between the noise subspace of the signal and the array manifold, the extended weighted form is The maximum likelihood equation based on the sine transform exponential kernel low-order matrix is where, ||·|| F represents the Frobenius norm, tr(·) is a function for calculating the trace of a matrix, and P B(θ) = Β(θ)·(B H (θ)B(θ)) -1 ·B H (θ) is the projection matrix of B(θ), and W n represents the noise weight matrix and satisfies where I n represents the identity matrix;

[0024] Thus, the fitting equation of the maximum likelihood joint weighted signal subspace and the weighted noise subspace of the infinite norm normalized signal of the virtual uniform linear array based on the sine transform exponential kernel low-order matrix is where α1 ∈ {0, 1}, α2 ∈ {0, 1}, and α3 ∈ {0, 1}, and α1 + α2 + α3 = 1.

[0025] Furthermore, the quantum positions, positions, and related parameters of each quantum honey badger in the quantum honey badger group initialized in step three include:

[0026] Set the population size of the quantum honey badger group to the search space dimension, that is, the number of unknown parameters to be optimized is B, and the maximum number of iterations is T max , ε represents the number of iterations; each quantum honey badger in the population has its own quantum position and position. For the quantum positions of quantum honey badgers are randomly initialized within [0, 1], and the quantum position of the nth quantum honey badger is where Its mapping rules are as follows: Among them, represents the lower boundary of the b-th dimensional variable, represents the upper boundary of the b-th dimensional variable.

[0027] Furthermore, calculating the fitness value of each quantum honey badger in step four to obtain the initial global optimal quantum position includes:

[0028] According to the fitness function, the position of the n-th quantum honey badger is used for fitness calculation. Substitute the position into the fitness function. The fitness value of the position of the n-th quantum honey badger in the ε-th generation is Among them n = 1, 2,..., N; Sort the calculated fitness values from smallest to largest, find the quantum position with the smallest fitness value so far in the current generation, and determine it as the global optimal quantum position

[0029] Furthermore, for each quantum honey badger in step five, determine the update strategy of the quantum position according to the probability selection constant, and generate the corresponding quantum rotation angle according to the quantum evolution rule. Using the simulated simplified quantum rotation gate to update the quantum position of the quantum honey badger includes:

[0030] For the n-th quantum honey badger, when is satisfied, use the first update strategy. Among them, is a uniform random number between [0, 1], and η * is the probability selection constant between [0, 1]; The first update strategy is to update the quantum position through the simplified simulated quantum rotation gate according to the current quantum position of the quantum honey badger. Then, the quantum rotation angle corresponding to updating the b-th dimensional quantum position of the n-th quantum honey badger is: Among them and are both random numbers between [0, 1]; is the weight constant; is the source intensity of the n-th quantum honey badger in the ε-th iteration, also called the concentration intensity of the n-th quantum honey badger, which represents the distance between the n-th quantum honey badger and the first quantum honey badger; represents the distance between the prey and the n-th quantum honey badger in the ε-th iteration; then represents the corresponding quantum rotation angle, which is used to represent the evolutionary trend corresponding to the n-th quantum honey badger in the (ε + 1)-th iteration; is used as a flag to change the search direction of the b-th dimensional variable of the n-th quantum honey badger, is defined as the density factor α ε is |·| is the absolute value function; when occurs, the second search strategy is used. The update strategy of the second quantum position changes the search direction and step size. At this time, the updated definition of the b - dimensional quantum rotation angle of the n - th quantum honey badger is where is a random number between [0, 1];

[0031] The update formula for updating the b - dimensional quantum position of the n - th quantum honey badger using the simulated quantum rotation gate is where is the b - dimensional quantum position of the n - th quantum honey badger is the updated b - dimensional quantum position of the (ε + 1) - th generation, n = 1, 2,..., N, b = 1, 2,..., B.

[0032] Further, mapping the newly generated quantum position of each quantum honey badger to the position of the quantum honey badger and calculating the fitness value of the corresponding position, and updating its current global optimal quantum position includes:

[0033] Mapping the newly generated b - dimensional quantum position of the n - th quantum honey badger to the newly generated b - dimensional position of the n - th quantum honey badger according to the mapping rule, n = 1, 2,..., N, b = 1, 2,..., B; calculating the fitness value of the newly generated position of the n - th quantum honey badger according to the fitness function Then, use the greedy selection method to select the quantum position of the quantum honey badger. If then

[0034] The beneficial effects of the present invention:

[0035] To solve the problem of quickly achieving high-precision direction-of-arrival (DOA) estimation under the complex background of impulse noise, in the presence of small snapshots, strong impulses, and coherent sources, a DOA estimation method for non-uniform linear arrays based on the exponential kernel of sine transform and quantum honey badger mechanism with higher effectiveness and robustness is designed. The received data after infinity-norm normalization is used to construct a low-order matrix of the exponential kernel of sine transform, obtaining the low-order matrix of the exponential kernel of sine transform of the corresponding virtual array, while eliminating the weak anti-impulse noise ability of the second and higher moments. And the quantum optimization theory is applied to the calculation method of the honey badger bionic mechanism, designing a weighted signal subspace fitting equation based on the low-order matrix of the exponential kernel of sine transform, a weighted noise subspace fitting equation based on the low-order matrix of the exponential kernel of sine transform, and a maximum likelihood equation based on the low-order matrix of the exponential kernel of sine transform, solving the problem of large computational amount of the multi-dimensional non-linear optimization problem involved in the maximum likelihood algorithm and the weighted subspace fitting algorithm, improving the search efficiency while also enhancing the estimation accuracy. In addition, a quantum honey badger search mechanism based on the quantum rotation angle, simulated simplified quantum rotation gate, and simulated quantum evolution equation is constructed, thereby further improving the convergence performance of the existing calculation method and obtaining the global optimal solution of DOA estimation more quickly and accurately.

