A method for direction of arrival estimation of small snapshot coherent sources in impulsive noise environment

Abstract

The present invention provides a method for estimating the direction of arrival (DOA) of a small snapshot coherent source in an impulsive noise environment. The method includes establishing a uniform linear array small snapshot sampling signal model, constructing an infinite-norm median covariance matrix based on a Sigmoid neural network kernel, and obtaining an infinite-norm small snapshot maximum likelihood equation based on the Sigmoid neural network kernel. Because there is a high probability of very large singular values ​​occurring in α-stable distributed noise environments, especially when the characteristic exponent is small, traditional mean estimation methods can result in large deviations. However, using the median is unaffected by data that is too large or too small, resulting in good DOA estimation results in impulsive noise environments. The present invention selects the optimal kernel length through performance simulation and designs a continuous quantum cloud search mechanism to efficiently solve the maximum likelihood direction-finding equation based on the infinite-norm of the Sigmoid neural network kernel. The invented small snapshot DOA estimation method can effectively estimate the direction of arrival (DOA) of both independent and coherent sources in the presence of impulsive noise.

Description

Technical Field

[0001] The present invention relates to a method for estimating the direction of arrival of an ultra-small snapshot coherent source based on a quantum cloud search mechanism in an impact noise environment, and belongs to the field of array signal processing. Background Art

[0002] Direction of Arrival (DOA) estimation is an important research area in array signal processing, particularly in communications, radar, and sonar systems. While traditional methods such as the Multiple Signal Classification (MUSIC) algorithm and the Rotationally Invariant Subspace Technique for Signal Parameter Estimation (ESPRIT) have demonstrated high estimation performance, these algorithms are based on eigenvalue decomposition, which often requires a large number of snapshots to achieve good estimation performance. This results in poor real-time performance and high computational complexity. To reduce the computational complexity of DOA estimation and improve system real-time performance, single-snapshot DOA estimation has attracted considerable attention. However, single-snapshot DOA estimation often requires a high signal-to-noise ratio (SNR) and a low eigenvalue index for impulse noise, otherwise its robustness is compromised. Therefore, it is imperative to design DOA estimation methods that are highly accurate and applicable to complex impulse noise environments.

[0003] According to existing technical literature, the "Nested Array DOA Estimation Algorithm Based on Single Snapshot Data" published by Han Jiahui et al. in "Fire and Control Command" (2019, Vol. 44, No. 3, pp. 112-115.) uses the single snapshot data received by the two sub-arrays to construct the Toeplitz matrix respectively, and then performs eigenvalue decomposition combined with the MUSIC algorithm for DOA estimation. It has good real-time performance and high wave direction estimation accuracy. However, this method constructs the Toeplitz matrix separately through nested arrays and performs two spectral peak searches, which increases the amount of calculation and cannot perform effective wave direction estimation in an impact noise environment. Jiao Yameng et al. published a paper titled "A Fast Algorithm for Small Snapshot Weighted Subspace Fitting Based on Continuous Ant Colony Optimization Algorithm" in the Journal of Electronics and Information Technology (2011, Vol. 33, No. 4, pp. 972-976). The paper uses the information Gaussian kernel probability distribution function in the continuous ant colony algorithm and obtains the nonlinear global optimal solution of the weighted subspace fitting algorithm after a finite number of iterations. The algorithm has good estimation performance under low signal-to-noise ratio and small snapshot conditions, but the number of snapshots is still around 100 to 200, which is still relatively large, and DOA estimation fails in an impulsive noise environment. Summary of the Invention

[0004] Existing literature shows that small snapshot DOA estimation can improve the real-time performance of the system, reduce the amount of calculation, and has better estimation accuracy than the poor robustness of a single snapshot. However, the existing literature on small snapshot DOA estimation still requires a large number of snapshots, and the noise environment is all Gaussian white noise, which is not suitable for DOA estimation research in complex electromagnetic environments. Especially in electronic information warfare, due to the presence of various interferences, the number of snapshots obtained per unit time is limited. The performance of most existing algorithms is seriously degraded in this case, and even effective DOA estimation cannot be performed. Therefore, it is very necessary to design a high-performance small snapshot DOA estimation method suitable for impulsive noise background. The present invention designs a small snapshot coherent source DOA estimation method based on a quantum cloud search mechanism in an impulsive noise environment. This method can construct a pseudo-covariance matrix by median processing the snapshot data in a complex impulsive noise environment, and use the Sigmoid neural network kernel infinite norm maximum likelihood method to effectively estimate the DOA of the signal source. This method can not only realize DOA estimation in the case of extremely small snapshots, but also obtain good DOA estimation results in other harsh environments such as Gaussian noise, weak impulse noise and strong impulse noise.

