A Direction of Arrival Estimation Method Based on Optimal Correlation Entropy in Impulsive Noise

Abstract

This invention proposes a method for estimating direction of arrival (DOA) based on optimal correlation entropy under impulsive noise. The method includes establishing a maximum likelihood broadband signal direction-finding model based on median deviation correlation entropy under impulsive noise; initializing parameters of a continuous quantum chimpanzee search mechanism; calculating the fitness values ​​of all chimpanzee positions and initializing the quantum positions of attackers, blockers, pursuers, and expellees; updating the quantum positions of other chimpanzees in the population based on the quantum positions of the attackers, blockers, pursuers, and expellees; calculating the fitness values ​​of all chimpanzee positions and updating the positions of attackers, blockers, pursuers, and expellees in the entire chimpanzee population; determining whether the maximum number of attempts has been reached; and mapping the attacker's quantum position in the chimpanzee population to the global optimal position according to a mapping rule to obtain the signal's arrival angle. This method can effectively find direction in an impulsive noise environment with high accuracy and excellent decorrelation capability.

Description

Technical Field

[0001] The present invention belongs to the field of array signal processing, and in particular relates to a direction of arrival estimation method based on optimal correlation entropy under impulse noise. Background Art

[0002] Array signal processing has a wide range of applications in communications, radar, and sonar systems, and Direction of Arrival (DOA) estimation is a fundamental problem and a research hotspot in array signal processing. Traditional multiple signal classification (MUSIC) and the rotationally invariant subspace technique for signal parameter estimation (ESPRIT) have achieved high estimation performance. However, these algorithms are based on eigenvalue decomposition and often require tens of thousands of snapshots to achieve good estimation performance, resulting in low real-time performance and high computational complexity. Furthermore, the DOA estimation environment is becoming increasingly complex. Therefore, it is imperative to design DOA estimation methods that are highly accurate and applicable to complex impulsive noise environments.

[0003] According to existing literature, Dai Jiangan et al. published a paper titled "DOA Estimation Method Based on Median Deviation Correlation Entropy under Impulse Noise" in Signal Processing (2021, Vol. 37, No. 10, pp: 1914-1922). This paper estimates the direction of arrival by constructing a MUSIC algorithm based on median deviation correlation entropy. However, this method is based on a large number of snapshots, which is not conducive to real-time processing and cannot estimate the direction of arrival of coherent sources. Zhang Heyong et al. published a paper titled "Single-Snapshot DOA Estimation Method Based on Spatial Smoothing" in Firepower and Command and Control (2021, Vol. 46, No. 6, pp: 105-109+114). This paper combines spatial smoothing technology with the properties of the Toeplitz matrix and proposes a single-snapshot DOA estimation algorithm based on spatial smoothing. However, this method cannot effectively find the direction under impulse noise. Therefore, the present invention designs a quantum chimpanzee search mechanism, designs a low-order moment of optimal correlation entropy based on the optimal parameters of the exponential kernel, and then designs a direction of arrival estimation and method based on the optimal correlation entropy. Summary of the Invention

[0004] The object of the present invention is to provide a direction of arrival estimation method based on optimal correlation entropy under impulse noise.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A method for estimating direction of arrival based on optimal correlation entropy under impulse noise is characterized by the following specific steps:

[0007] Step 1: Establish a maximum likelihood direction of arrival estimation model based on correlation entropy under impulse noise;

[0008] Step 2: Initialization of the core length solution population based on the quantum chimpanzee search mechanism; initialization of the continuous quantum chimpanzee search mechanism;

[0009] Step 3: Establish the direction-finding model and design the objective function for solving the optimal kernel length of the kernel function;

[0010] Step 4: Calculate the fitness values ​​of all chimpanzee locations and classify the chimpanzee locations;

[0011] Step 5: The quantum positions of the attacker, blocker, pursuer, and evictor are used to update the quantum positions of other chimpanzees in the population;

[0012] Step 6: Calculate the fitness values ​​of all chimpanzees at their new locations and update the positions of attackers, blockers, pursuers, and evictors in the entire chimpanzee population.

[0013] Step 7: Determine whether the maximum number of iterations has been reached. If not, set t = t + 1 and return to step 5 to continue. If it has been reached, map the quantum position of the attacker in the chimpanzee group to the global optimal position according to the mapping rule, and the optimal parameters of the exponential kernel are obtained as and

[0014] Step 8: Define the received k-th snapshot narrowband signal as z(k) = [z1(k),z2(k),…,z M (k)] T , using the obtained exponential kernel optimal parameters m1, m2, σ and the snapshot data received by the array to construct the correlation entropy matrix in, The orthogonal projection matrix is ​​P A(θ) =A(θ)(A H (θ)A(θ)) -1 A H (θ), the angle estimate of the maximum likelihood equation is Where H represents the conjugate transpose, and tr() is the matrix trace operation;

[0015] Step 9: Initialization of the continuous quantum chimpanzee search mechanism;

[0016] Step 10: Calculate the fitness values ​​of all chimpanzee locations and classify the chimpanzee locations;

[0017] Step 11: The quantum positions of the attacker, blocker, pursuer, and evictor are used to update the quantum positions of other chimpanzees in the population. The specific steps are the same as step 5.

