A method and system for amplitude and phase error self-correction and direction finding of nested arrays under impulsive noise

Abstract

The application discloses a method and system for self-correction of amplitude-phase error and direction finding of nested array under impact noise, and relates to the field of array signal processing. The method is used for solving the problem that the existing method depends on an additional correction source, and an algorithm is trapped in a local optimal solution. The method comprises the following steps: step one, establishing a data model of a nested array for receiving signals with amplitude-phase error; step two, constructing a low-order matrix of a cosine transform Sigmoid kernel of the signals; step three, performing initial amplitude-phase error compensation, and improving direction finding accuracy by a diagonal loading method; step four, performing self-correction of the amplitude-phase error; step five, virtually extending the low-order covariance matrix, and estimating a direction of wave arrival; step six, establishing a fitness function, updating an amplitude-phase error estimation matrix, and converging the amplitude-phase error estimation value; step seven, performing phase error estimation based on a quantum lizard algorithm; and step eight, repeatedly performing steps three to seven until a maximum number of cycles is reached, and outputting an estimated angle of wave arrival and an estimated result of the amplitude-phase error.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and more specifically, to a method and system for self-correction of amplitude and phase errors and direction finding of nested arrays under impulse noise. Background Technology

[0002] Direction of arrival (DOA) estimation, also known as direction finding, primarily studies the direction of arrival of signals in space. It is a core technology in array signal processing and has wide applications in battlefield communications and geological exploration. With the increasing complexity of the electromagnetic environment in modern civilian and military communications, the accuracy requirements for DOA technology are becoming increasingly stringent. Traditional uniform linear arrays can only accurately estimate the number of signals, not exceeding the number of array elements. To address this issue, researchers have proposed nested arrays, which, by increasing the effective aperture of the array, can estimate DOAs exceeding the number of array elements. However, in practical applications, arrays often face undesirable conditions, including array position errors, amplitude and phase errors, and array mutual coupling. Among these, amplitude and phase errors are particularly common and can significantly affect DOA accuracy, even leading to algorithm failure. Furthermore, noise in real-world communication environments is often impulsive, which can also degrade the performance of classical DOA algorithms or even cause them to fail completely. Therefore, research on amplitude and phase error correction and direction finding methods for nested arrays in impulsive noise environments has significant theoretical and practical value.

[0003] In practical applications, direction-finding arrays often face the problem of amplitude and phase errors, which significantly reduce the array's direction-finding accuracy. With the deepening research on array amplitude and phase errors, scholars began modeling them around the 1990s. For a one-dimensional linear array, the amplitude and phase error is usually represented as a diagonal matrix, where each diagonal element corresponds to the amplitude and phase error of the corresponding array element. Thus, the problem of array amplitude and phase error correction is transformed into a parameter estimation problem. The most classic amplitude and phase error correction method is the auxiliary source correction method, which can be extended to the amplitude and phase error correction of nested arrays and can achieve high correction accuracy. However, the auxiliary source correction method requires the angle of the auxiliary source to be precisely known, and its real-time performance is poor, making it difficult to adapt to actual communication environments. Another classic method is the self-calibration algorithm, which is often used for the self-calibration of amplitude and phase errors in uniform arrays. Although this method can provide relatively accurate correction results, it requires a large number of iterative calculations and only performs well when the amplitude and phase error is small. In the correction process of nested arrays, due to the use of covariance matrix expansion, the performance of the self-calibration algorithm degrades significantly under large amplitude and phase errors, and may even fail completely.

[0004] A search of existing literature revealed that Zhao Haizhou et al., in their paper "Simultaneous Estimation Algorithm for Amplitude and Phase Error and DOA Based on Auxiliary Array Elements" published in *Modern Defense Technology* (2023, 51(2): 84-90), changed the structure of the error matrix by setting a small number of corrected array elements on one side of the array. They then constructed a transformation matrix based on the characteristics of the changed matrix and used the constructed transformation matrix and subspace algorithm to achieve simultaneous estimation of the amplitude and phase error (DOA) of the array elements. This algorithm requires additional auxiliary array elements as prior knowledge, increasing the difficulty of implementation in practical applications. Furthermore, a search of existing literature indicates that most direction-finding methods are proposed under the assumption that the array element noise is independent Gaussian self-noise. However, in practical applications, many noises have impulse characteristics and belong to non-Gaussian noise, such as underwater noise, low-frequency atmospheric noise, and some man-made noise. These noises can be described by processes with different characteristic exponents. Since non-Gaussian noise does not possess the characteristics of higher-order moments, methods based on Gaussian models are incompatible with it, causing traditional algorithms based on second-order or higher-order statistics to fail. Summary of the Invention

[0005] The technical problem to be solved by this invention is:

[0006] Existing methods rely on additional calibration sources and require high initial measurement accuracy. If the initial estimation deviation is large, the algorithm is prone to getting trapped in a local optimum.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] This invention provides a method for self-correction of amplitude and phase errors and direction finding of nested arrays under impulse noise, comprising the following steps:

[0009] Step 1: Establish a nested array receiving data model with amplitude and phase errors under impulse noise environment;

[0010] Step 2: Construct a low-order Sigmoid kernel matrix of the signal using the data received from the array;

[0011] Step 3: Perform initial amplitude and phase error compensation on the low-order matrix of the cosine transform sigmoid kernel, and set the diagonal matrix of the amplitude and phase error of the first cycle as the identity matrix to improve the direction finding accuracy through the diagonal loading method.