[0036] Compared with the prior art, the technical features of the present invention include:

[0037] (1) Compared with the existing DOA estimation methods based on uniform linear arrays, etc., the DOA estimation model based on non-uniform special linear arrays in the present invention realizes the expansion of the array aperture, eliminates the influence caused by mutual coupling between antennas, and solves the problem of direction finding when the placement of the array is restricted by space in practical applications, indicating that the present invention has a wider applicability and the research on this is also very necessary.

[0038] (2) Aiming at the actual requirements of DOA estimation of special non-uniform linear arrays under the complex electromagnetic environment in practical applications, under the background of impulse noise, as well as under low signal-to-noise ratio and small snapshot conditions, when implemented by traditional methods, its robustness and accuracy are difficult to meet the actual requirements. Therefore, the new equations composed of the weighted signal subspace fitting equation based on the low-order matrix of the exponential kernel of sine transform, the weighted noise subspace fitting equation based on the low-order matrix of the exponential kernel of sine transform, and the maximum likelihood equation based on the low-order matrix of the exponential kernel of sine transform designed in the present invention can realize the de-impulse process, eliminate the influence of impulse noise, and can perform robust and high-precision DOA estimation under the conditions of low signal-to-noise ratio, small snapshot number, Gaussian noise, weak impulse noise, strong impulse noise, and multiple coherent signal sources, with a wider application range.

[0039] (3) By combining the quantum optimization theory with the honey badger bionic mechanism, the present invention designs a novel continuous quantum honey badger search mechanism as an evolutionary method, improves the calculation method through quantum coding and simulated quantum rotation gates, and can thus quickly and accurately solve the proposed weighted signal subspace fitting, weighted noise subspace fitting, and maximum likelihood equations. Moreover, on the basis of reducing the amount of computation, the accuracy and robustness of the algorithm solution are improved, solving the drawback of large computational amount of existing algorithms. The designed method has the advantages of fast convergence speed and high convergence accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a schematic diagram of the direction-of-arrival estimation process of a special non-uniform linear array based on the quantum honey badger mechanism under impulse noise;

[0041] Figure 2 is a comparison diagram of direction finding of two direction-of-arrival estimation methods for two independent signal sources under weak impulse noise;

[0042] Figure 3 is a comparison diagram of direction finding of two direction-of-arrival estimation methods for two independent signal sources under strong impulse noise;

[0043] Figure 4 is a comparison diagram of direction finding of two direction-of-arrival estimation methods when there are three coherent signal sources among five signal sources under weak impulse noise;

[0044] Figure 5 is a comparison diagram of direction finding of two direction-of-arrival estimation methods when there are three coherent signal sources among five signal sources under strong impulse noise;

[0045] Figure 6 is a comparison curve of the estimation success rate and the generalized signal-to-noise ratio of two direction-of-arrival estimation methods for two signal sources;

[0046] Figure 7 is a comparison curve of the estimation success rate and the impulse noise characteristic index of two direction-of-arrival estimation methods for two signal sources;

[0047] Figure 8 is a comparison curve of the estimation success rate and the generalized signal-to-noise ratio of two direction-of-arrival estimation methods for five signal sources;

[0048] Figure 9 is a comparison curve of the estimation success rate and the impulse noise characteristic index of two direction-of-arrival estimation methods for five signal sources. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] The following further describes the present invention with reference to the accompanying drawings of the specification and embodiments.

[0050] The overall process of the direction finding method of the present invention is as Figure 1 shown, and the present invention includes the following steps:

[0051] Step 1: Establish a special non-uniform linear array reception data model under an impulse noise environment, obtain the snapshot sampling data of the received signal of the special non-uniform linear array, and perform infinity norm normalization processing.

[0052] A special non-uniform linear array refers to a non-equidistant linear array with a certain pattern in element spacing. Assume that the special non-uniform linear array consists of M isotropic antenna elements. According to the characteristics of the special non-uniform linear array, the non-uniform linear array can virtualize a uniform linear array with more elements. If the maximum correlation delay calculated according to the non-uniform linear array is then the number of virtual elements of the virtual linear array is elements. Define a position vector p = [p1, p2,..., p M of the elements of the special non-uniform linear array, where p1 < p2 <... < p M , and p m represents the position of the m-th element from the first element, and m = 1, 2,..., M. The position of the first element of the special non-uniform linear array is expressed as p1 = 0, then H = [h1, h2,..., h M and p = Hd = [h1d, h2d,..., h M d], where d is the minimum element spacing of the uniform linear array that can be virtualized by the formed special uniform linear array, and it satisfies λ is the wavelength of the incident signal. Form a set The elements in are consecutive natural numbers from 1 to , and the maximum difference of the virtualized uniform linear array is and the natural numbers in the relative position difference set are consecutive.