[0018] Step 12: Calculate the fitness values ​​of all chimpanzees at their new locations and update the positions of attackers, blockers, pursuers, and evictors in the entire chimpanzee population. The specific steps are the same as step 6.

[0019] Step 13: Determine whether the maximum number of iterations has been reached. If not, set t = t + 1 and return to step 11 to continue. If it has been reached, map the quantum position of the attacker in the chimpanzee group to the global optimal position according to the mapping rule to obtain the incoming angle of the signal.

[0020] The present invention may also include:

[0021] 1. Step 1 is as follows: In an impact noise environment, there are N far-field narrowband signals with direction angles θ1, θ2, ..., θ N The incident signal is incident on a uniform linear array with M elements in space, with a wavelength of λ, an element spacing of d, an incident signal frequency of f0, a snapshot number of S, and the incident signal and noise are uncorrelated; taking the first element as the reference element, the signal received by the mth element can be expressed as in, Indicates that the incident direction is θ n The narrowband signal represents the impulse noise on the mth array element, then the kth snapshot narrowband signal received by the array is z(k)=A(θ)s(k)+n(k), k=1,2,…,S, where z(k)=[z1(k),z2(k),…,z M (k)] T , A(θ)=[a(θ1),a(θ2),…,a(θ N )] M×N is the steering matrix, where the i-th steering vector is θ=[θ1,θ2,…,θ N ] is the incoming wave direction vector, s(k)=[s1(k),s2(k),…,s N (k)] T is the signal vector, n(k)=[n1(k),n2(k),…,n M (k)[ T is the array noise vector; the snapshot data received by the array is used to construct the correlation entropy low-order matrix matrix in represents the median operation, |·| represents the absolute value operation, (·) * represents the conjugate operation, σ represents the kernel function κ σ (·)=exp(-|·|2σ 2 ), m1 and m2 are numbers between [0,1], i=1,2,…,M, j=1,2,…,M; the orthogonal projection matrix is ​​P A(θ)=A(θ)(A H (θ)A(θ)) -1 A H (θ), the angle estimate of the maximum likelihood equation is Where H stands for conjugate transpose and tr() is the matrix trace operation.

[0022] 2. Step 2 is as follows: The size of the chimpanzee group is The maximum number of iterations is t max , the search space dimension is D, and the quantum position of the i-th chimpanzee at the t-th iteration is The quantum rotation angle of the i-th chimpanzee is in n=1,2,…,D, maps the quantum position of the i-th chimpanzee at the t-th iteration to the position The specific mapping rules are: n=1, 2, ..., D, where and are the lower and upper bounds of the exponential kernel parameters respectively. t is the number of iterations, and t is initially set to 1.

[0023] 3. Step 3 is as follows: when finding the optimal core length, the spatial wave direction is N=1, the search space dimension is D=3; the value of the spatial wave being a cooperative signal is The received k-th snapshot narrowband signal is z(k)=[z1(k),z2(k),…,z M (k)] T , using the snapshot data received by the array to construct the relevant entropy matrix ,in Perform eigenvalue decomposition on the low-order matrix of related entropy, Q = AQ s A H +Q n , where Q s is the signal correlation matrix, Q n The noise correlation matrix is ​​then sorted by eigenvalue size, and the eigenvalues ​​and corresponding eigenvectors equal to the number of signals N are regarded as the signal part space, and the eigenvalues ​​and eigenvectors of the remaining MN are regarded as the noise part space, and the noise matrix is ​​obtained. i=N+1,N+2,…,M,E n =[v N+1 ,v N+2 ,…,v M ], and finally change θ from -90 to 90. The classic MUSIC algorithm is based on the formula To calculate the spectrum function, we can find the peak value to get the estimated value of the direction of arrival. According to the classic MUSIC algorithm, we can get the location of the i-th chimpanzee. The direction of arrival corresponding to the exponential kernel parameter is Then the objective function can be determined as Minimum optimization of .

[0024] 4. Step 4 is as follows: Calculate the location of the i-th chimpanzee at the t-th iteration The fitness value of Determine the global optimal quantum position that the chimpanzee has searched for until the tth iteration as and divide it into the position of the attacker in the chimpanzee; the second best quantum position is and divide it into the position of the blocker in the chimpanzee; the third optimal quantum position is and divide it into the position of the pursuer in the chimpanzee; the fourth optimal quantum position is And divide it into the position of the ouster among the chimpanzees, and the other quantum positions are divided into the positions of other chimpanzees among the chimpanzees, where i = 1, 2, ...,