[0005] The purpose of the present invention is achieved as follows: Step 1: Establish a small snapshot sampling signal model in an impact noise environment:

[0006] Given an equidistant uniform linear array with Q elements and an element spacing of d, the i-th far-field narrowband signal is transmitted from θ i The incident signal is incident on the array in the direction with a wavelength of λ and a snapshot number of L (L<Q). The incident signal and the noise signal are independent of each other, i=1,2,…,N, and the first array element is selected as the reference array element. The signal received by the kth array element at time is in, for The incident signal of the i-th source at time t, for The noise signal of the kth array element at time, represents the impulse noise satisfying the SαS stable distribution on the kth array element, k=1,2,…,Q, then the lth snapshot signal received by the array can be expressed as y(l)=A(θ)s(l)+n(l), l=1,2,…,L, where y(l)=[y1(l),y2(l),…,y Q (l)] T , A(θ)=[a(θ1),a(θ2),…,a(θ N )] QXN is the steering matrix, where the i-th steering vector is θ=[θ1,θ2,…,θ N] is the incoming wave direction vector, s(l)=[s1(l),s2(l),…,s N (l)] T is the lth snapshot signal vector, n(l)=[n1(l),n2(l),…,n Q (l)] T is the l-th snapshot array noise vector, and T represents transpose.

[0007] Step 2: Use the snapshot data received by the array to construct the infinite norm median covariance matrix based on the Sigmoid neural network kernel, and then use the steering matrix of the uniform linear array to construct the orthogonal projection matrix to obtain the infinite norm small snapshot maximum likelihood direction finding equation based on the Sigmoid neural network kernel: directly use the received snapshot data to construct the following matrix in Take the median operation of the L snapshot data received by the k-th array element, that is, where y k =[y k (1),y k (2),…y k (L)], k = 1, 2, ..., Q, med{·} is the median operation, and the infinite norm low-order moment covariance matrix based on the Sigmoid neural network kernel can be expressed as The elements can be specifically expressed as Where R y (:,k) represents R y All elements in the kth column of ; tanh(·) is the activation function of the neural network, σ represents the kernel length of the kernel function; 1≤q≤Q; 1≤k≤Q; is the matrix R y The The element in the row and column k; R y (q,k) is the matrix R y The qth row and kth column element in ; (·) * Indicates conjugate; the orthogonal projection matrix is ​​P A(θ) =A(θ)(A H (θ)A(θ)) -1 A H (θ), the angle estimate of the infinite norm small snapshot maximum likelihood direction finding equation based on the Sigmoid neural network kernel is in,(·) H stands for conjugate transpose; tr(·) is the matrix trace function.

[0008] Step 3: Initialize the quantum cloud quantum position and set parameters:

[0009] First, the following parameters are set: the number of quantum clouds is CP , the number of quantum water droplets in each quantum cloud is W P , the radius of the quantum cloud is U = ρ, where ρ∈(0,1) is the radius factor; the rainfall rate of the quantum cloud is r a ; The rainfall drift algebra is r t ; Contraction and expansion algebra is r s , the contraction coefficient is ε; the maximum number of iterations is G. The position of the quantum water droplet is a potential solution to the optimization problem. The quantum water droplet is a component of the quantum cloud. The first quantum cloud The quantum position of a quantum water droplet in the M-dimensional search space is in The quantum water droplet at the center of the quantum cloud is the central quantum position of the quantum cloud. If the quantum water droplet numbered 1 in each quantum cloud represents the central quantum water droplet of the quantum cloud, then the g-th generation The quantum position of the central quantum droplet of a quantum cloud is recorded as The fitness value of the quantum water droplet is the function value corresponding to the quantum water droplet in the maximum optimization problem, then the g-th generation The first quantum cloud The quantum position of a quantum water droplet The fitness value is recorded as The average fitness value of the quantum cloud is the average fitness value of all quantum water droplets in the quantum cloud, so the g-th generation The average fitness value of a quantum cloud is recorded as The optimal quantum water droplet in the quantum cloud is the quantum water droplet with the largest fitness value in the quantum cloud, then the g-th generation The quantum position of the optimal quantum water droplet in a quantum cloud is recorded as The global optimal quantum droplet is the one with the largest fitness among all quantum droplets in all quantum clouds. The quantum position of the g-th generation global optimal quantum droplet is recorded as The optimal quantum water droplet cloud is the quantum cloud where the global optimal quantum water droplet is located. Then the optimal quantum water droplet cloud of the g generation is The quantum position of a quantum water droplet is recorded as The pressure value of the quantum cloud is set to the opposite of the average fitness value of each quantum cloud; the temperature value of the quantum cloud is set to the average fitness value of each quantum cloud; the optimal quantum cloud is the quantum cloud with the smallest pressure value, then the optimal quantum cloud of the gth generation is The quantum position of a quantum water droplet is recorded as

[0010] Initialize the quantum position of the quantum cloud: randomly generate C in the [0,1] space p points, as C pThe quantum position of the central quantum water droplet of a quantum cloud, where the radius of each quantum cloud is U, and the radius factor ρ is selected according to different parameters of the optimization problem to be solved.