[0012] Step 4: Further perform amplitude and phase error self-correction on the low-order matrix of the cosine transform sigmoid kernel;

[0013] Step 5: Perform virtual expansion on the low-order covariance matrix to estimate the direction of arrival;

[0014] Step 6: Using the angle of arrival estimated in the previous iteration, establish a fitness function based on the orthogonality of the steering vector and the noise subspace and the constraint condition of normalizing the amplitude and phase error of the first array element, and update the amplitude and phase error estimation matrix until the amplitude and phase error estimates converge.

[0015] Step 7: Design a fitness function, construct a quantum lizard algorithm based on the lizard's biomimetic mechanism, quantum rotation angle, simulated simplified quantum rotation gate, and simulated quantum evolution equation to solve for phase error estimation and obtain the estimated value of the amplitude-phase error matrix;

[0016] Step 8: Determine whether the number of self-calibration cycles has reached the set maximum value. If it has, output the estimated direction of arrival angle and amplitude and phase error estimation results. If it has not, continue to execute Step 3.

[0017] Furthermore, the method for constructing the nested array receiving data model with amplitude and phase errors under the impulsive noise environment described in step one is as follows:

[0018] There are N narrowband point sources in the far field of the array, with directions θ = [θ1, θ2, ..., θ3]. N If the incident wavelength is λ, then the k-th snapshot sampled data received by the array with amplitude and phase errors is z(k)=ΓA(θ)s(k)+n(k), where k=1,2,...,K, and K is the maximum number of snapshots. In the formula, z(k)=[z1(k), z2(k),..., z M (k)] T Let Γ be the data vector of the k-th snapshot received by the M×1 dimensional array, where M is the total number of array elements in the nested array; Γ is the amplitude and phase error matrix of the array, where Γ = diag{1, ρ2exp(jφ2), ..., ρ M exp(jφ M )},ρ m and φ m These are the amplitude and phase errors of the m-th array element, respectively, where m = 1, 2, ..., M; s(k) = [s1(k), s2(k), ..., sm(k)]. N (k)] T Let n(k) be an N×1 dimensional signal vector; n(k) = [n1(k), n2(k), ..., n M (k)] T Let A(θ) be an M×1 dimensional noise vector, where the noise is spatially and temporally independent and follows a complex impulse noise distribution SαS. N )] is an M×N dimensional array manifold matrix, where θ=[θ1, θ2, ..., θ N ] is the direction vector of the information source, a(θ) n) represents the nth guiding vector of the array manifold matrix, where n = 1, 2, ..., N; for nested arrays with an incident angle of θ n The array steering vector is Where j is the complex unit.

[0019] Furthermore, step 1 also includes: constructing the infinite norm normalized signal of the received k-th snapshot sampling data as follows: Where max{·} is the function to find the maximum value.

[0020] Furthermore, step two includes the following steps:

[0021] The low-order matrix of the cosine transform sigmoid kernel of the infinity norm normalized signal of the data received by the array elements is defined as follows: In the formula, Representation matrix The Middle Line number Column elements, Here is the weighting constant. and These represent the data vectors of the received k-th snapshot signal, respectively. The first in peacekeeping 3D signal, and satisfying |·| represents the absolute value operation, and (·)* represents the conjugate operation. is the kernel length of the kernel function.

[0022] Furthermore, in step three, initial amplitude and phase error compensation is performed on the low-order matrix of the cosine transform sigmoid kernel: For unit array, Design a diagonal loading method: in Let I be the loading factor, and let I denote the identity matrix.

[0023] Furthermore, step four includes the following steps:

[0024] The amplitude and phase error matrix estimated at the t-th time is: T represents the maximum number of cycles for amplitude and phase error self-correction. Amplitude and phase error compensation is performed on the low-order matrix of the cosine transform sigmoid kernel of the infinite norm normalized signal. in(·) -1 This indicates finding the inverse of a matrix, (·). H This represents finding the conjugate transpose of a matrix; the magnitude error value of the m-th element in the t-th iteration is obtained. Where γ n R is the dispersion factor of the impact noise. t (m, m) represents matrix R tThe element in the m-th row and m-th column of R t (1, 1) represents matrix R. t The element in the first row and first column, m = 1, 2, ..., M, sqrt(·) represents the root mean square of the matrix.

[0025] Furthermore, step five includes the following steps:

[0026] The low-order matrix R of the compensated cosine transform sigmoid kernel is expressed as follows: The maximum correlation delay calculated based on the nested array is: The number of virtual array elements is then: make E is the expected value, uv = h l -h f , h l -h f If ∈H, then the lower-order matrix after compensation and virtual expansion is The expanded guidance matrix is ​​B(θ) = [b(θ1), b(θ2), ..., b(θ)]. N )], where the extended steering vector corresponding to the nth angle is n = 1, 2, ..., N;

[0027] The direction-of-arrival angle is estimated using the maximum likelihood equation. At the t-th estimation, the objective function corresponding to the n-th source is: In the formula, tr(·) is the function for finding the trace of a matrix, and P B(θ) =B(θ)·(B H (θ)B(θ)) -1 ·B H (θ) is the projection matrix of B(θ).