[0025] 5. Step 5 is as follows: At the t+1 iteration, for the i-th chimpanzee in the population, its quantum position consists of four parts; the first part is updated by the attacker's quantum position, where the n-th dimension quantum rotation angle variable is the convergence factor, is a nonlinear random variable between [0,1]. is the position of the attacker in the chimpanzee group up to generation t The nth dimension of For all chimpanzee populations up to generation t The average of the quantum positions of the chimpanzees The nth dimension, m t is a uniform random number between [0,1], is a uniform random number between [-1,1], sign(·) represents the sign function, and its value is between {-1,0,1}. is a nonlinear random variable between [0,1], then the n-th dimension update method of the first part of the quantum position of the i-th chimpanzee is n=1,2,...,D, abs(·) is the absolute value operation; the second part is updated by the quantum position of the blocker, where the n-th dimension quantum rotation angle is a nonlinear random variable between [0,1]. is the position of the blocker in the chimpanzee group up to generation t The nth dimension of is a uniform random number between [-1,1], is a nonlinear random variable between [0,1], then the n-th dimension update method of the second part of the quantum position of the i-th chimpanzee is n=1,2,...,D; the third part is updated by the pursuer's quantum position, where the n-th dimension quantum rotation angle is a nonlinear random variable between [0,1]. is the position of the pursuer in the chimpanzee group up to generation t The nth dimension of is a uniform random number between [-1,1], is a nonlinear random variable between [0,1], then the n-th dimension update method of the third part of the quantum position of the i-th chimpanzee is n=1,2,...,D; the fourth part is updated by the quantum position of the evictor, where the n-th dimension quantum rotation angle is a nonlinear random variable between [0,1]. is the position of the evictor in the chimpanzee group up to generation t The nth dimension of is a uniform random number between [-1,1], is a nonlinear random variable between [0,1], then the n-th dimension update method of the fourth part of the quantum position of the i-th chimpanzee is n=1,2,...,N; therefore, at iteration t+1, the nth dimension of the quantum position of the i-th chimpanzee is n=1,2,...,N。

[0026] 6. Step 6 is as follows: Map the quantum position of the i-th chimpanzee in the t+1th iteration to the position Calculate the location of the i-th chimpanzee at the t+1th iteration The fitness value of If the i-th chimpanzee has the same quantum position in the t+1th iteration The fitness of is better than the fitness of g1t, then otherwise If the i-th chimpanzee has the same quantum position in the t+1th iteration Fitness is inferior to The fitness is better than The fitness of otherwise If the i-th squirrel has a quantum position at the t+1th iteration Fitness is inferior to The fitness is better than The fitness of otherwise If the i squirrels have quantum positions in the t+1th iteration Fitness is inferior to The fitness is better than The fitness of otherwise

[0027] 7. The method for estimating direction of arrival based on optimal correlation entropy under impulse noise according to claim 1, wherein step nine is specifically as follows: the size of the chimpanzee group is The maximum number of iterations is t max , the dimension of the search space is D = N, and the quantum position of the i-th chimpanzee at the t-th iteration is The quantum rotation angle of the i-th chimpanzee is in n=1,2,…,D, t is the number of iterations, and initially t=1.

[0028] 8. Step 10 is as follows: Map the quantum position of the i-th chimpanzee in the t-th iteration to the position The specific mapping rules are: Among them A n,min and A n,max are the lower and upper bounds of the angle search space respectively; calculate the position of the i-th chimpanzee at the t-th iteration The fitness value of Determine the global optimal quantum position that the chimpanzee has searched for until the tth iteration as and divide it into the position of the attacker in the chimpanzee; the second best quantum position is and divide it into the position of the blocker in the chimpanzee; the third optimal quantum position is and divide it into the position of the pursuer in the chimpanzee; the fourth optimal quantum position is And divide it into the position of the ouster among the chimpanzees, and the other quantum positions are divided into the positions of other chimpanzees among the chimpanzees, where i = 1, 2, ...,

[0029] The beneficial effects of the present invention are:

[0030] To address the challenges of traditional narrowband direction-finding methods, which suffer from low real-time performance, ineffective direction-finding under impulsive noise, and inability to estimate coherent sources, this paper proposes a maximum likelihood direction-of-arrival (DOA) estimation method based on correlation entropy. This method effectively estimates the direction of arrival of narrowband signals in impulsive noise environments, exhibits excellent deallocation capabilities, and exhibits high real-time performance. Furthermore, a continuous chimpanzee search mechanism is designed to efficiently solve the maximum likelihood equation based on correlation entropy. This DOA estimation method has a wide range of applications and, in practical engineering applications, effectively addresses the failure of existing DOA estimation methods in complex noise environments, such as impulsive noise.

[0031] In contrast, most existing DOA estimation methods are performed under the assumption of Gaussian noise. In complex environments such as impact noise, direction finding fails and has poor real-time performance. They cannot meet the DOA estimation needs in complex environments, and the DOA estimation effect is poor when processing coherent signal sources. The present invention constructs a low-order matrix based on correlation entropy under impact noise, and designs a maximum likelihood DOA estimation method based on the low-order matrix of correlation entropy. The designed DOA estimation method can effectively find the direction in an impact noise environment and has good decoherence capability. A continuous quantum chimpanzee search mechanism is designed to solve the maximum likelihood equation based on correlation entropy, which can improve the solution accuracy while reducing the amount of calculation, making the DOA estimation result more accurate and robust. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart of the narrowband direction finding system of the present invention;

[0033] Figure 2 This is the narrowband direction finding result of two independent sources when the impulse noise characteristic index is 1.5;

[0034] Figure 3 The narrowband direction finding result of two coherent sources when the impulse noise characteristic index is 1.5. DETAILED DESCRIPTION

[0035] The present invention will be further described below with reference to the accompanying drawings.