[0011] Step 4: In the quantum cloud The quantum rotation angle parameters randomly generated by a quantum droplet and etc. are used to generate other W except the central quantum water droplet p -1 quantum water droplet, is a random number between [0, U], and the first generation is generated by simplifying the simulation of quantum rotation gate. In the quantum cloud The quantum position of a quantum water droplet is

[0012]

[0013] Among them Quantum cloud cluster The quantum rotation angles of each dimension of a quantum water droplet can be expressed as

[0014]

[0015] Step 5: Map the quantum water droplets in the quantum cloud to the solution space and calculate the fitness value:

[0016] The gth generation In the quantum cloud The position of the solution space mapped by the quantum position of a quantum water droplet is defined as Indicates the gth generation Quantum cloud cluster The mapping state position of a quantum water droplet, its mapping equation is in, represents the lower limit of the m-th dimension, Indicates the upper limit of the mth dimension. According to the above mapping rule, the quantum water droplets in the quantum cloud are mapped to the solution space, and the position of the mapped state is brought into the fitness expression. Then, the gth generation of the mth dimension is In the quantum cloud The mapping state fitness value expression of a quantum water droplet is For the maximum optimization problem, compare the fitness values ​​and find all C p The optimal quantum water droplet in a quantum cloud Globally optimal quantum water droplet Optimal quantum water droplet cloud Optimal quantum cloud

[0017] Step 6: The quantum cloud floats: First, the quantum positions of the non-optimal quantum water droplet cloud and the non-optimal quantum cloud are updated by simulating the quantum rotating door. Then the g+1 generation Quantum cloud cluster The update equation for a quantum water droplet is

[0018] Among them, the g+1th generation In the quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is The elements in a=[a(1),a(2),…,a(G)] are random numbers in the interval [0,1], a(g) is the random number of the gth generation, b1, b2 and b3 are the fluctuation factors, is the drift factor generated by the three pressure differences of the g-th generation, and For the gth generation The drift of a quantum cloud is affected by three factors: Indicates the gth generation The factor by which each quantum cloud is affected by the optimal quantum cloud; Indicates the gth generation The factor by which a quantum cloud is affected by the global optimal quantum water droplet; Indicates the gth generation The quantum cloud is affected by The influence factor of the optimal quantum water droplet on the quantum cloud. The following definitions are given: Where ||·|| is the Euclidean distance.

[0019] By simulating the quantum rotating door, the position of the quantum water droplet in the optimal quantum cloud is updated. The update equation for the m-th dimension quantum position of a quantum water droplet is: Among them, the g+1th generation optimal quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is Determination and similar,

[0020] Finally, the quantum cloud where the global optimal quantum water droplet is located is updated. The update equation for the m-th dimension quantum position of a quantum water droplet is: The g+1th generation of the global optimal quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is

[0021] Step 7: Calculate the fitness value of all quantum water droplets inside the quantum cloud and the temperature value of the quantum cloud, and sort the quantum clouds from high to low according to the temperature value, and find the one with the lowest temperature. a quantum cloud.

[0022] Step 8: The quantum cloud clusters meet certain conditions for rainfall: In step 7, the quantum cloud clusters are arranged in descending order of temperature, and the last r a And the drift algebra of the quantum cloud is greater than or equal to r t disappears instantly, and a new quantum cloud is generated according to steps three and four.

[0023] Step 9: The contraction and expansion process of the quantum cloud: The contraction and expansion of the quantum cloud requires the quantum cloud to drift for a certain number of generations. When the quantum water droplets in the quantum cloud are stably gathered and the quantum cloud drifts to r s The contraction and expansion will only occur after the g+1 generation. The contraction process can be simplified as the process of all quantum water droplets in the quantum cloud gathering towards the central quantum water droplet. In the quantum cloud The quantum position of a quantum water droplet and the quantum position of the central quantum water droplet of the quantum cloud When the distance between them is greater than ε, the quantum cloud will shrink. The first quantum cloud The contraction update formula of the m-th dimension quantum position of a quantum water droplet is: The g+1th generation contraction process The first quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is When the distance between the quantum water droplet and the central quantum water droplet is less than ε, the central quantum water droplet will expand along the coordinate axis to produce a new quantum water droplet. The first quantum cloud The formula for updating the m-th dimension quantum position of a quantum water droplet is: The g+1th generation expansion process The first quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is r b =[r b (1),r b (2),…,r b (G)] is a random number in the interval [0,ρ], r b (g) is the random number of the gth generation, It takes turns to be one of [1,0,…,0],[0,1,…,0],…,[0,0,…,1],[-1,0,…,0],[0,-1,…,0],…,[0,0,…,-1].

[0024] Step 10: Determine whether the maximum number of iterations G has been reached. If not, set g = g + 1 and return to step 5. If reached, terminate the iteration and map the quantum position of the global optimal quantum droplet in the last generation to the solution space position as the output of the direction of arrival estimation result.

[0025] Compared with the existing technology, the present invention has the following advantages: in response to the existing small-snapshot direction-of-arrival estimation methods, which suffer from excessively large sampled snapshot data, high computational complexity, and low real-time performance in low signal-to-noise ratio and strong impulse noise environments, and the fact that most existing single-snapshot direction-finding methods are set to DOA estimation under high signal-to-noise ratio conditions and known Gaussian white noise distribution, and are unable to adapt to the characteristics of actual complex electromagnetic environments, the present invention designs a maximum likelihood direction-of-arrival estimation method based on the infinite-norm low-order moment median covariance matrix of the Sigmoid neural network kernel in the study of DOA estimation under ultra-small snapshot conditions under impulse noise. This method can effectively estimate the direction of arrival of coherent source signals in extremely low signal-to-noise ratio and strong impulse noise environments. The designed quantum cloud search mechanism solves the infinite-norm maximum likelihood equation of the Sigmoid neural network kernel, which can improve the accuracy and stability of the solution while reducing the computational complexity, making the direction-of-arrival estimation result more robust. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 : Schematic diagram of the maximum likelihood direction finding method based on the infinite norm low-order moment median covariance matrix of the Sigmoid neural network kernel designed by the present invention based on the quantum cloud search mechanism.