[0028] Furthermore, step six includes the following steps:

[0029] Set the convergence threshold for phase error to Δθ. When the difference between the phase error estimated in the current iteration and the previous estimate exceeds the convergence threshold, let... It is the steering vector corresponding to the direction of arrival angle of the nth source estimated in the t-th iteration; for the matrix Perform eigenvalue decomposition to obtain the noise subspace U N Define matrix in The estimation of amplitude and phase errors is transformed into a constrained minimum optimization problem. Based on the orthogonality of the steering vector and the noise subspace, and the constraint of normalizing the amplitude and phase errors of the first array element, the fitness function is established as follows: The constraint condition is ξ Hω = 1, where ξ is the amplitude and phase error vector to be estimated, and ω is an M-dimensional column vector with all elements except the first element being 1 and the rest being 0. The amplitude and phase error matrix at the t-th cycle is estimated as follows:

[0030] When the difference between the phase error estimated in this iteration and the previous estimate is less than or equal to the convergence threshold Δθ, proceed to step seven.

[0031] Furthermore, step seven includes the following steps:

[0032] (1) Initialize the quantum lizard population, setting the population size to [value missing]. The number of unknown parameters to be optimized is D, the maximum number of iterations is G, and ε represents the number of iterations; the quantum positions of the quantum lizard are randomly initialized as follows: in d = 1, 2, ..., D, mapped to the corresponding positions as The mapping rule is: in, This represents the lower bound of the d-th dimension variable. Denotes the upper bound of the d-th dimension variable, the d-th dimension variable... The actual location after mapping of a quantum lizard The d-th dimension corresponds to the phase error value of the d-th array element;

[0033] No. The amplitude and phase error estimation matrix mapped by the quantum lizards at the εth iteration is: Where ⊙ denotes matrix dot product; the matrix obtained by performing amplitude and phase error compensation on the covariance matrix is: definition The fitness function is constructed based on the maximum likelihood algorithm. Where tr(·) represents the trace operation;

[0034] The fitness of the quantum lizard's position is calculated based on the fitness function, and the quantum position with the lowest fitness is determined as the globally optimal quantum position.

[0035] (2) When At this point, the quantum lizard is in the encirclement phase. Using an exploration-update strategy, the quantum position is updated through a simplified simulated quantum rotation gate based on the quantum lizard's current quantum position. Then, the... The quantum lizard updates the quantum rotation angle corresponding to the d-th quantum position as follows: Where β is the sensitivity parameter; r1 is a random number between [0, 1]; As a marker to narrow down the search space, Where r2 is Random integers between; hunting operator In the formula, Let d be the dimension of the globally optimal quantum position at iteration ε. This represents the percentage difference between the optimal solution and the current solution in the d-th dimension. Where τ is the sensitivity coefficient, and ζ is a very small positive number. Indicates the first The average position of the candidate solutions

[0036] when At that time, the quantum lizard was in the hunting phase, using the development and update strategy, the first The quantum lizard updates the d-th dimension quantum rotation angle as defined by Where r3 is a random number between [0, 1]; the th The d-th quantum position of a quantum lizard is updated using a simulated quantum rotation gate: in For the first The quantum lizard's d-th dimension quantum position The updated d-dimensional quantum position of the ε+1 generation;

[0037] The first The newly generated d-th dimension quantum position of the quantum lizard Mapped to the first according to the mapping rules The newly generated d-th dimension position of the quantum lizard Calculate the fitness function based on the first The location where the quantum lizard is newly generated fitness value Then, a greedy selection method is used to select the quantum position of the quantum lizard. but Then, the quantum lizards after the greedy selection are sorted in ascending order of fitness. The quantum lizard with the lowest fitness is found and its quantum position is recorded as the globally optimal quantum position up to generation ε+1. This position is then updated to...

[0038] (3) Map the updated quantum lizard position to a position, calculate the fitness value of the new quantum position according to the fitness function, and then update the global optimal quantum position;

[0039] (4) Determine whether the iterative model has reached its maximum number of iterations G; if not, return to step (2) and iterate again; otherwise, output the global optimal quantum position of the quantum lizard population. The globally optimal position obtained after mapping Then the estimated amplitude and phase error matrix at the t-th iteration is:

[0040] The present invention also provides a self-correction and direction-finding system for amplitude and phase errors of nested arrays under impact noise. The system has a program module corresponding to the steps of any of the above-described technical solutions, and executes the steps in the above-described self-correction and direction-finding method for amplitude and phase errors of nested arrays under impact noise when running.

[0041] Compared with the prior art, the beneficial effects of the present invention are:

[0042] (1) Unlike existing nested array amplitude and phase error correction techniques, the method proposed in this invention can achieve amplitude and phase error correction and direction of arrival estimation without relying on an additional correction source, which greatly improves its real-time performance and operability in practical applications. This invention introduces a diagonal loading method, thereby enhancing the stability of the initial direction of arrival estimation.

[0043] (2) To address the practical needs of nested array direction-of-arrival estimation in complex electromagnetic environments under impact noise conditions, and with low signal-to-noise ratios and short snapshot times, this invention proposes a cosine transform sigmoid kernel function to effectively suppress impact noise, thereby further improving the stability and accuracy of the algorithm in complex noise environments and expanding its application range.

[0044] (3) In the error correction process, this invention constructs a quantum lizard algorithm based on the quantum lizard biomimetic mechanism, rotation angle, simulated simplified quantum rotation gate and simulated quantum evolution equation to search for and estimate phase error, which can find more accurate solutions in high-dimensional complex optimization problems.