[0036] This invention proposes a maximum likelihood narrowband direction of arrival estimation method based on correlation entropy. This method utilizes a kernel function to transform a nonlinear problem in the original image space into a linear problem in the reproducing kernel Hilbert space through a nonlinear transformation. The inner product mapped to the high-dimensional feature space can be quickly calculated using a simple mathematical expression. The invention uses an exponential kernel function to construct the correlation entropy. Exponential functions satisfy Mercer's theorem and can be used as kernel functions. By adjusting parameters, the exponential kernel function can achieve performance similar to that of the Gaussian kernel function while reducing computational complexity. Leveraging the exponential function's attenuation characteristics, the correlation entropy suppresses outliers in the array's received signal, thereby better adapting to impulse noise environments. Furthermore, the correlation entropy uses the median instead of the mean to represent the general level of the overall data. This is because in a stable distributed noise environment, especially when the characteristic exponent is small, very large outliers may occur, and the estimated mean in such cases often exhibits significant deviations. The median, on the other hand, is unaffected by excessively large or small data, making it more adaptable to impulse noise environments. The kernel length setting in the kernel function is closely related to its application domain. The invention selects the optimal kernel length through performance simulations, and subsequent experiments discuss kernel length selection. A continuous quantum chimpanzee search mechanism is then designed to efficiently solve the maximum likelihood equation based on correlation entropy. The invented direction-of-arrival estimation method can effectively estimate the direction of arrival of both independent and coherent sources in the presence of impulse noise.

[0037] The maximum likelihood wideband signal direction finding method based on the median deviation correlation entropy low-order matrix of the continuous quantum Chimpanzee search mechanism designed in the present invention is abbreviated as "QCHIMP-DCME-ML", and the maximum likelihood wideband direction finding method based on the fractional low-order covariance of the Chimpanzee algorithm is abbreviated as "CHIMP-FLOC-ML".

[0038] The invention solves the direction-finding equation by using the continuous quantum chimpanzee mechanism. The narrowband signal direction-of-arrival estimation method can effectively find the direction of both independent sources and coherent sources under impulse noise.

[0039] Figure 1 The block diagram of the direction of arrival estimation system of the present invention is introduced, and the detailed process is as follows:

[0040] Step 1: Establish a maximum likelihood direction of arrival estimation model based on correlation entropy under impulse noise. In the impulse noise environment, there are N far-field narrowband signals with direction angles θ1, θ2, ..., θ N The incident signal is incident on a uniform linear array with M elements in space, with a wavelength of λ, an element spacing of d, an incident signal frequency of f0, a snapshot number of S, and the incident signal and noise are uncorrelated. Taking the first element as the reference element, the signal received by the mth element can be expressed as m=1,2,…,M. Among them, Indicates that the incident direction is θ n The narrowband signal represents the impulse noise on the mth array element, then the kth snapshot narrowband signal received by the array is z(k)=A(θ)s(k)+n(k), k=1,2,…,S, where z(k)=[z1(k),z2(k),…,z M (k)] T , A(θ)=[a(θ1),a(θ2),…,a(θ N )] M×N is the steering matrix, where the i-th steering vector is θ=[θ1,θ2,…,θ N ] is the incoming wave direction vector, s(k)=[s1(k),s2(k),…,s N (k)] T is the signal vector, n(k)=[n1(k),n2(k),…,n M (k)] T is the array noise vector. The snapshot data received by the array is used to construct the low-order matrix of correlation entropy in represents the median operation, |·| represents the absolute value operation, (·) * represents the conjugate operation, σ represents the kernel function κ σ (·)=exp(-|·| / 2σ 2 ), m1 and m2 are numbers between [0,1], i=1,2,…,M, j=1,2,…,M. The orthogonal projection matrix is ​​P A(θ) =A(θ)(A H (θ)A(θ)) -1 A H (θ), the angle estimate of the maximum likelihood equation is Where H stands for conjugate transpose and tr() is the matrix trace operation.

[0041] Step 2: Initialization of the core length solving population based on the quantum chimpanzee search mechanism. The continuous quantum chimpanzee search mechanism is initialized. The chimpanzee population size is The maximum number of iterations is t max , the search space dimension is D, and the quantum position of the i-th chimpanzee at the t-th iteration is The quantum rotation angle of the i-th chimpanzee is in n=1,2,…,D, maps the quantum position of the i-th chimpanzee at the t-th iteration to the position The specific mapping rules are: n=1, 2, ..., D, where and are the lower and upper bounds of the exponential kernel parameters respectively. t is the number of iterations, and t is initially set to 1.

[0042] Step 3: Establish the direction-finding model and design the objective function for solving the optimal kernel length of the kernel function. When solving the optimal kernel length, the spatial wave direction is N = 1 and the search space dimension is D = 3. The value of the spatial wave being a cooperative signal is The received k-th snapshot narrowband signal is z(k)=[z1(k),z2(k),…,z M (k)] T , using the snapshot data received by the array to construct the low-order matrix of correlation entropy in Perform eigenvalue decomposition on the low-order matrix of related entropy, Q = AQ s A H +Q n , where Q s is the signal correlation matrix, Q n The noise correlation matrix is ​​then sorted by eigenvalue size, and the eigenvalues ​​and corresponding eigenvectors equal to the number of signals N are regarded as the signal part space, and the eigenvalues ​​and eigenvectors of the remaining MN are regarded as the noise part space, and the noise matrix E is obtained. n , A H v i =0, i=N+1, N+2,…, M, E n =[v N+1 ,v N+2 ,…,v M ], and finally change θ from -90 to 90. The classic MUSIC algorithm is based on the formula To calculate the spectrum function, we can find the peak value to get the estimated value of the direction of arrival. According to the classic MUSIC algorithm, we can get the location of the i-th chimpanzee. The direction of arrival corresponding to the exponential kernel parameter is Then the objective function can be determined as Minimum optimization of .