[0027] Figure 2 : Rendering of DOA estimation effect of coherent source in strong impulse noise and low signal-to-noise ratio environment.

[0028] Figure 3 : Rendering of DOA estimation effect of coherent source in weak impulse noise and high signal-to-noise ratio environment.

[0029] Figure 4 : Graph of independent source DOA estimation effect in strong impulse noise and low signal-to-noise ratio environment.

[0030] Figure 5 :DOA estimation effect diagram of independent source in weak impulse noise and high signal-to-noise ratio environment. DETAILED DESCRIPTION

[0031] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0032] The present invention relates to a small-snapshot Direction of Arrival (DOA) estimation method in an impulsive noise environment. The method includes establishing a uniform linear array small-snapshot sampling signal model, constructing an infinite-norm median covariance matrix based on a Sigmoid neural network kernel, and obtaining an infinite-norm small-snapshot maximum likelihood equation based on the Sigmoid neural network kernel. In an α-stable distributed noise environment, especially when the characteristic exponent is small, there is a high probability of very large singular values. Traditional mean estimation methods, however, suffer from significant deviations. Using the median, however, is unaffected by excessively large or small data, resulting in good DOA estimation results in impulsive noise environments. Furthermore, the kernel function can effectively transform a nonlinear problem in the original image space into a linear problem in the reproducing kernel Hilbert space through a nonlinear transformation and rapidly calculate the inner product mapped to a high-dimensional feature space using simple mathematical expressions. The kernel length setting is closely related to its application domain. The present invention selects the optimal kernel length through performance simulation and designs a continuous quantum cloud search mechanism to efficiently solve the maximum likelihood direction-finding equation based on the infinite-norm of the Sigmoid neural network kernel. The invented small snapshot DOA estimation method can perform effective DOA estimation for both independent sources and coherent sources under impulse noise.

[0033] With reference to the accompanying drawings, the steps of the present invention are as follows:

[0034] Step 1: Establish a small snapshot sampling signal model in an impact noise environment:

[0035] Assume an equidistant uniform linear array with Q elements and an element spacing of d. The i-th far-field narrowband signal is transmitted from θ i The incident signal is incident on the array in the direction with a wavelength of λ and a snapshot number of L (L<Q). The incident signal and the noise signal are independent of each other, i=1,2,…,N, and the first array element is selected as the reference array element. The signal received by the kth array element at time is in, for The incident signal of the i-th source at time t, for The noise signal of the kth array element at time, represents the impulse noise satisfying the SαS stable distribution on the kth array element, k=1,2,…,Q, then the lth snapshot signal received by the array can be expressed as y(l)=A(θ)s(l)+n(l), l=1,2,…,L, where y(l)=[y1(l),y2(l),…,y Q (l)] T , A(θ)=[a(θ1),a(θ2),…,a(θ N )] QXN is the steering matrix, where the i-th steering vector is θ=[θ1,θ2,…,θ N ] is the incoming wave direction vector, s(l)=[s1(l),s2(l),…,s N (l)] T is the lth snapshot signal vector, n(l)=[n1(l),n2(l),…,n Q (l)] T is the l-th snapshot array noise vector, and T represents transpose.

[0036] Step 2: Use the snapshot data received by the array to construct the infinite norm median covariance matrix based on the Sigmoid neural network kernel, and then use the steering matrix of the uniform linear array to construct the orthogonal projection matrix to obtain the infinite norm small snapshot maximum likelihood direction finding equation based on the Sigmoid neural network kernel: directly use the received snapshot data to construct the following matrix in Take the median operation of the L snapshot data received by the k-th array element, that is, where y k =[y k (1),y k (2),…y k (L)], k = 1, 2, ..., Q, med{·} is the median operation, and the infinite norm low-order moment covariance matrix based on the Sigmoid neural network kernel can be expressed as The elements can be specifically expressed as Where R y (:,k) represents R y All elements in the kth column of ; tanh(·) is the activation function of the neural network, σ represents the kernel length of the kernel function; 1≤q≤Q; 1≤k≤Q; is the matrix R y The The element in the row and column k; R y (q,k) is the matrix R y The qth row and kth column element in ; (·) * Indicates conjugate; the orthogonal projection matrix is ​​P A(θ) =A(θ)(A H (θ)A(θ)) -1 A H (θ), the angle estimate of the infinite norm small snapshot maximum likelihood direction finding equation based on the Sigmoid neural network kernel is in,(·) H stands for conjugate transpose; tr(·) is the matrix trace function.