[0045] (4) In the process of phase error estimation, the present invention adopts an adaptive strategy to dynamically adjust the number of iterations of the self-calibration algorithm. When the error estimation reaches the convergence threshold, it switches to the quantum lizard algorithm for accurate estimation, which further enhances the reliability of the self-calibration method. Attached Figure Description

[0046] Figure 1 This is a flowchart of the amplitude and phase error self-correction and direction finding method of nested array under impact noise in an embodiment of the present invention;

[0047] Figure 2 This is a graph showing the relationship between the root mean square error of the direction finding angle and the upper and lower limits of the phase error in an embodiment of the present invention.

[0048] Figure 3 This is a graph showing the relationship between the root mean square error of the direction finding angle and the generalized signal-to-noise ratio under weak impact noise in an embodiment of the present invention.

[0049] Figure 4This is a graph showing the relationship between the success probability of direction finding angle estimation under weak impact noise in an embodiment of the present invention and the generalized signal-to-noise ratio.

[0050] Figure 5 This is a graph showing the relationship between the root mean square error of the direction finding angle and the generalized signal-to-noise ratio under strong impact noise in an embodiment of the present invention.

[0051] Figure 6 This is a graph showing the relationship between the success probability of direction finding angle estimation under strong impact noise and the generalized signal-to-noise ratio in an embodiment of the present invention. Detailed Implementation

[0052] To enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments or examples are merely some, not all, of the embodiments or examples of the present invention. All other embodiments or examples obtained by those skilled in the art based on the embodiments or examples of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0053] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0054] Specific Implementation Plan 1: Combining Figure 1 As shown, the present invention provides a method for self-correction of amplitude and phase error and direction finding of nested arrays under impulse noise, comprising the following steps:

[0055] Step 1: Establish a nested array receiving data model with amplitude and phase errors under impulse noise environment;

[0056] Step 2: Construct a low-order Sigmoid kernel matrix of the signal using the data received from the array;

[0057] Step 3: Perform initial amplitude and phase error compensation on the low-order matrix of the cosine transform sigmoid kernel, and set the diagonal matrix of the amplitude and phase error of the first cycle as the identity matrix to improve the direction finding accuracy through the diagonal loading method.

[0058] Step 4: Further perform amplitude and phase error self-correction on the low-order matrix of the cosine transform sigmoid kernel;

[0059] Step 5: Perform virtual expansion on the low-order covariance matrix and use the maximum likelihood method to estimate the direction of arrival;

[0060] Step 6: Using the angle of arrival estimated in the previous iteration, establish a fitness function based on the orthogonality of the steering vector and the noise subspace and the constraint condition of normalizing the amplitude and phase error of the first array element, and update the amplitude and phase error estimation matrix until the amplitude and phase error estimates converge.

[0061] Step 7: Design a fitness function based on the maximum likelihood algorithm, construct a quantum lizard algorithm based on the lizard's biomimetic mechanism, quantum rotation angle, simulated simplified quantum rotation gate, and simulated quantum evolution equation to solve for phase error estimation and obtain the estimated value of the amplitude-phase error matrix;

[0062] Step 8: Determine whether the number of self-calibration cycles has reached the set maximum value. If it has, output the estimated direction of arrival angle and amplitude and phase error estimation results. If it has not, continue to execute Step 3.

[0063] Specific Implementation Plan Two: The method for constructing the nested array receiving data model with amplitude and phase errors under the impulsive noise environment described in Step One is as follows:

[0064] A nested array is composed of two or more uniform arrays joined end-to-end. Assume the first uniform subarray contains M1 subarray elements with an element spacing of d′, and the second uniform subarray contains M2 subarray elements with an element spacing of (M1+1)d′. Then the nested array contains a total of M = M1 + M2 elements. Define a nested array element position vector p = [p1, p2, ..., P...]. M ], p1 < p2 < ... < p M p m Let p1 represent the position of the m-th element from the first element, where m = 1, 2, ..., M. The position of the first element in a nested array is represented as p1 = 0, then H = [h1, h2, ..., h...]. M And p = Hd′ = [h1d′, h2d′, ..., h M d′], where λ is the wavelength of the incident signal. This forms a relative position difference set. This set is a set of continuous or approximately continuous natural numbers.

[0065] There are N narrowband point sources in the far field of the array, with directions θ = [θ1, θ2, ..., θ3]. N If the incident wavelength is λ, then the k-th snapshot sampled data received by the array with amplitude and phase errors is z(k)=ΓA(θ)s(k)+n(k), where k=1,2,...,K, and K is the maximum number of snapshots. In the formula, z(k)=[z1(k), z2(k),..., z M (k)] TLet Γ be the data vector of the k-th snapshot received by the M×1 dimensional array, where M is the total number of array elements in the nested array; Γ is the amplitude and phase error matrix of the array, where Γ = diag{1, p2exp(jφ2), ..., ρ M exp(jφ M )},ρ m and φ m These are the amplitude and phase errors of the m-th array element, respectively, where m = 1, 2, ..., M; s(k) = [s1(k), s2(k), ..., sm(k)]. N (k)] T Let n(k) be an N×1 dimensional signal vector; n(k) = [n1(k), n2(k), ..., n M (k)] T Let A(θ) be an M×1 dimensional noise vector, where the noise is spatially and temporally independent and follows a SaS distribution. N )] is an M×N dimensional array manifold matrix, where θ=[θ1, θ2, ..., θ N ] is the direction vector of the information source, a(θ) n ) represents the nth guiding vector of the array manifold matrix, where n = 1, 2, ..., N; for nested arrays with an incident angle of θ n The array steering vector is Where j is a complex unit. This implementation plan is otherwise the same as specific implementation plan one.