[0053] There are N narrowband point sources at the far field of the array incident on the special non-uniform array from directions θ = [θ1, θ2,..., θ N , and the incident wavelength is λ. Then the k-th snapshot sampling data received by the array is z(k) = A(θ)s(k) + n(k), where k = 1, 2,..., K, and K is the maximum number of snapshots. In the formula, z(k) = [z1(k), z2(k),..., z M (k)] T is the k-th snapshot data vector received by the M×1-dimensional array; s(k) = [s1(k), s2(k),..., s N (k)] T is the N×1-dimensional signal vector; n(k) = [n1(k), n2(k),..., n M ]>(k)] Tis an M×1 dimensional noise vector, and the noise is complex impulsive noise that is independent in both space and time and follows the SαS distribution. A(θ)=[a(θ1),a(θ2),...,a(θ N )] is an M×N dimensional array manifold matrix, where θ=[θ1,θ2,...,θ N is the direction vector of the signal source, and a(θ i ) is the i-th steering vector of the array manifold matrix, i = 1, 2,..., N. The steering vector of the non-uniform linear array for the incident angle θ i is where j is the imaginary unit. The infinity-norm normalized signal of the k-th snapshot sampling data received is constructed as where max{·} is the maximum function.

[0054] Step 2: Use the data received by the array to construct a sine transform exponential kernel low-rank matrix based on the infinity-norm normalized signal, and then obtain a direction-of-arrival estimation equation based on the sine transform exponential kernel low-rank matrix, thereby obtaining the objective function of the angle estimation value.

[0055] Define the sine transform exponential kernel low-rank matrix of the infinity-norm normalized signal of the array element received data as In the formula, represents the element in the matrix at the -th row and the -th column, is the weight constant, and respectively represent the -th dimension and the -th dimension signals in the k-th snapshot signal data vector received, and satisfy |·| represents the absolute value operation, (·) * represents the conjugate operation, is the kernel length of the kernel function. The sine transform exponential kernel low-rank matrix can be further expressed as Then, the sine transform exponential kernel low-rank matrix of the normalized signal is constructed according to the virtual uniform array as is the maximum dimension after the matrix is extended, E is the mathematical expectation, r - m = h l - h f , h l - h f ∈ H. The steering matrix after the non-uniform linear array is virtually extended into a virtual uniform linear array is B(θ)=[b(θ1),b(θ2),...,b(θN )], where the extended steering vector corresponding to the \(i\) -th angle is \(i = 1,2,\cdots,N\).

[0056] Then the maximum - likelihood equation based on the low - order matrix of the sine - transform exponential kernel can be written as In the formula, \(tr(\cdot)\) is the function for calculating the trace of a matrix, \(P\) B(θ) =\(\mathbf{B}(\theta)\cdot(\mathbf{B}\) H (\theta)\mathbf{B}(\theta))\) -1 \(\cdot\mathbf{B}\) H (\theta)\) is the projection matrix of \(\mathbf{B}(\theta)\).

[0057] Performing eigenvalue decomposition on the low - order matrix of the sine - transform exponential kernel to obtain its signal subspace and noise subspace, that is where, \(\mathbf{U}\) s is the signal subspace spanned by the eigenvectors corresponding to the large eigenvalues, and the corresponding \(\mathbf{U}\) n is the noise subspace spanned by the eigenvectors corresponding to the small eigenvalues; \(\boldsymbol{\Sigma}\) s is the diagonal matrix composed of large eigenvalues, and \(\boldsymbol{\Sigma}\) n is the diagonal matrix composed of small eigenvalues.

[0058] When the estimated number of signal sources is equal to the actual number of signal sources, the space spanned by the signal subspace is the same as the space spanned by the array - manifold steering matrix. At this time, \(span\{\mathbf{U}\) s \}=span\{\mathbf{B}(\theta)\}. In the noise background, the space spanned by the signal subspace and the array - manifold steering matrix is not equal, and the above formula does not necessarily hold. Therefore, a weighted - subspace fitting relationship can be constructed to find an auxiliary matrix \(\mathbf{T}\) such that the two fit best in the least - squares sense, that is: In the formula, represents the angle vector of the estimated signal sources, \(\mathbf{W}\) represents the weighted matrix, is an auxiliary parameter. Fixing \(\mathbf{B}\) can find the least - squares solution of Then the weighted - signal - subspace fitting equation based on the low - order matrix of the sine - transform exponential kernel for the parameter \(\theta\) can be obtained as In the formula, \(\|\cdot\|\) F represents the Frobenius norm, \(tr(\cdot)\) is the function for calculating the trace of a matrix, \(P\) B(θ) =\(\mathbf{B}(\theta)\cdot(\mathbf{B}\) H (\theta)\mathbf{B}(\theta))\) -1 \(\cdot\mathbf{B}\) H (\theta)\) is the projection matrix of \(\mathbf{B}(\theta)\), \(\mathbf{W}\) represents the signal - weight matrix. When the weight matrix satisfies it is the optimal signal - weight matrix, where, \(\sigma\) 2 represents the noise variance, that is The average value of the small eigenvalues, I s Represents the identity matrix.

[0059] According to the relationship between the noise subspace of the signal and the array flow pattern, the generalized weighted form is The maximum likelihood equation based on the sine transform exponential kernel low-order matrix is: In the formula, ||·|| F represents the Frobenius norm, tr(·) is the function for finding the matrix trace, and P B(θ) =Β(θ)·(B H (θ)B(θ)) -1 ·B H (θ) is the projection matrix of B(θ), W n Represents the noise weight matrix, satisfying Among them I n Represents the identity matrix.