[0037] Step 3: Initialize the quantum cloud quantum position and set parameters:

[0038] First, the following parameters are set: the number of quantum clouds is C P , the number of quantum water droplets in each quantum cloud is W P , the radius of the quantum cloud is U = ρ, where ρ∈(0,1) is the radius factor; the rainfall rate of the quantum cloud is r a ; The rainfall drift algebra is r t ; Contraction and expansion algebra is r s , the contraction coefficient is ε; the maximum number of iterations is G. The position of the quantum water droplet is a potential solution to the optimization problem. The quantum water droplet is a component of the quantum cloud. The first quantum cloud The quantum position of a quantum water droplet in the M-dimensional search space is in The quantum water droplet at the center of the quantum cloud is the central quantum position of the quantum cloud. If the quantum water droplet numbered 1 in each quantum cloud represents the central quantum water droplet of the quantum cloud, then the g-th generation The quantum position of the central quantum droplet of a quantum cloud is recorded as The fitness value of the quantum water droplet is the function value corresponding to the quantum water droplet in the maximum optimization problem, then the g-th generation The first quantum cloud The quantum position of a quantum water droplet The fitness value is recorded as The average fitness value of the quantum cloud is the average fitness value of all quantum water droplets in the quantum cloud, so the g-th generation The average fitness value of a quantum cloud is recorded as The optimal quantum water droplet in the quantum cloud is the quantum water droplet with the largest fitness value in the quantum cloud, then the g-th generation The quantum position of the optimal quantum water droplet in a quantum cloud is recorded as The global optimal quantum droplet is the one with the largest fitness among all quantum droplets in all quantum clouds. The quantum position of the g-th generation global optimal quantum droplet is recorded as The optimal quantum water droplet cloud is the quantum cloud where the global optimal quantum water droplet is located. Then the optimal quantum water droplet cloud of the g generation is The quantum position of a quantum water droplet is recorded as The pressure value of the quantum cloud is set to the opposite of the average fitness value of each quantum cloud; the temperature value of the quantum cloud is set to the average fitness value of each quantum cloud; the optimal quantum cloud is the quantum cloud with the smallest pressure value, then the optimal quantum cloud of the gth generation is The quantum position of a quantum water droplet is recorded as

[0039] Initialize the quantum position of the quantum cloud: randomly generate C in the [0,1] space p points, as C p The quantum position of the central quantum water droplet of a quantum cloud, where the radius of each quantum cloud is U, and the radius factor ρ is selected according to different parameters of the optimization problem to be solved.

[0040] Step 4: In the quantum cloud The quantum rotation angle parameters randomly generated by a quantum droplet and etc. are used to generate other W except the central quantum water droplet p -1 quantum water droplet, is a random number between [0, U], and the first generation is generated by simplifying the simulation of quantum rotation gate. In the quantum cloud The quantum position of a quantum water droplet is

[0041]

[0042] Among them Quantum cloud cluster The quantum rotation angles of each dimension of a quantum water droplet can be expressed as

[0043]

[0044] Step 5: Map the quantum water droplets in the quantum cloud to the solution space and calculate the fitness value:

[0045] The gth generation In the quantum cloud The position of the solution space mapped by the quantum position of a quantum water droplet is defined as Indicates the gth generation Quantum cloud cluster The mapping state position of a quantum water droplet, its mapping equation is in, represents the lower limit of the m-th dimension, Indicates the upper limit of the mth dimension. According to the above mapping rule, the quantum water droplets in the quantum cloud are mapped to the solution space, and the position of the mapped state is brought into the fitness expression. Then, the gth generation of the mth dimension is In the quantum cloud The mapping state fitness value expression of a quantum water droplet is For the maximum optimization problem, compare the fitness values ​​and find all C p The optimal quantum water droplet in a quantum cloud Globally optimal quantum water droplet Optimal quantum water droplet cloud Optimal quantum cloud

[0046] Step 6: The quantum cloud floats: First, the quantum positions of the non-optimal quantum water droplet cloud and the non-optimal quantum cloud are updated by simulating the quantum rotating door. Then the g+1 generation Quantum cloud cluster The update equation for a quantum water droplet is

[0047] Among them, the g+1th generation In the quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is The elements in a=[a(1),a(2),…,a(G)] are random numbers in the interval [0,1], a(g) is the random number of the gth generation, b1, b2 and b3 are the fluctuation factors, is the drift factor generated by the three pressure differences of the g-th generation, and For the gth generation The drift of a quantum cloud is affected by three factors: Indicates the gth generation The factor by which each quantum cloud is affected by the optimal quantum cloud; represents the factor by which the i-th quantum cloud of the g-th generation is affected by the global optimal quantum water droplet; Indicates the gth generation The quantum cloud is affected by The influence factor of the optimal quantum water droplet on the quantum cloud. The following definitions are given: Where ||·|| is the Euclidean distance.

[0048] By simulating the quantum rotating gate to update the position of the quantum water droplet of the optimal quantum cloud, the position of the quantum water droplet in the g+1 generation optimal quantum cloud is updated. The update equation for the m-th dimension quantum position of a quantum water droplet is: Among them, the g+1th generation optimal quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is Determination and similar,

[0049] Finally, the quantum cloud where the global optimal quantum water droplet is located is updated. The update equation for the m-th dimension quantum position of a quantum water droplet is: The g+1th generation of the global optimal quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is

[0050] Step 7: Calculate the fitness value of all quantum water droplets inside the quantum cloud and the temperature value of the quantum cloud, and sort the quantum clouds from high to low according to the temperature value, and find the one with the lowest temperature. a quantum cloud.

[0051] Step 8: The quantum cloud clusters meet certain conditions for rainfall: In step 7, the quantum cloud clusters are arranged in descending order of temperature, and the last r a And the drift algebra of the quantum cloud is greater than or equal to r t disappears instantly, and a new quantum cloud is generated according to steps three and four.