[0043] Step 4: Calculate the fitness values ​​of all chimpanzee locations and classify the chimpanzee locations. Calculate the location of the i-th chimpanzee at the t-th iteration The fitness value of Determine the global optimal quantum position that the chimpanzee has searched for until the tth iteration as and divide it into the position of the attacker in the chimpanzee; the second best quantum position is and divide it into the position of the blocker in the chimpanzee; the third optimal quantum position is and divide it into the position of the pursuer in the chimpanzee; the fourth optimal quantum position is And divide it into the position of the ouster among the chimpanzees, and the other quantum positions are divided into the positions of other chimpanzees among the chimpanzees, where i = 1, 2, ...,

[0044] Step 5: The quantum positions of the attacker, blocker, pursuer, and evictor are used to update the quantum positions of the other chimpanzees in the population. At the t+1 iteration, the quantum position of the i-th chimpanzee in the population consists of four parts. The first part is updated by the quantum position of the attacker, where the n-th quantum rotation angle variable is the convergence factor, is a nonlinear random variable between [0,1]. is the position of the attacker in the chimpanzee group up to generation t The nth dimension of For all chimpanzee populations up to generation t The average of the quantum positions of the chimpanzees The nth dimension, m t is a uniform random number between [0,1], is a uniform random number between [-1,1], sign(·) represents the sign function, and its value is between {-1,0,1}. is a nonlinear random variable between [0,1], then the n-th dimension update method of the first part of the quantum position of the i-th chimpanzee is n=1,2,...,D, abs(·) is the absolute value operation; the second part is updated by the quantum position of the blocker, where the n-th dimension quantum rotation angle is a nonlinear random variable between [0,1]. is the position of the blocker in the chimpanzee group up to generation t The nth dimension of is a uniform random number between [-1,1], is a nonlinear random variable between [0,1], then the n-th dimension update method of the second part of the quantum position of the i-th chimpanzee is n=1,2,...,D; the third part is updated by the pursuer's quantum position, where the n-th dimension quantum rotation angle is a nonlinear random variable between [0,1]. is the position of the pursuer in the chimpanzee group up to generation t The nth dimension of is a uniform random number between [-1,1], is a nonlinear random variable between [0,1], then the n-th dimension update method of the third part of the quantum position of the i-th chimpanzee is n=1,2,...,D; the fourth part is updated by the quantum position of the evictor, where the n-th dimension quantum rotation angle is a nonlinear random variable between [0,1]. is the position of the evictor in the chimpanzee group up to generation t The nth dimension of is a uniform random number between [-1,1], is a nonlinear random variable between [0,1], then the n-th dimension update method of the fourth part of the quantum position of the i-th chimpanzee is n=1,2,...,N. Therefore, at iteration t+1, the nth dimension of the quantum position of the i-th chimpanzee is n=1,2,...,N。

[0045] Step 6: Calculate the fitness values ​​of all chimpanzees at their new positions and update the positions of attackers, blockers, pursuers, and evictors in the entire chimpanzee population. Map the quantum position of the i-th chimpanzee at the t+1th iteration to the position Calculate the location of the i-th chimpanzee at the t+1th iteration The fitness value of If the i-th chimpanzee has the same quantum position in the t+1th iteration The fitness is better than The fitness of otherwise If the i-th chimpanzee has the same quantum position in the t+1th iteration Fitness is inferior to The fitness is better than The fitness of otherwise If the i-th squirrel has a quantum position at the t+1th iteration Fitness is inferior to The fitness is better than The fitness of otherwise If the i squirrels have quantum positions in the t+1th iteration Fitness is inferior to The fitness is better than The fitness of otherwise

[0046] Step 7: Determine whether the maximum number of iterations has been reached. If not, set t = t + 1 and return to step 5 to continue. If it has been reached, map the quantum position of the attacker in the chimpanzee group to the global optimal position according to the mapping rule, and the optimal parameters of the exponential kernel are obtained as and

[0047] Step 8: Define the received k-th snapshot narrowband signal as z(k) = [z1(k),z2(k),…,z M (k)] T , using the obtained exponential kernel optimal parameters m1, m2, σ and the snapshot data received by the array to construct the low-order matrix of correlation entropy in The orthogonal projection matrix is ​​P A(θ) =A(θ)(A H (θ)A(θ)) -1 A H (θ), the angle estimate of the maximum likelihood equation is Where H stands for conjugate transpose and tr() is the matrix trace operation.

[0048] Step 9: Initialize the continuous quantum chimpanzee search mechanism. The chimpanzee group size is The maximum number of iterations is t max , the dimension of the search space is D = N, and the quantum position of the i-th chimpanzee at the t-th iteration is The quantum rotation angle of the i-th chimpanzee is in n=1,2,…,D, t is the number of iterations, and initially t=1.