[0060] The fitting equation of the infinite norm normalized signal of the virtual uniform linear array based on the maximum likelihood joint weighted signal subspace and weighted noise subspace of the sine transform exponential kernel low-order matrix is: Among them, α1∈{0,1}, α2∈{0,1} and α3∈{0,1}, and satisfy α1+α2+α3=1.

[0061] Step 3: Initialize the quantum position, location and related parameters of each quantum honey badger in the quantum honey badger group.

[0062] Set the size of the quantum honey badger group to The dimension of the search space, that is, the number of unknown parameters to be optimized is B, and the maximum number of iterations is T max , ε represents the number of iterations. Each quantum honey badger in the group has its own quantum position and position. The quantum positions of quantum honey badgers are randomly initialized in [0,1], and the quantum position of the nth quantum honey badger is in b=1,2,...,B, and the mapping to the corresponding position is The mapping rules are as follows: in, represents the lower bound of the b-th dimension variable, Indicates the upper bound of the b-th dimension variable.

[0063] Step 4: Calculate the fitness value of each quantum honey badger and obtain the initial global optimal quantum position.

[0064] According to the fitness function, the position of the nth quantum honey badger Perform fitness calculation and set the position Substitute it into the fitness function, and the fitness value of the quantum honey badger at the nth position in the εth generation is where n = 1, 2, ..., N. Sort the calculated fitness values from smallest to largest, find the quantum position with the smallest fitness value up to the current generation, and determine it as the global optimal quantum position

[0065] Step 5: For each quantum honey badger, use two quantum position update strategies with a certain probability, generate the corresponding quantum rotation angle according to the quantum evolution rule, and update the quantum position of the quantum honey badger using the simulated simplified quantum rotation gate.

[0066] For the nth quantum honey badger, when use the first update strategy, where is a uniform random number between [0, 1], and η * is a probability selection constant between [0, 1]. The first update strategy is to update the quantum position through the simplified simulated quantum rotation gate according to the current quantum position of the quantum honey badger. Then, the quantum rotation angle corresponding to updating the bth - dimensional quantum position of the nth quantum honey badger is: where and are both random numbers between [0, 1]; is the weight constant; is the source intensity of the nth quantum honey badger in the εth iteration, also called the concentration intensity of the nth quantum honey badger, representing the distance between the nth quantum honey badger and the first quantum honey badger; represents the distance between the prey and the nth quantum honey badger at the εth iteration; then represents the corresponding quantum rotation angle, used to represent the evolutionary trend corresponding to the nth quantum honey badger in the (ε + 1)th iteration; is used as a flag to change the search direction of the bth - dimensional variable of the nth quantum honey badger, is defined as the density factor α ε is |·| is the absolute - value function. When use the second search strategy. The second quantum - position update strategy changes the search direction and step size. At this time, the quantum rotation angle for updating the bth dimension of the nth quantum honey badger is defined as where is a random number between [0, 1].

[0067] The update process of the quantum position is mainly completed through the simulated simplified quantum rotation gate. The update formula for updating the bth - dimensional quantum position of the nth quantum honey badger using the simulated quantum rotation gate is where is the b - dimensional quantum position of the n - th quantum honey badger The updated b - dimensional quantum position of the (ε + 1)-th generation, where n = 1, 2, …, N and b = 1, 2, …, B.

[0068] Step 6: Map the newly generated quantum position of each quantum honey badger to the position of the quantum honey badger, calculate the fitness value of the corresponding position, and update its current global optimal quantum position.

[0069] The newly generated b - dimensional quantum position of the n - th quantum honey badger is mapped to the newly generated b - dimensional position of the n - th quantum honey badger according to the mapping rule where n = 1, 2, …, N and b = 1, 2, …, B. Calculate the fitness value of the newly generated position of the n - th quantum honey badger according to the fitness function of Then, use the greedy selection method to select the quantum position of the quantum honey badger. If then Then, sort the quantum honey badgers after greedy selection in ascending order of fitness, find the quantum honey badger with the minimum fitness and record its quantum position as the global optimal quantum position up to the (ε + 1)-th generation, and update it to

[0070] Step 7: Determine whether the maximum number of iterations T has been reached max . If not, let ε = ε + 1 and return to Step 5 to continue the iteration; if the maximum number of iterations has been reached, terminate the iteration and output the optimal quantum position of the quantum honey badger population up to the (ε + 1)-th generation, which is the global optimal quantum position. The global optimal position obtained after mapping is the estimated value of the incoming wave direction.

[0071] The present invention designs a special non-uniform linear array high-precision direction-of-arrival (DOA) estimation method applicable to complex environments such as small snapshot numbers, low signal-to-noise ratios, multi-coherent signal sources, and impulse noise by constructing a weighted signal subspace fitting equation based on a sine transform exponential kernel low-order matrix, a weighted noise subspace fitting equation based on a sine transform exponential kernel low-order matrix, and a maximum likelihood equation based on a sine transform exponential kernel low-order matrix. The method includes the following steps: establishing a received data model of a special non-uniform linear array in an impulse noise environment, obtaining snapshot sampling data of the received signal of the special non-uniform linear array, and performing infinity norm normalization processing; constructing a sine transform exponential kernel low-order matrix based on the infinity norm normalized signal by using the data received by the array, and further obtaining a DOA estimation equation based on the sine transform exponential kernel low-order matrix, thereby obtaining an objective function of the angle estimation value; initializing the quantum positions, positions, and related parameters of each quantum honey badger in the quantum honey badger swarm; calculating the fitness value of each quantum honey badger to obtain the initial global optimal quantum position; for each quantum honey badger, using two quantum position update strategies with a certain probability, generating a corresponding quantum rotation angle according to the quantum evolution rule, and updating the quantum position of the honey badger using a simulated simplified quantum rotation gate; mapping the newly generated quantum position of each quantum honey badger to the position of the honey badger, calculating the fitness value of the corresponding position, and updating its current global optimal quantum position; determining whether the maximum number of iterations is reached. If not, let the number of iterations be incremented by 1, and return to step five to continue the iteration; if the maximum number of iterations has been reached, terminate the iteration, and output the optimal quantum position up to the current generation, which is the global optimal quantum position. The global optimal position obtained after mapping is the DOA estimation value of the incoming wave. The present invention realizes effective estimation of the DOA of the signal source of the special non-uniform linear array with higher direction-finding accuracy, better ability to expand the array aperture, and ability to measure coherent signal sources at a lower time cost, and can perform direction finding under Gaussian noise, weak impulse noise, and strong impulse noise, with a wide range of applications.