[0052] Step 9: The contraction and expansion process of the quantum cloud: The contraction and expansion of the quantum cloud requires the quantum cloud to drift for a certain number of generations. When the quantum water droplets in the quantum cloud are stably gathered and the quantum cloud drifts to r s The contraction and expansion will only occur after the g+1 generation. The contraction process can be simplified as the process of all quantum water droplets in the quantum cloud gathering towards the central quantum water droplet. In the quantum cloud The quantum position of a quantum water droplet and the quantum position of the central quantum water droplet of the quantum cloud When the distance between them is greater than ε, the quantum cloud will shrink. The first quantum cloud The contraction update formula of the m-th dimension quantum position of a quantum water droplet is: The g+1th generation contraction process The first quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is When the distance between the quantum water droplet and the central quantum water droplet is less than ε, the central quantum water droplet will expand along the coordinate axis to produce a new quantum water droplet. The first quantum cloud The formula for updating the m-th dimension quantum position of a quantum water droplet is: The g+1th generation expansion process The first quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is r b =[r b (1),r b (2),…,r b (G)] is a random number in the interval [0,ρ], r b (g) is the random number of the gth generation, It takes turns to be one of [1,0,…,0],[0,1,…,0],…,[0,0,…,1],[-1,0,…,0],[0,-1,…,0],…,[0,0,…,-1].

[0053] Step 10: Determine whether the maximum number of iterations G has been reached. If not, set g = g + 1 and return to step 5. If reached, terminate the iteration and map the quantum position of the global optimal quantum droplet in the last generation to the solution space position as the output of the direction of arrival estimation result.

[0054] The maximum likelihood direction finding method based on the infinite norm low-order moment median covariance matrix of the Sigmoid neural network kernel designed in the present invention is abbreviated as "QCSO-MSINF-ML"; the direction finding method based on the fractional low-order moment multiple signal classification algorithm is abbreviated as "FLOM-MUSIC"; and the direction finding method based on the fractional low-order moment covariance matrix multiple signal classification algorithm is abbreviated as "FLOC-MUSIC".

[0055] In the simulation experiment, three signals are incident on a uniform linear array with a spacing of d = λ / 2 (λ is the carrier wavelength) from three directions of {60.25°, 20.75°, -10.78°}. The simulation experiment parameters are designed as follows: the number of antenna array elements M = 64, the number of signal sources is 3, the core length of the Sigmoid neural network is set to σ = 5, the number of runs for each experiment is 30, the maximum number of iterations G = 200, and the number of quantum clouds C n =20, number of quantum water droplets W n =20, quantum cloud radius factor ρ = 0.06, then U = 0.06, the lower limit of the mapping space Upper limit The drift factor b1=0.2, b2=0.3, b3=0.2, and the rainfall rate r a =5%, drift algebra r t =10; contraction and expansion algebra is r s =50, the contraction coefficient is ε=10 -7 .

[0056] Figure 2 In the simulation, three coherent signal sources are incident from the directions of {60.25°, 20.75°, -10.78°}, the impulse noise characteristic index is 0.95, the generalized signal-to-noise ratio is 1 dB, the fractional low-order moment covariance characteristic index p1 = 0.6, the number of snapshots is 5, and the number of Monte Carlo experiments is 30. Figure 2It can be seen that most of the simulated estimated values ​​of the QCSO-MSINF-ML method are close to the true values, with a few having large deviations. In contrast, about half of the estimated values ​​of the FLOC-MUSIC algorithm have large deviations. Therefore, the designed maximum likelihood direction finding method based on the infinite norm low-order moment median covariance matrix of the Sigmoid neural network kernel can accurately estimate the direction of the coherent source in harsh environments, namely, strong impulse noise, low signal-to-noise ratio and small snapshot data.

[0057] Figure 3 In the simulation, three coherent signal sources are incident from the directions of {60.25°, 20.75°, -10.78°}, the impulse noise characteristic index is 1.2, the generalized signal-to-noise ratio is 10 dB, the fractional low-order moment characteristic index p2 = 1.1, the number of snapshots is 5, and the number of Monte Carlo experiments is 30. Figure 3 As can be seen from the figure, all the estimated values ​​simulated by the QCSO-MSINF-ML method are close to the true values, with almost no deviation. However, some of the simulated estimates by the FLOM-MUSIC algorithm have large deviations, with only a few successfully estimating the source direction. Therefore, the designed maximum likelihood direction finding method based on the infinite norm low-order moment median covariance matrix of the Sigmoid neural network kernel can still accurately estimate the direction of the coherent source in a weak impact environment.

[0058] Figure 4 In the simulation, three independent signal sources are incident from the directions of {60.25°, 20.75°, -10.78°}, the impulse noise characteristic index is 0.95, the generalized signal-to-noise ratio is 0 dB, the fractional low-order moment covariance characteristic index p1 = 0.6, the number of snapshots is 5, and the number of Monte Carlo experiments is 30. Figure 4 As can be seen from the results, the QCSO-MSINF-ML method produces nearly identical estimates and true values ​​for almost all simulations, with virtually no deviation. While the FLOC-MUSIC algorithm produces accurate estimates for most simulations, several estimates exhibit significant deviations from the true values. Therefore, the proposed maximum likelihood direction finding method, based on the infinite-norm low-order moment median covariance matrix of a Sigmoid neural network kernel, can still accurately estimate the direction of independent sources in environments with strong impulsive noise and extremely low signal-to-noise ratios.