[0066] Specific implementation plan three: Step 1 also includes: constructing the infinite norm normalized signal of the received kth snapshot sampling data as follows: Where max{·} is the function for finding the maximum value. This implementation scheme is otherwise the same as specific implementation scheme two.

[0067] Specific implementation plan four: Step two includes the following steps:

[0068] The low-order matrix of the cosine transform sigmoid kernel of the infinity norm normalized signal of the data received by the array elements is defined as follows: In the formula, Representation matrix The Middle Line number Column elements, Here is the weighting constant. and These represent the data vectors of the received k-th snapshot signal, respectively. The first in peacekeeping 3D signal, and satisfying |·| represents the absolute value operation, and (·)* represents the conjugate operation. This is the kernel length of the kernel function. All other aspects of this implementation scheme are the same as in specific implementation scheme three.

[0069] Specific implementation plan five: In step three, the initial amplitude and phase error compensation is performed on the low-order matrix of the cosine transform Sigmoid kernel. For unit array, Design a diagonal loading method: in Let I be the loading factor, and denot I represent the identity matrix. This implementation scheme is otherwise identical to specific implementation scheme four.

[0070] Specific implementation plan six: Step four includes the following steps:

[0071] The amplitude and phase error matrix estimated at the t-th time is: T represents the maximum number of cycles for amplitude and phase error self-correction. Amplitude and phase error compensation is performed on the low-order matrix of the cosine transform sigmoid kernel of the infinite norm normalized signal. in(·) -1 This indicates finding the inverse of a matrix, (·). H This represents finding the conjugate transpose of a matrix; the magnitude error value of the m-th element in the t-th iteration is obtained. Where γ n R is the dispersion factor of the impact noise. t (m, m) represents matrix R t The element in the m-th row and m-th column of R t (1, 1) represents matrix R. t The element in the first row and first column, m = 1, 2, ..., M, sqrt(·) represents the root mean square of the matrix. This implementation scheme is otherwise the same as specific implementation scheme five.

[0072] Specific implementation plan seven: Step five includes the following steps:

[0073] The low-order matrix R of the compensated cosine transform sigmoid kernel is expressed as follows: The maximum correlation delay calculated based on the nested array is: The number of virtual array elements is then: make E is the expected value, uv = h l -h f , h l -h f If ∈H, then the lower-order matrix after compensation and virtual expansion is The expanded guidance matrix is ​​B(θ) = [b(θ1), b(θ2), ..., b(θ)]. N )], where the extended steering vector corresponding to the nth angle is n = 1, 2, ..., N;

[0074] The direction-of-arrival angle is estimated using the maximum likelihood equation. At the t-th estimation, the objective function corresponding to the n-th source is: In the formula, tr(·) is the function for finding the trace of a matrix, and P B(θ) =B(θ)·(B H (θ)B(θ)) -1 ·B H (θ) is the projection matrix of B(θ). This implementation scheme is otherwise the same as specific implementation scheme six.

[0075] Specific implementation plan eight: Step six includes the following steps:

[0076] Set the convergence threshold for phase error to Δθ. When the difference between the phase error estimated in the current iteration and the previous estimate exceeds the convergence threshold, let... It is the steering vector corresponding to the direction of arrival angle of the nth source estimated in the t-th iteration; for the matrix Perform eigenvalue decomposition to obtain the noise subspace U N Define matrix in The estimation of amplitude and phase errors is transformed into a constrained minimum optimization problem: the fitness function established based on the orthogonality of the steering vector and the noise subspace, as well as the constraint of normalizing the amplitude and phase errors of the first array element, is as follows: The constraint condition is ξ H ω = 1, where ξ is the amplitude and phase error vector to be estimated, and ω is an M-dimensional column vector with all elements except the first element being 1 and the rest being 0. The amplitude and phase error matrix at the t-th cycle is estimated as follows: This implementation plan is otherwise the same as Specific Implementation Plan VII.

[0077] If the difference between the phase error estimated in this iteration and the previous estimate is less than or equal to the convergence threshold Δθ, then the quantum lizard algorithm in step seven is executed to solve for the phase error estimation. If, in the iteration number T′, the difference between the current estimate and the previous estimate is still not less than the convergence threshold Δθ, then the quantum lizard algorithm is also used to estimate the phase error.

[0078] Specific implementation plan nine: Step seven includes the following steps:

[0079] (1) Initialize the quantum lizard population, setting the population size to [value missing]. The number of unknown parameters to be optimized is D, the maximum number of iterations is G, and ε represents the number of iterations; for The quantum position of the quantum lizard is randomly initialized within [0, 1]. The random initialization of the quantum position of the quantum lizard is as follows: in d = 1, 2, ..., D, mapped to the corresponding positions as The mapping rule is: in, This represents the lower bound of the d-th dimension variable. Denotes the upper bound of the d-th dimension variable, the d-th dimension variable... The actual location after mapping of a quantum lizard The d-th dimension corresponds to the phase error value of the d-th array element;

[0080] No. The amplitude and phase error estimation matrix mapped by the quantum lizards at the εth iteration is: Where ⊙ denotes matrix dot product; the matrix obtained by performing amplitude and phase error compensation on the covariance matrix is: definition The fitness function is constructed based on the maximum likelihood algorithm. Where tr(·) represents the trace operation;

[0081] The fitness of the quantum lizard's position is calculated based on the fitness function, and the quantum position with the lowest fitness is determined as the globally optimal quantum position.