[0072] For the convenience of description, the special non-uniform linear array DOA estimation method based on the quantum honey badger mechanism and the sine transform exponential kernel low-order matrix is abbreviated as "the method designed by the present invention", the special non-uniform array DOA estimation method based on the fractional lower order moment MUSIC algorithm is abbreviated as FLOM-MUSIC, and the special non-uniform array DOA estimation method based on the multi-dimensional MUSIC algorithm of the fractional lower order moment is abbreviated as Mul-FLOM-MUSIC. The reference for the comparative direction-finding method involved is "Research on DOA Estimation of Coherent Signal Sources under Impulse Noise Background" published by Wan Wenlong in the master's thesis of Harbin Engineering University. Other parameters are set the same as those in the method designed by the present invention.

[0073] The specific parameter settings for the simulation of the model are as follows:

[0074] The number of array elements M of the non-uniform linear array is 4, and the array element position vector is p = [0, 1, 4, 6]. When the number of signal sources is set to 2, the incident wave directions are [0, 20], with the unit being degrees; when the number of signal sources is set to 5, the incident wave directions are [-30, -15, 0, 15, 30], with the unit being degrees. The signal-to-noise ratio is 10 dB, γ = 1.3, the maximum number of snapshots K = 100, and the kernel length of the sine transform exponential kernel is set to 125. The number of extended virtual array elements The simulation is carried out in a strong impulse noise or weak impulse noise environment.

[0075] The parameter settings of the method designed by the present invention are as follows:

[0076] Population size The search space of the incident wave direction is between -90 degrees and 90 degrees, and the weight constant Weight constant The maximum number of iterations T of the entire population max = 100, the density factor ε represents the number of iterations, and the learning factor The probability selection constant η * = 0.5.

[0077] Figure 2 : The figure shows the direction finding comparison diagram between the method designed by the present invention and FLOM-MUSIC when there are two independent signal sources. At this time, the two independent signal sources are incident from the directions of {0°, 20°}, the impulse noise characteristic index is 1.2, the generalized signal-to-noise ratio is 10 dB, the number of snapshots is 30, the number of Monte Carlo experiments is 100 times, α1 = 0, α2 = 1, and α3 = 0. From the simulation Figure 2 It can be seen that the method designed by the present invention has an ideal direction finding effect, with a very small deviation from the value of the true incident wave direction and stable performance, while FLOM-MUSIC cannot achieve accurate direction finding.

[0078] Figure 3 : The figure shows the direction finding comparison diagram between the method designed by the present invention and FLOM-MUSIC when there are two independent signal sources. At this time, the two independent signal sources are incident from the directions of {0°, 20°}, the impulse noise characteristic index is 0.8, the generalized signal-to-noise ratio is 10 dB, the number of snapshots is 30, the number of Monte Carlo experiments is 100 times, α1 = 0, α2 = 1, and α3 = 0. From the simulation Figure 3 It can be seen that the method designed by the present invention has an ideal direction finding effect, with a very small deviation from the value of the true incident wave direction and stable performance, while FLOM-MUSIC has failed and cannot achieve accurate direction finding.

[0079] Figure 4 : In Figure 4 there are five signal sources, Figure 4The figure shows the comparison diagram of the direction finding between the method designed by the present invention and FLOM-MUSIC when the signal sources 1, 3, and 5 are coherent and the signal sources 1, 2, and 4 are independent. At this time, the five signal sources are incident from the directions of {-30°, -15°, 0°, 15°, 30°} respectively, the impact noise characteristic index is 1.8, the generalized signal-to-noise ratio is 10 dB, the number of snapshots is 100, the number of Monte Carlo experiments is 100 times, and α1 = 1, α2 = 0, and α3 = 0. From the simulation Figure 4 It can be seen that the method designed by the present invention can realize the expansion of the array aperture, and can perform high-precision direction finding for coherent signal sources. The obtained direction finding effect is ideal, the deviation from the value of the true incoming wave direction is extremely small, and the performance is stable. In contrast, FLOM-MUSIC cannot achieve accurate direction finding.