[0059] Figure 5 In the simulation, three independent signal sources are incident from the directions of {60.25°, 20.75°, -10.78°}, the impulse noise characteristic index is 1.4, the generalized signal-to-noise ratio is 10dB, the fractional low-order moment characteristic index p2=1.1, the number of snapshots is 5, and the number of Monte Carlo experiments is 30. Figure 5It can be seen that the estimated values ​​of all simulations of the QCSO-MSINF-ML method are consistent with the true values ​​without deviation, while the FLOM-MUSIC algorithm is Figure 2 Although there has been a significant improvement, there are still many estimation errors. Therefore, the maximum likelihood direction finding method designed based on the infinite norm low-order moment median covariance matrix of the Sigmoid neural network kernel can accurately estimate the direction of independent sources in weak impact environments.

Claims

1. A method for estimating the direction of arrival of a small snapshot coherent source in an impulsive noise environment, characterized by: Here are the steps: Step 1: Establish a small snapshot sampling signal model in an impulsive noise environment. Given an equidistant uniform linear array with Q elements and an element spacing of d, the i-th far-field narrowband signal is transmitted from θ i The direction of the incident signal is incident on the array, the wavelength is λ, the number of snapshots is L, and the incident signal and the noise signal are independent of each other, i = 1, 2, ..., N, and the first array element is selected as the reference array element. Then the signal received by the kth array element at time t is: in, for The incident signal of the i-th source at time t, for The noise signal of the kth array element at time, represents the impulse noise satisfying the SαS stable distribution on the kth array element, k = 1, 2, …, Q, then the lth snapshot signal received by the array is: y(l)=A(θ)s(l)+n(l),l=1,2,…,L In the formula: y(l)=[y1(l),y2(l),…,y Q (l)] T , A(θ)=[a(θ1),a(θ2),…,a(θ N )] QXN is the steering matrix, and the i-th steering vector is θ=[θ1,θ2,…,θ N ] is the incoming wave direction vector, s(l)=[s1(l),s2(l),…,s N (l)] T is the lth snapshot signal vector, n(l)=[n1(l),n2(l),…,n Q (l)] T is the l-th snapshot array noise vector, T represents transpose; Step 2: Use the snapshot data received by the array to construct an infinite-norm median covariance matrix based on the Sigmoid neural network kernel, and then use the steering matrix of the uniform linear array to construct an orthogonal projection matrix to obtain the infinite-norm small snapshot maximum likelihood direction finding equation based on the Sigmoid neural network kernel; Step 3: Initialize the quantum cloud quantum position and set parameters: Set the number of quantum clouds to C P , the number of quantum water droplets in each quantum cloud is W P , the radius of the quantum cloud is U = ρ, where ρ∈(0,1) is the radius factor; the rainfall rate of the quantum cloud is r a ; The rainfall drift algebra is r t ; Contraction and expansion algebra is r s , the shrinkage coefficient is ε; the maximum number of iterations is G; The position of the quantum water droplet is a potential solution to the optimization problem. The quantum water droplet is a component of the quantum cloud. The first quantum cloud The quantum position of a quantum water droplet in the M-dimensional search space is in The quantum water droplet at the center of the quantum cloud is the central quantum position of the quantum cloud. If the quantum water droplet numbered 1 in each quantum cloud represents the central quantum water droplet of the quantum cloud, then the g-th generation The quantum position of the central quantum droplet of a quantum cloud is recorded as The fitness value of the quantum water droplet is the function value corresponding to the quantum water droplet in the maximum optimization problem, then the g-th generation The first quantum cloud The quantum position of a quantum water droplet The fitness value is recorded as The average fitness value of the quantum cloud is the average fitness value of all quantum water droplets in the quantum cloud, so the g-th generation The average fitness value of a quantum cloud is recorded as The optimal quantum water droplet in the quantum cloud is the quantum water droplet with the largest fitness value in the quantum cloud, then the g-th generation The quantum position of the optimal quantum water droplet in a quantum cloud is recorded as The global optimal quantum droplet is the one with the largest fitness among all quantum droplets in all quantum clouds. The quantum position of the g-th generation global optimal quantum droplet is recorded as The optimal quantum water droplet cloud is the quantum cloud where the global optimal quantum water droplet is located. Then the optimal quantum water droplet cloud of the g generation is The quantum position of a quantum water droplet is recorded as The air pressure value of the quantum cloud is set to the opposite of the average fitness value of each quantum cloud; The temperature value of the quantum cloud is set as the average fitness value of each quantum cloud; The optimal quantum cloud is the one with the smallest pressure value, so the optimal quantum cloud of the g-th generation is The quantum position of a quantum water droplet is recorded as Initialize the quantum position of the quantum cloud: randomly generate C in the [0,1] space p points, as C p The quantum position of the central quantum water droplet of a quantum cloud, where the radius of each quantum cloud is U, and the radius factor ρ is selected according to the optimization problem; Step 4: In the quantum cloud The quantum rotation angle parameters randomly generated by a quantum droplet and etc. are used to generate other W except the central quantum water droplet p -1 quantum water droplet, is a random number between [0, U], and the first generation is generated by simplifying the simulation of quantum rotation gate. In the quantum cloud The quantum position of a quantum water droplet is: Among