[0049] Step 10: Calculate the fitness values ​​of all chimpanzee positions and classify the chimpanzee positions. Map the quantum position of the i-th chimpanzee in the t-th iteration to the position The specific mapping rules are: Among them A n,min and A n,max are the lower and upper bounds of the angle search space respectively. Calculate the position of the i-th chimpanzee at the t-th iteration The fitness value of Determine the global optimal quantum position that the chimpanzee has searched for until the tth iteration as and divide it into the position of the attacker in the chimpanzee; the second best quantum position is and divide it into the position of the blocker in the chimpanzee; the third optimal quantum position is and divide it into the position of the pursuer in the chimpanzee; the fourth optimal quantum position is And divide it into the position of the ouster among the chimpanzees, and the other quantum positions are divided into the positions of other chimpanzees among the chimpanzees, where i = 1, 2, ...,

[0050] Step 11: The quantum positions of the attacker, blocker, pursuer, and evictor are used to update the quantum positions of other chimpanzees in the population. The specific steps are the same as step 5.

[0051] Step 12: Calculate the fitness values ​​of all chimpanzees at their new locations and update the positions of attackers, blockers, pursuers, and evictors in the entire chimpanzee population. The specific steps are the same as step 6.

[0052] Step 13: Determine whether the maximum number of iterations has been reached. If not, set t = t + 1 and return to step 11 to continue. If it has been reached, map the quantum position of the attacker in the chimpanzee group to the global optimal position according to the mapping rule to obtain the incoming angle of the signal.

[0053] The specific parameters of the model are set as follows:

[0054] Narrowband far-field signal, transmission frequency f0 = 100MHz, wavelength where c = 3 × 10 8 m / s represents the speed of light, antenna spacing The number of antennas is 16, the number of snapshots is 16, the number of signal sources is 2, the signal incident angles are 20° and 10° respectively, the signal incident angle used for determining the correlation entropy parameter by the MUSIC algorithm is 60°, and the incident signal is a linear frequency modulation signal. Figure 2 According to the test results, the kernel length of the correlation entropy can be set to σ = 2.3, the fractional low-order covariance characteristic index p1 = 0.1, and the number of Monte Carlo experiments is 30.

[0055] The parameters of the continuous quantum chimpanzee search mechanism are as follows: population size Maximum number of iterations t max =200, A n,max =90, A n,min = -90. For other parameter settings, refer to "Chimp optimization algorithm" published by M. Khishe and MR Mosavi in ​​"Expert Systems With Applications" (2020).

[0056] The parameter settings based on the chimpanzee algorithm are as follows: population size Maximum number of iterations t max=200. For other parameter settings, refer to “Chimp optimization algorithm” published by M. Khishe and MR Mosavi in ​​“Expert Systems With Applications”, 2020.

[0057] Figure 2 The simulation comparison curves of the root mean square error of the DOA estimation method designed by the present invention and the maximum likelihood DOA estimation method based on fractional low-order covariance of the chimpanzee algorithm under different generalized signal-to-noise ratios are given for two independent sources with an impulse noise characteristic index of 1.5. Figure 3 It can be seen from the figure that the direction finding method of narrowband signal designed by the present invention has excellent direction finding performance.

[0058] Figure 3 The simulation comparison curves of the root mean square error of the narrowband signal direction finding method designed by the present invention and the maximum likelihood narrowband signal direction finding method based on the fractional low-order covariance of the chimpanzee algorithm under different generalized signal-to-noise ratios are given when the impulse noise characteristic index is 1.5. Figure 3 It can be seen from the figure that the narrowband signal direction finding method designed in the present invention has excellent decorrelation capability under impulse noise.

[0059] The present invention utilizes a continuous quantum chimpanzee search mechanism to perform direction finding on narrowband signals in the presence of impulsive noise, overcoming the shortcomings of traditional narrowband direction finding methods, such as direction finding failure and poor real-time performance, in the presence of impulsive noise. The method comprises the following steps: establishing a maximum likelihood broadband signal direction finding model based on median deviation correlation entropy in the presence of impulsive noise; initializing the parameters of the continuous quantum chimpanzee search mechanism; calculating the fitness values ​​of all chimpanzee positions and initializing the quantum positions of attackers, blockers, pursuers, and expellees; updating the quantum positions of other chimpanzees in the population based on the quantum positions of the attackers, blockers, pursuers, and expellees; calculating the fitness values ​​of all chimpanzee positions at their new locations and updating the positions of attackers, blockers, pursuers, and expellees in the entire chimpanzee population; determining whether the maximum number of attempts has been reached; and mapping the quantum positions of attackers in the chimpanzee population to the global optimal position according to a mapping rule to obtain the angle of arrival of the signal. The present invention uses a continuous quantum chimpanzee search mechanism to solve the maximum likelihood direction of arrival estimation equation based on correlation entropy, can effectively find the direction in an impact noise environment, has good decoherence capability, high direction finding accuracy, and a wide range of applications.