[0080] Figure 5 : When there are five signal sources, Figure 5 The figure shows the comparison diagram of the direction finding between the method designed by the present invention and FLOM-MUSIC when the signal sources 2, 3, and 4 are coherent and the signal sources 1, 2, and 5 are independent. At this time, the five coherent signal sources are incident from the directions of {-30°, -15°, 0°, 15°, 30°} respectively, the impact noise characteristic index is 0.9, the generalized signal-to-noise ratio is 10 dB, the number of snapshots is 100, the number of Monte Carlo experiments is 100 times, and α1 = 1, α2 = 0, and α3 = 0. From the simulation Figure 5 It can be seen that the method designed by the present invention can realize the expansion of the array aperture, and can perform high-precision direction finding for coherent signal sources. In a strong impact noise environment, the obtained direction finding effect is ideal, the deviation from the value of the true incoming wave direction is extremely small, and the performance is stable. In contrast, FLOM-MUSIC cannot achieve accurate direction finding.

[0081] Figure 6 : When α = 1.2, Figure 6 The relationship between the estimated success probability and the generalized signal-to-noise ratio is given. When the impact noise characteristic index α = 1.2, 500 Monte Carlo experiments are adopted, α1 = 0, α2 = 1, and α3 = 0, and the incoming wave directions of the two independent signal sources are 0° and 20°, the performance advantages of the proposed algorithm are verified. When drawing the curve of the successful estimated probability of the angle measurement of the independent signal source changing with the generalized signal-to-noise ratio, it is set that the absolute deviation between the estimated value and the true value is within 1.5° as the successful estimation. It can be seen from the experimental results of Simulation 6 that in an impact noise environment, the method designed by the present invention has good performance in terms of direction finding accuracy under low signal-to-noise ratio conditions, and can still complete the estimation of the direction of arrival in a situation with poor communication quality.

[0082] Figure 7 : When the generalized signal-to-noise ratio is 5 dB, Figure 7The relationship between the estimated success probability and the characteristic exponent is given. When the generalized signal-to-noise ratio is 5 dB, 500 Monte Carlo experiments are carried out, α1 = 0, α2 = 1 and α3 = 0, and the incident directions of two independent signal sources are 0° and 20°, the performance advantage of the algorithm is verified. When plotting the curve of the angle-of-arrival successful estimation probability of independent signal sources versus the characteristic exponent, it is set that the absolute deviation between the estimated value and the true value is within 1.5° as a successful estimation. From the simulation Figure 7 It can be seen from the experimental results of the simulation that under the background of impulsive noise, the method proposed in this paper has greater superiority and can better complete the direction-of-arrival estimation in a harsh environment with strong impulsive noise and low signal-to-noise ratio, and the accuracy is higher. In contrast, the classical Mul-FLOM-MUSIC method cannot accurately measure the direction in this environment.

[0083] Figure 8 : When α = 1.8, Figure 8 The relationship between the estimated success probability and the generalized signal-to-noise ratio is given. When the characteristic exponent of impulsive noise α = 1.8, 500 Monte Carlo experiments are carried out. When α1 = 1, α2 = 0 and α3 = 0, the incident directions of five signal sources are {-30°, -15°, 0°, 15°, 30°} respectively, and signal sources 1, 3 and 5 are coherent, and signal sources 1, 2 and 4 are independent, the performance advantage of the proposed algorithm is verified. When plotting the curve of the angle-of-arrival successful estimation probability of independent signal sources versus the generalized signal-to-noise ratio, it is set that the absolute deviation between the estimated value and the true value is within 1.5° as a successful estimation. It can be seen from the experimental results of simulation 8 that in the impulsive noise environment, the method designed in the present invention can realize the direction measurement of coherent signal sources, and at the same time realize the expansion of the array aperture. Under the condition of low signal-to-noise ratio, the direction measurement accuracy also has a good performance, and the direction-of-arrival estimation can still be completed in the case of poor communication quality.

[0084] Figure 9 : When the generalized signal-to-noise ratio is 10 dB, Figure 9 The relationship between the estimated success probability and the characteristic exponent is given. When the generalized signal-to-noise ratio is 10 dB, 500 Monte Carlo experiments are carried out, α1 = 1, α2 = 0 and α3 = 0, the incident directions of five signal sources are {-30°, -15°, 0°, 15°, 30°} respectively, and signal sources 2, 3 and 4 are coherent, and signal sources 1, 2 and 5 are independent, the performance advantage of the algorithm is verified. When plotting the curve of the angle-of-arrival successful estimation probability of independent signal sources versus the characteristic exponent, it is set that the absolute deviation between the estimated value and the true value is within 1.5° as a successful estimation. From the simulation Figure 9It can be seen from the experimental results that, in the background of impulse noise, the method designed by the present invention can achieve the direction finding of coherent signal sources, and at the same time achieve the expansion of the array aperture, with greater superiority, and can better complete the direction of arrival estimation in the harsh environment of strong impulse noise, with higher accuracy. In contrast, the classical FLOM-MUSIC method cannot perform accurate direction finding in this environment.

Claims

1. A method for estimating the direction of arrival of a non-uniform linear array based on a quantum honey badger search mechanism, characterized in that Including: Step 1: Establish a special non-uniform linear array reception data model in an impulse noise environment, obtain the snapshot sampling data of the received signal of the special non-uniform linear array, and perform infinity norm normalization processing; Step 2: Use the data received by the array to construct a sine transform exponential kernel low-order matrix based on the infinity norm normalized signal, and then obtain the direction-of-arrival estimation equation based on the sine transform exponential kernel low-order matrix, thereby obtaining the objective function of the angle estimation value; Step 3: Initialize the quantum positions, positions and related parameters of each quantum honey badger in the quantum honey badger group; Step 4: Calculate the fitness value of each quantum honey badger to obtain the initial global optimal quantum position; Step 5: For each quantum honey badger, determine the quantum position update strategy according to the probability selection constant, generate the corresponding quantum rotation angle according to the quantum evolution rule, and update the quantum position of the quantum honey badger using the simulated simplified quantum rotation gate; Step 6: Map the newly generated quantum position of each quantum honey badger to the position of the quantum honey badger, calculate the fitness value of the corresponding position, and update its current global optimal quantum position; Step 7: Determine whether the maximum number of iterations T is reached max . If not, let ε = ε + 1, and return to Step 5 to continue the iteration; if the maximum number of iterations is reached, terminate the iteration, and output the optimal quantum position of the quantum honey badger population up to the (ε + 1)-th generation, which is the global optimal quantum position. The global optimal position obtained after mapping is the estimated value of the incoming wave direction.