them Quantum cloud cluster The quantum rotation angles of each dimension of a quantum water droplet are expressed as: Step 5: Map the quantum water droplets in the quantum cloud to the solution space and calculate the fitness value: The gth generation In the quantum cloud The position in the solution space mapped by the quantum position of a quantum water droplet is defined as: in, Indicates the gth generation Quantum cloud cluster The mapping state position of a quantum water droplet, its mapping equation is represents the lower limit of the m-th dimension, represents the upper limit of the mth dimension; The gth generation In the quantum cloud The mapping state fitness value expression of a quantum water droplet is: For the maximum optimization problem, compare the fitness values ​​and find all C p The optimal quantum water droplet in a quantum cloud Globally optimal quantum water droplet Optimal quantum water droplet cloud Optimal quantum cloud Step 6: The quantum cloud floats; Step 6.1: Update the quantum positions of the non-optimal quantum water droplet cloud and the non-optimal quantum cloud by simulating the quantum rotating gate. Quantum cloud cluster The update equation for a quantum water droplet is: The g+1th generation In the quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is: Among them, the elements in a=[a(1),a(2),…,a(G)] are random numbers in the interval [0,1], a(g) is the random number of the gth generation, b1, b2 and b3 are the fluctuation factors, is the drift factor generated by the three pressure differences in the gth generation; Indicates the gth generation The factor by which each quantum cloud is affected by the optimal quantum cloud; Indicates the gth generation The factor by which a quantum cloud is affected by the global optimal quantum water droplet; Indicates the gth generation The quantum cloud is affected by The influence factor of the optimal quantum water droplet of a quantum cloud on the quantum cloud; ||·|| is to find the Euclidean distance; Step 6.2: Update the position of the quantum water droplet in the optimal quantum cloud by simulating the quantum rotating gate. The update equation for the m-th dimensional quantum position of a quantum water droplet is: The g+1th generation optimal quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is: Step 6.3: Update the quantum cloud where the global optimal quantum water droplet is located, the g+1th generation The update equation for the m-th dimensional quantum position of a quantum water droplet is: The g+1th generation of the global optimal quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is: Step 7: Calculate the fitness value of all quantum water droplets inside the quantum cloud and the temperature value of the quantum cloud, and sort the quantum clouds from high to low according to the temperature value, and find the one with the lowest temperature. a Quantum clouds; Step 8: The quantum cloud clusters meet certain conditions for rainfall: In step 7, the quantum cloud clusters are arranged in descending order of temperature, and the last r a And the drift algebra of the quantum cloud is greater than or equal to r t disappears instantly, and a new quantum cloud is generated according to steps three and four; Step 9: The contraction and expansion process of the quantum cloud: When the g+1th In the quantum cloud The quantum position of a quantum water droplet and the quantum position of the central quantum water droplet of the quantum cloud When the distance is greater than ε, the quantum cloud shrinks; The g+1th generation The first quantum cloud The contraction update formula of the m-th dimension quantum position of a quantum water droplet is: The g+1th generation contraction process The first quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is: When the distance between the quantum water droplet and the central quantum water droplet is less than ε, the central quantum water droplet will expand along the coordinate axis to produce a new quantum water droplet. The first quantum cloud The formula for updating the m-th dimension quantum position of a quantum water droplet is: The g+1th generation expansion process The first quantum cloud The m-th dimension quantum rotation angle of a quantum water droplet is: Among them, r b =[r b (1),r b (2),…,r b (G)] is a random number in the interval [0,ρ]; r b (g) is the random number of the gth generation, Take turns to be one of [1,0,…,0],[0,1,…,0],…,[0,0,…,1],[-1,0,…,0],[0,-1,…,0],…,[0,0,…,-1]; Step 10: Determine whether the maximum number of iterations G has been reached. If not, set g = g + 1 and return to step 5. If reached, terminate the iteration and map the quantum position of the global optimal quantum droplet in the last generation to the solution space position as the output of the direction of arrival estimation result.

2. The method for estimating the direction of arrival of a small snapshot coherent source in an impulsive noise environment according to claim 1, wherein: Step 2 specifically includes: constructing the following matrix using the received snapshot data in Take the median operation of the L snapshot data received by the k-th array element, that is, y k =[y k (1),y k (2),…y k (L)], k = 1, 2, ..., Q, med{·} is the median operation, and the infinite norm low-order moment covariance matrix based on the Sigmoid neural network kernel can be expressed as The elements are represented as Where R y (:,k) represents R y All elements in the kth column of ; tanh(·) is the activation function of the neural network, σ represents the kernel length of the kernel function; 1≤q≤Q; 1≤k≤Q; is the matrix R y The The element in the row and column k; R y (q,k) is the matrix R y The qth row and kth column element in ; (·) * Indicates conjugate; the orthogonal projection matrix is ​​P A(θ) =A(θ)(A H (θ)A(θ)) -1 A H (θ), the angle estimate of the infinite norm small snapshot maximum likelihood direction finding equation based on the Sigmoid neural network kernel is in,(·) H stands for conjugate transpose; tr(·) is the matrix trace function.

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