[0082] (2) When At this point, the quantum lizard is in the encirclement phase. Using an exploration-update strategy, the quantum position is updated through a simplified simulated quantum rotation gate based on the quantum lizard's current quantum position. Then, the... The quantum lizard updates the quantum rotation angle corresponding to the d-th quantum position as follows: Where β is the sensitivity parameter; r1 is a random number between [0, 1]; As a marker to narrow down the search space, Where r2 is Random integers between; hunting operator In the formula, Let d be the dimension of the globally optimal quantum position at iteration ε. This represents the percentage difference between the optimal solution and the current solution in the d-th dimension. Where τ is the sensitivity coefficient, and ζ is a very small positive number. Indicates the first The average position of the candidate solutions

[0083] when At that time, the quantum lizard was in the hunting phase, using the development and update strategy, the first The quantum lizard updates the d-th dimension quantum rotation angle as defined by Where r3 is a random number between [0, 1]; the th The d-th quantum position of a quantum lizard is updated using a simulated quantum rotation gate: in For the first The quantum lizard's d-th dimension quantum position The updated d-dimensional quantum position of the ε+1 generation;

[0084] The first The newly generated d-th dimension quantum position of the quantum lizard Mapped to the first according to the mapping rules The newly generated d-th dimension position of the quantum lizard Calculate the fitness function based on the first The location where the quantum lizard is newly generated fitness value Then, a greedy selection method is used to select the quantum position of the quantum lizard. but Then, the quantum lizards after the greedy selection are sorted in ascending order of fitness. The quantum lizard with the lowest fitness is found and its quantum position is recorded as the globally optimal quantum position up to generation ε+1. This position is then updated to...

[0085] (3) Map the updated quantum lizard position to a position, calculate the fitness value of the new quantum position according to the fitness function, and then update the global optimal quantum position;

[0086] (4) Determine whether the iterative model has reached its maximum number of iterations G; if not, return to step (2) and iterate again; otherwise, output the global optimal quantum position of the quantum lizard population. The globally optimal position obtained after mapping Then the estimated amplitude and phase error matrix at the t-th iteration is: This implementation plan is otherwise the same as Specific Implementation Plan 8.

[0087] The self-correction method (algorithm) for amplitude and phase error of nested arrays under impact noise proposed in this invention is the underlying technical core of this invention, and various products can be derived based on the algorithm.

[0088] Based on the method proposed in this invention, a self-correction and direction-finding system for amplitude and phase error of nested arrays under impact noise is developed using a programming language. This system has program modules corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned self-correction and direction-finding method for amplitude and phase error of nested arrays under impact noise during operation.

[0089] The developed system (software) computer program is stored on a computer-readable storage medium. This computer program is configured to, when called by a processor, implement the steps of the aforementioned method for self-correction of amplitude and phase errors and direction finding of nested arrays under impact noise. In other words, the invention is materialized on a carrier, becoming a computer program product.

[0090] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, application-specific integrated circuits (ASICs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0091] The computational programs (also referred to as programs, software, software applications, or code) of this invention include machine instructions of a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0092] The beneficial effects of the present invention will be described below with reference to specific embodiments.

[0093] Example 1

[0094] For ease of description, this embodiment will refer to the method based on cosine transform sigmoid kernel function, quantum lizard mechanism, diagonal loading method and adaptive self-calibration method as "amplitude and phase error self-calibration method proposed in this invention". The method based on fractional low-order moments of nested array maximum likelihood direction of arrival estimation is referred to as FLOM-NA-ML. The method based on fractional low-order moments of nested array maximum likelihood estimation and self-calibration method is referred to as FLOM-NA-ML-WF. The method based on fractional low-order moments of nested array maximum likelihood estimation and quantum lizard algorithm and adaptive self-calibration method is referred to as FLOM-CTSK-NA-ML-WF. The fractional low-order moment parameters in the comparative direction finding methods are referenced from "Research on DOA Estimation of Coherent Sources under Impulsive Noise Background" published by Wan Wenlong in Harbin Engineering University (Master's Thesis). Other parameters are set in the same way as those in the method designed in this invention.

[0095] The specific parameters for the model simulation are set as follows:

[0096] The nested array subarray 1 has 3 elements (M1=3), subarray 2 has 5 elements (M2=5), and the element spacing is... λ is the signal wavelength of the far-field narrowband signal source, λ = 1. The number of signal sources N = 3, and the direction of arrival of the signal is [-25, 0, 25], in degrees. The number of snapshots for the nested array receiving the signal is set to K = 1000, and the weighting constant is... The kernel length of the kernel function is The array element amplitude error is set to a random number between [0.8, 1.2], the maximum number of self-calibration cycles is T = 10, T′ = 8, and the loading factor is... The convergence threshold is Δθ = 0.15, in degrees. The number of Monte Carlo experiments is set to 100.

[0097] The parameter settings for the quantum lizard method designed in this invention are as follows:

[0098] Population size The maximum number of iterations for the quantum lizard algorithm is G = 100, the sensitivity parameter is β = 0.1, the sensitivity coefficient is τ = 0.1, and the minimum positive number is ζ = 10. -5 .