2. The method for estimating the direction of arrival of a non-uniform linear array based on the quantum honey badger search mechanism according to claim 1, wherein: The establishment of the special non-uniform linear array reception data model in the impulse noise environment in Step 1, obtaining the snapshot sampling data of the received signal of the special non-uniform linear array, and performing infinity norm normalization processing includes: Define a position vector p = [p1, p2,..., p M of the elements of a special non-uniform linear array, where p1 < p2 <... < p M , and p m represents the position of the m-th element relative to the first element, where m = 1, 2,..., M; the position of the first element is represented as p1 = 0. Then H = [h1, h2,..., h M and p = Hd = [h1d, h2d,..., h M d], where d is the minimum element spacing of the uniform linear array that can be virtually formed by the special uniform linear array formed, and satisfies λ is the wavelength of the incident signal; form a set The elements in are consecutive natural numbers from 1 to , and the maximum difference of the virtual uniform linear array is and the relative position difference set The natural numbers in are consecutive; There are N narrowband point sources at the far field of the array incident from directions θ = [θ1, θ2,..., θ N onto a special non-uniform array. The incident wavelength is λ. Then the k-th snapshot sampling data received by the array is z(k) = A(θ)s(k) + n(k), where k = 1, 2,..., K, and K is the maximum number of snapshots. In the formula, z(k) = [z1(k), z2(k),..., z M (k)] T is the k-th snapshot data vector received by the M×1 array; s(k) = [s1(k), s2(k),..., s N (k)] T is the N×1 signal vector; n(k) = [n1(k), n2(k),..., n M (k)] T is the M×1 noise vector. The noise is complex impulsive noise that is independent in both space and time and follows the SαS distribution; A(θ) = [a(θ1), a(θ2),..., a(θ N )] is the M×N array manifold matrix, where θ = [θ1, θ2,..., θ N is the direction vector of the signal source, and a(θ i ) is the i-th steering vector of the array manifold matrix, i = 1, 2,..., N; the steering vector of the non-uniform linear array for the incident angle θ i is where j is the imaginary unit; the infinity-norm normalized signal of the k-th snapshot sampling data received is constructed as where max{·} is the maximum value function.

3. A method for estimating the direction of arrival of a non-uniform linear array based on a quantum honey badger search mechanism according to claim 2, characterized in that: The use of the data received by the array to construct a sine transform exponential kernel low-order matrix based on the infinity norm normalized signal in Step 2, and then obtaining the direction-of-arrival estimation equation based on the sine transform exponential kernel low-order matrix, thereby obtaining the objective function of the angle estimation value includes: Define the sine transform exponential kernel low-order matrix of the infinite norm normalized signal of the array element received data as In the formula, represents the element in the th row and th column of the matrix , is the weight constant, and respectively represent the th and th dimensional signals in the received kth snapshot signal data vector , and satisfy |·| represents the absolute value operation, (·) * represents the conjugate operation, is the kernel length of the kernel function; the sine transform exponential kernel low-order matrix can be further expressed as Then, according to the virtual uniform array, the sine transform exponential kernel low-order matrix of the normalized signal is constructed as is the maximum dimension after the expansion of the matrix , E is the mathematical expectation, r - m = h l - h f , h l - h f ∈H; the steering matrix after the non-uniform linear array is virtually extended into a virtual uniform linear array is B(θ) = [b(θ1), b(θ2),..., b(θ N )], where the extended steering vector corresponding to the ith angle is Then the maximum likelihood equation based on the low-order matrix of the sine transform exponential kernel can be written as where tr(·) is the function for finding the trace of a matrix, P B(θ) = Β(θ)·(B H (θ)B(θ)) -1 ·B H (θ) is the projection matrix of B(θ); The eigen - decomposition of the low - order matrix of the sine - transform exponential kernel is performed to obtain its signal subspace and noise subspace, that is where U s is the signal subspace spanned by the eigen - vectors corresponding to the large eigenvalues, and the corresponding U n is the noise subspace spanned by the eigen - vectors corresponding to the small eigenvalues; Σ s is the diagonal matrix composed of large eigenvalues, and Σ n is the diagonal matrix composed of small eigenvalues; Construct a weighted subspace fitting relationship and find an auxiliary matrix \(T\) that satisfies: In the formula, represents the angle vector of the estimated signal source, \(W\) represents the weighted matrix, is an auxiliary parameter. By fixing \(B\), the least-squares solution can be obtained. Then, the weighted signal subspace fitting equation of the low-order matrix based on the sine transform exponential kernel with respect to the parameter \(\theta\) is In the formula, \(\|\cdot\|\) F represents the Frobenius norm, \(tr(\cdot)\) is the function for finding the trace of a matrix, \(P\) B(θ) =\(B(\theta)\cdot(B\) H (\theta)B(\theta))\) -1 \(\cdot B\) H (\theta)\) is the projection matrix of \(B(\theta)\), \(W\) represents the signal weight matrix. When the weight matrix satisfies , it is the optimal signal weight matrix, where \(\sigma\) 2 represents the noise variance, that is, the average value of the small eigenvalues, \(I\) s represents the identity matrix; Based on the relationship between the noise subspace of the signal and the array manifold, the extended weighted form is The maximum likelihood equation based on the sine transform exponential kernel low-order matrix is In the formula, ||·|| F represents the Frobenius norm, tr(·) is the function to find the trace of the matrix, P B(θ) = Β(θ)·(B H (θ)B(θ)) -1 ·B H (θ) is the projection matrix of B(θ), W n represents the noise weight matrix, satisfying where I n represents the identity matrix; The fitting equation of the maximum likelihood joint weighted signal subspace and weighted noise subspace of the low-order matrix based on the sine transform exponential kernel for the infinite norm normalized signal of the virtual uniform linear array is as follows where α1 ∈ {0, 1}, α2 ∈ {0, 1}, and α3 ∈ {0, 1}, and α1 + α2 + α3 = 1 is satisfied.