[0060] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for estimating direction of arrival based on optimal correlation entropy under impulse noise, characterized by: The specific steps are as follows: Step 1: Establish a maximum likelihood direction of arrival estimation model based on correlation entropy under impulse noise; Step 2: Initialization of the core length solving population based on the quantum chimpanzee search mechanism; Initialization of the continuous quantum chimpanzee search mechanism; Step 3: Establish the direction-finding model and design the objective function for solving the optimal kernel length of the kernel function; Step 4: Calculate the fitness values ​​of all chimpanzee locations and classify the chimpanzee locations; Step 5: The quantum positions of the attacker, blocker, pursuer, and evictor are used to update the quantum positions of other chimpanzees in the population; Step 6: Calculate the fitness values ​​of all chimpanzees at their new locations and update the positions of attackers, blockers, pursuers, and evictors in the entire chimpanzee population. Step 7: Determine whether the maximum number of iterations has been reached. If not, set t = t + 1 and return to step 5 to continue. If it has been reached, map the quantum position of the attacker in the chimpanzee group to the global optimal position according to the mapping rule, and the optimal parameters of the exponential kernel are obtained as and Step 8: Define the received k-th snapshot narrowband signal as z(k) = [z1(k),z2(k),…,z M (k)] T , using the obtained exponential kernel optimal parameters m1, m2, σ and the snapshot data received by the array to construct the correlation entropy matrix in, The orthogonal projection matrix is ​​P A(θ) =A(θ)(A H (θ)A(θ)) -1 A H (θ), where A(θ) is the steering vector matrix, and its specific form is A(θ)=[a(θ1),a(θ2),…,a(θ N )] M×N , where the i-th steering vector is θ=[θ1,θ2,…,θ N ] is the incoming wave direction vector, d is the array element spacing, M is the number of array elements, and λ is the wavelength of the narrowband incident signal; the angle estimate of the maximum likelihood equation is Where H represents the conjugate transpose, and tr() is the matrix trace operation; Step 9: Initialization of the continuous quantum chimpanzee search mechanism; Step 10: Calculate the fitness values ​​of all chimpanzee locations and classify the chimpanzee locations; Step 11: The quantum positions of the attacker, blocker, pursuer, and evictor are used to update the quantum positions of other chimpanzees in the population. The specific steps are the same as those in step 5. Step 12: Calculate the fitness values ​​of all chimpanzees at their new locations and update the positions of attackers, blockers, pursuers, and evictors in the entire chimpanzee population. The specific steps are the same as step 6. Step 13: Determine whether the maximum number of iterations has been reached. If not, set t = t + 1 and return to step 11 to continue. If it has been reached, map the quantum position of the attacker in the chimpanzee group to the global optimal position according to the mapping rule to obtain the incoming angle of the signal.

2. The method for DOA estimation based on optimal correlation entropy under impulse noise according to claim 1, characterized in that: The specific step 1 is: in an impact noise environment, there are N far-field narrowband signals with direction angles θ1, θ2, ..., θ N The incident signal is incident on a uniform linear array with M elements in space, with a wavelength of λ, an element spacing of d, an incident signal frequency of f0, a snapshot number of S, and the incident signal and noise are uncorrelated; taking the first element as the reference element, the signal received by the mth element can be expressed as in, Indicates that the incident direction is θ n The narrowband signal represents the impulse noise on the mth array element, then the kth snapshot narrowband signal received by the array is z(k)=A(θ)s(k)+n(k), k=1,2,…,S, where z(k)=[z1(k),z2(k),…,z M (k)] T , A(θ)=[a(θ1),a(θ2),…,a(θ N )] M×N is the steering matrix, where the i-th steering vector is θ=[θ1,θ2,…,θ N ] is the incoming wave direction vector, s(k)=[s1(k),s2(k),…,s N (k)] T is the signal vector, n(k)=[n1(k),n2(k),…,n M (k)] T is the array noise vector; the snapshot data received by the array is used to construct the correlation entropy low-order matrix Q: in med(·) means to find the median value, |·| means to find the absolute value, (·) * represents the conjugate operation, σ represents the kernel function κ σ (·)=exp(-|·| / 2σ 2 ), m1 and m2 are numbers between [0,1], i=1,2,…,M, j=1,2,…,M; the orthogonal projection matrix is ​​P A(θ) =A(θ)(A H (θ)A(θ)) -1 A H (θ), the angle estimate of the maximum likelihood equation is Where H stands for conjugate transpose and tr() is the matrix trace operation.

3. The method for DOA estimation based on optimal correlation entropy under impulse noise according to claim 1, characterized in that: Step 2 is as follows: The chimpanzee group size is The maximum number of iterations is t max , the search space dimension is D, and the quantum position of the i-th chimpanzee at the t-th iteration is The quantum rotation angle of the i-th chimpanzee is in Map the quantum position of the i-th chimpanzee at the t-th iteration to the position The specific mapping rules are: in and are the lower and upper bounds of the exponential kernel parameters respectively; t is the number of iterations, and t=1 is set initially.

4. The method for DOA estimation based on optimal correlation entropy under impulse noise according to claim 1, characterized in that: The specific step 3 is as follows: when finding the optimal core length, the spatial wave direction is N=1, the search space dimension is D=3; the determination value of the spatial wave as a cooperative signal is The received k-th snapshot narrowband signal is z(k)=[z1(k),z2(k),…,z M (k)] T , using the snapshot data received by the array to construct the relevant entropy matrix in Perform eigenvalue decomposition on the low-order matrix of related entropy, Q = AQ s A H +Q n , where Q s is the signal correlation matrix, Q n The noise correlation matrix is ​​then sorted by eigenvalue size, and the eigenvalues ​​and corresponding eigenvectors equal to the number of signals N are regarded as the signal part space, and the eigenvalues ​​and eigenvectors of the remaining MN are regarded as the noise part space, and the noise matrix E is obtained. n , A H v i =0, i=N+1, N+2,…, M, E n =[v N+1 ,v N+2 ,…,v M ], and finally change θ from -90 to 90. The classic MUSIC algorithm is based on the formula To calculate the spectral function, we can find the peak value to get the estimated value of the direction of arrival; according to the classic MUSIC algorithm, we can get the location of the i-th chimpanzee. The direction of arrival corresponding to the exponential kernel parameter is Then the objective function can be determined as Minimum optimization of .