[0099] exist Figure 2 The phase error is set to a random number between [-q, q], where q is 5, 10, 20, and 30, in degrees. The generalized signal-to-noise ratio is set to 10 dB, and the characteristic index γ of the impulse noise is 1.2. Figures 3 to 6 The phase error is set to a random number between [-20, 20], in degrees. A successful estimation is defined as an absolute deviation of less than 1° between the estimated and true values. Figure 3 and Figure 4 The characteristic index of the medium-impact noise is γ1 = 1.5. Figure 5and Figure 6 The characteristic index in the model is γ = 0.8.

[0100] The simulation results demonstrate that the proposed amplitude and phase error self-correction method exhibits higher direction-finding accuracy and better robustness at low generalized signal-to-noise ratios. Comparison with the FLOM-NA-ML-WF algorithm verifies the effectiveness of the proposed cosine transform-based sigmoid kernel low-order moment in suppressing impulse noise. Compared to the FLOM-CTSK-NA-ML-WF method, it showcases the superiority of the quantum lizard algorithm-based optimization in the latter part of the adaptive phase error estimation method, as well as the accuracy improvement brought by the diagonal loading method designed in the initial loop, which is particularly effective at low generalized signal-to-noise ratios.

[0101] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for self-correction of amplitude and phase error and direction finding of nested arrays under impulse noise, characterized in that, The steps include the following: Step 1: Establish a nested array receiving data model with amplitude and phase errors under impulse noise environment; Step 2: Construct a low-order Sigmoid kernel matrix of the signal using the data received from the array; Step 3: Perform initial amplitude and phase error compensation on the low-order matrix of the cosine transform sigmoid kernel, and set the diagonal matrix of the amplitude and phase error of the first cycle as the identity matrix to improve the direction finding accuracy through the diagonal loading method. Step 4: Further perform amplitude and phase error self-correction on the low-order matrix of the cosine transform sigmoid kernel; Step 5: Perform virtual expansion on the low-order covariance matrix to estimate the direction of arrival; Step 6: Using the angle of arrival estimated in the previous iteration, establish a fitness function based on the orthogonality of the steering vector and the noise subspace and the constraint condition of normalizing the amplitude and phase error of the first array element, and update the amplitude and phase error estimation matrix until the amplitude and phase error estimates converge. Step 7: Design a fitness function, construct a quantum lizard algorithm based on the lizard's biomimetic mechanism, quantum rotation angle, simulated simplified quantum rotation gate, and simulated quantum evolution equation to solve for phase error estimation and obtain the estimated value of the amplitude-phase error matrix; Step 8: Determine whether the number of self-calibration cycles has reached the set maximum value. If it has, output the estimated direction of arrival angle and amplitude and phase error estimation results. If it has not, continue to execute Step 3.

2. The method for self-correction of amplitude and phase error and direction finding of nested arrays under impact noise according to claim 1, characterized in that, The method for constructing the nested array receiving data model with amplitude and phase errors under the impulse noise environment described in step one is as follows: There are N narrowband point sources in the far field of the array, with directions θ = [θ1, θ2, ..., θ3]. N If the incident wavelength is λ, then the k-th snapshot sampled data received by the array with amplitude and phase errors is z(k)=ΓA(θ)s(k)+n(k), where k=1,2,...,K, and K is the maximum number of snapshots. Let Γ be the data vector of the k-th snapshot received by the M×1 dimensional array, where M is the total number of array elements in the nested array; Γ is the amplitude and phase error matrix of the array, where Γ = diag{1, ρ2exp(jφ2), ..., ρ M exp(jφ M )},ρ m and φ m These are the amplitude and phase error of the m-th array element, respectively, where m = 1, 2, ..., M; It is an N×1 dimensional signal vector; Let A(θ) be an M×1 dimensional noise vector, where the noise is a complex impulse noise that is spatially and temporally independent and follows a SaS distribution; A(θ) = [a(θ1), a(θ2), ..., a(θ...]. N )] is an M×N dimensional array manifold matrix, where θ=[θ1, θ2, ..., θ N ] is the direction vector of the information source, a(θ) n ) is the nth guiding vector of the array manifold matrix, where n = 1, 2, ..., N; Nested arrays for incident angle θ n The array steering vector is Where j is the complex unit.

3. The method for self-correction of amplitude and phase error and direction finding of nested arrays under impact noise according to claim 2, characterized in that, Step 1 also includes: constructing the infinite norm normalized signal of the received k-th snapshot sampling data as follows: Where max{·} is the function to find the maximum value.

4. The method for self-correction of amplitude and phase error and direction finding of nested arrays under impact noise according to claim 3, characterized in that, Step two includes the following steps: Define the low-order matrix of the cosine transform sigmoid kernel of the infinity norm normalized signal of the data received by the array elements as follows: In the formula, Representation matrix The Middle Line 1 Column elements, Here is the weighting constant. and These represent the data vectors of the received k-th snapshot signal, respectively. The first in peacekeeping 3D signal, and satisfying |·| represents the absolute value operation, (·) * This indicates the conjugate operation. is the kernel length of the kernel function.

5. The method for self-correction of amplitude and phase error and direction finding of nested arrays under impact noise according to claim 4, characterized in that, In step three, the initial amplitude and phase error compensation is performed on the low-order matrix of the cosine transform sigmoid kernel: For unit array, Design a diagonal loading method: in Let I be the loading factor, and let I denote the identity matrix.