4. A method for estimating the direction of arrival of a non-uniform linear array based on a quantum honey badger search mechanism according to claim 3, characterized in that: The initialization of the quantum positions, positions and related parameters of each quantum honey badger in the quantum honey badger group in Step 3 includes: Set the population size of the quantum honey badger swarm to The dimension of the search space, that is, the number of unknown parameters to be optimized is B, and the maximum number of iterations is T max , ε represents the number of iterations; each quantum honey badger in the population has its own quantum position and position. For The quantum positions of the quantum honey badgers are randomly initialized within [0, 1], and the quantum position of the nth quantum honey badger is where b = 1, 2,..., B, and the corresponding position after mapping is The mapping rule is as follows: where, represents the lower bound of the b-th dimension variable, represents the upper bound of the b-th dimension variable.

5. A method for estimating the direction of arrival of a non-uniform linear array based on a quantum honey badger search mechanism according to claim 4, characterized in that: The calculation of the fitness value of each quantum honey badger to obtain the initial global optimal quantum position in Step 4 includes: According to the fitness function, the position of the nth quantum honey badger is subjected to fitness calculation. Substitute the position into the fitness function. The fitness value of the position of the nth quantum honey badger in the εth generation is where Sort the calculated fitness values from smallest to largest, find the quantum position with the smallest fitness so far in the current generation, and determine it as the global optimal quantum position 6. A method for estimating the direction of arrival of a non-uniform linear array based on a quantum honey badger search mechanism according to claim 5, characterized in that: For each quantum honey badger in Step 5, determining the quantum position update strategy according to the probability selection constant, generating the corresponding quantum rotation angle according to the quantum evolution rule, and updating the quantum position of the quantum honey badger using the simulated simplified quantum rotation gate includes: For the nth quantum honey badger, when , the first update strategy is used, where is a uniform random number in [0, 1], and η * is a probability selection constant between [0, 1]; the first update strategy is to update the quantum position through a simplified simulated quantum rotation gate according to the current quantum position of the quantum honey badger. Then, the quantum rotation angle corresponding to the update of the b - dimensional quantum position of the nth quantum honey badger is: Where and are both random numbers between [0, 1]; is a weight constant; is the source intensity of the nth quantum honey badger in the ε - th iteration, also called the concentration intensity of the nth quantum honey badger, which represents the distance between the nth quantum honey badger and the first quantum honey badger; represents the distance between the prey and the nth quantum honey badger at the ε - th iteration; then represents the corresponding quantum rotation angle, which is used to represent the evolutionary trend corresponding to the nth quantum honey badger in the (ε + 1)-th iteration; is used as a flag to change the search direction of the b - dimensional variable of the nth quantum honey badger, is defined as the density factor α ε is |·| is the absolute - value function; when , the second search strategy is used. The update strategy of the second quantum position changes the search direction and step size. At this time, the quantum rotation angle corresponding to the update of the b - dimensional quantum position of the nth quantum honey badger is defined as Where is a random number between [0, 1]; The update formula for updating the b - dimensional quantum position of the nth quantum honey badger using a simulated quantum rotation gate is where is the b - dimensional quantum position of the nth quantum honey badger The b - dimensional quantum position of the (ε + 1) - th generation after update, n = 1, 2,..., N, b = 1, 2,..., B.

7. A method for estimating the direction of arrival of a non-uniform linear array based on a quantum honey badger search mechanism according to claim 6, characterized in that: The mapping of the newly generated quantum position of each quantum honey badger to the position of the quantum honey badger in Step 6, calculating the fitness value of the corresponding position, and updating its current global optimal quantum position includes: The b - dimensional quantum position newly generated by the n - th quantum honey badger is mapped into the b - dimensional position newly generated by the n - th quantum honey badger according to the mapping rule where n = 1, 2, …, N and b = 1, 2, …, B; calculate the fitness value of the position newly generated by the n - th quantum honey badger according to the fitness function Then, select the quantum positions of the quantum honey badgers in a greedy selection manner. If then Then, sort the quantum honey badgers after greedy selection in ascending order of fitness, find the quantum honey badger with the minimum fitness and record its quantum position as the global optimal quantum position up to the (ε + 1)-th generation, and update it to ​

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