5. The method for DOA estimation based on optimal correlation entropy under impulse noise according to claim 1, characterized in that: Step 4 is as follows: Calculate the location of the i-th chimpanzee at the t-th iteration The fitness value of Determine the global optimal quantum position that the chimpanzee has searched for until the tth iteration as and divide it into the position of the attacker in the chimpanzee; the second best quantum position is and divide it into the position of the blocker in the chimpanzee; the third optimal quantum position is and divide it into the position of the pursuer in the chimpanzee; the fourth optimal quantum position is and divide it into the position of the ouster among the chimpanzees, and the other quantum positions into the positions of the other chimpanzees among the chimpanzees, where 6. The method for DOA estimation based on optimal correlation entropy under impulse noise according to claim 1, characterized in that: The specific step 5 is as follows: at the t+1 iteration, for the i-th chimpanzee in the population, its quantum position consists of four parts; the first part is updated by the attacker's quantum position, where the n-th dimension quantum rotation angle variable is the convergence factor, is a nonlinear random variable between [0,1]. is the position of the attacker in the chimpanzee group up to generation t The nth dimension of For all chimpanzee populations up to generation t The average of the quantum positions of the chimpanzees The nth dimension, m t is a uniform random number between [0,1], r1 t is a uniform random number between [-1,1], sign(·) represents the sign function, and its value is between {-1,0,1}. is a nonlinear random variable between [0,1], then the n-th dimension update method of the first part of the quantum position of the i-th chimpanzee is abs(·) is the absolute value operation; the second part is updated by the quantum position of the blocker, where the n-th dimension quantum rotation angle is a nonlinear random variable between [0,1]. is the position of the blocker in the chimpanzee group up to generation t The nth dimension of is a uniform random number between [-1,1], is a nonlinear random variable between [0,1], then the n-th dimension update method of the second part of the quantum position of the i-th chimpanzee is The third part is updated by the pursuer's quantum position, where the n-dimensional quantum rotation angle is a nonlinear random variable between [0,1]. is the position of the pursuer in the chimpanzee group up to generation t The nth dimension of is a uniform random number between [-1,1], is a nonlinear random variable between [0,1], then the n-th dimension update method of the third part of the quantum position of the i-th chimpanzee is The fourth part is updated by the quantum position of the evictor, where the n-th dimension quantum rotation angle is a nonlinear random variable between [0,1]. is the position of the evictor in the chimpanzee group up to generation t The nth dimension of is a uniform random number between [-1,1], is a nonlinear random variable between [0,1], then the n-th dimension update method of the fourth part of the quantum position of the i-th chimpanzee is Therefore, at iteration t+1, the nth dimension of the quantum position of the i-th chimpanzee is 7. The method for DOA estimation based on optimal correlation entropy under impulse noise according to claim 1, characterized in that: The specific step six is: map the quantum position of the i-th chimpanzee in the t+1th iteration to the position Calculate the location of the i-th chimpanzee at the t+1th iteration The fitness value of If the i-th chimpanzee has the same quantum position in the t+1th iteration The fitness is better than The fitness of otherwise If the i-th chimpanzee has the same quantum position in the t+1th iteration Fitness is inferior to The fitness is better than The fitness of otherwise If the i-th squirrel has a quantum position at the t+1th iteration Fitness is inferior to The fitness is better than The fitness of otherwise If the i squirrels have quantum positions in the t+1th iteration Fitness is inferior to The fitness is better than The fitness of otherwise 8. The method for DOA estimation based on optimal correlation entropy under impulse noise according to claim 1, characterized in that: Step nine is as follows: The chimpanzee group size is The maximum number of iterations is t max , the dimension of the search space is D = N, and the quantum position of the i-th chimpanzee at the t-th iteration is The quantum rotation angle of the i-th chimpanzee is in t is the number of iterations, and initially t=1.

9. The method for DOA estimation based on optimal correlation entropy under impulse noise according to claim 1, characterized in that: The specific step 10 is: map the quantum position of the i-th chimpanzee in the t-th iteration to the position The specific mapping rules are: Among them A n,min and A n,max are the lower and upper bounds of the angle search space respectively; calculate the position of the i-th chimpanzee at the t-th iteration The fitness value of Determine the global optimal quantum position that the chimpanzee has searched for until the tth iteration as and divide it into the position of the attacker in the chimpanzee; the second best quantum position is and divide it into the position of the blocker in the chimpanzee; the third optimal quantum position is and divide it into the position of the pursuer in the chimpanzee; the fourth optimal quantum position is and divide it into the position of the ouster among the chimpanzees, and the other quantum positions into the positions of the other chimpanzees among the chimpanzees, where

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