6. The method for self-correction of amplitude and phase error and direction finding of nested arrays under impact noise according to claim 5, characterized in that, Step four includes the following steps: The amplitude and phase error matrix estimated at the t-th time is: T represents the maximum number of cycles for amplitude and phase error self-correction. Amplitude and phase error compensation is performed on the low-order matrix of the cosine transform sigmoid kernel of the infinite norm normalized signal. in(·) -1 This indicates finding the inverse of a matrix, (·). H This represents finding the conjugate transpose of a matrix; the magnitude error value of the m-th element in the t-th iteration is obtained. Where γ n R is the dispersion factor of the impact noise. t (m, m) represents matrix R t The element in the m-th row and m-th column of R t (1, 1) represents matrix R. t The element in the first row and first column, m = 1, 2, ..., M, sqrt(·) represents the root mean square of the matrix.

7. The method for self-correction of amplitude and phase error and direction finding of nested arrays under impact noise according to claim 6, characterized in that, Step five includes the following steps: The low-order matrix R of the compensated cosine transform sigmoid kernel is expressed as follows: The maximum correlation delay calculated based on the nested array is: The number of virtual array elements is then: make E is the mathematical expectation, uv = h l -h f , h l -h f If ∈H, then the lower-order matrix after compensation and virtual expansion is The expanded guidance matrix is ​​B(θ) = [b(θ1), b(θ2), ..., b(θ)]. N )], where the extended steering vector corresponding to the nth angle is The direction-of-arrival angle is estimated using the maximum likelihood equation. At the t-th estimation, the objective function corresponding to the n-th source is: In the formula, tr(·) is the function for finding the trace of a matrix, and P B(θ) =B(θ)·(B H (θ)B(θ)) -1 ·B H (θ) is the projection matrix of B(θ).

8. The method for self-correction of amplitude and phase error and direction finding of nested arrays under impact noise according to claim 7, characterized in that, Step six includes the following steps: Set the convergence threshold for phase error to Δθ. When the difference between the phase error estimated in the current iteration and the previous estimate exceeds the convergence threshold, let... It is the steering vector corresponding to the direction of arrival angle of the nth source estimated in the t-th iteration; for the matrix Perform eigenvalue decomposition to obtain the noise subspace U N Define matrix in The estimation of amplitude and phase errors is transformed into a constrained minimum optimization problem. Based on the orthogonality of the steering vector and the noise subspace, and the constraint of normalizing the amplitude and phase errors of the first array element, the fitness function is established as follows: The constraint condition is ξ H ω = 1, where ξ is the amplitude and phase error vector to be estimated, and ω is an M-dimensional column vector with all elements except the first element being 1 and the rest being 0. The amplitude and phase error matrix at the t-th cycle is estimated as follows: When the difference between the phase error estimated in this iteration and the previous estimate is less than or equal to the convergence threshold Δθ, proceed to step seven.

9. The method for self-correction of amplitude and phase error and direction finding of nested arrays under impact noise according to claim 8, characterized in that, Step seven includes the following steps: (1) Initialize the quantum lizard population, setting the population size to [value missing]. The number of unknown parameters to be optimized is D, the maximum number of iterations is G, and ε represents the number of iterations; the quantum positions of the quantum lizard are randomly initialized as follows: in Mapped to the corresponding position The mapping rule is: in, This represents the lower bound of the d-th dimension variable. Denotes the upper bound of the d-th dimension variable, the... The actual location after mapping of a quantum lizard The d-th dimension corresponds to the phase error value of the d-th array element; No. The amplitude and phase error estimation matrix mapped by the quantum lizards at the εth iteration is: Where ⊙ denotes matrix dot product; the matrix obtained by performing amplitude and phase error compensation on the covariance matrix is: definition The fitness function is constructed based on the maximum likelihood algorithm. Where tr(·) represents the trace operation; The fitness of the quantum lizard's position is calculated based on the fitness function, and the quantum position with the lowest fitness is determined as the globally optimal quantum position. (2) When At this point, the quantum lizard is in the encirclement phase. Using an exploration-update strategy, the quantum position is updated through a simplified simulated quantum rotation gate based on the quantum lizard's current quantum position. Then, the... The quantum lizard updates the quantum rotation angle corresponding to the d-th quantum position as follows: Where β is the sensitivity parameter; r1 is a random number between [0, 1]; As a marker to narrow down the search space, Where r2 is Random integers between; hunting operator In the formula, Let d be the dimension of the globally optimal quantum position at iteration ε. This represents the percentage difference between the optimal solution and the current solution in the d-th dimension. Where τ is the sensitivity coefficient, and ζ is a very small positive number. Indicates the first The average position of each candidate solution when At that time, the quantum lizard was in the hunting phase, using the development and update strategy, the first The quantum lizard updates the d-th dimension quantum rotation angle as defined by Where r3 is a random number between [0, 1]; the th The d-th quantum position of a quantum lizard is updated using a simulated quantum rotation gate: in For the first The quantum lizard's d-th dimension quantum position The updated d-dimensional quantum position of the ε+1 generation; The first The newly generated d-th dimension quantum position of the quantum lizard Mapped to the first according to the mapping rules The newly generated d-th dimension position of the quantum lizard Calculate the fitness function based on the first The location where the quantum lizard is newly generated fitness value Then, a greedy selection method is used to select the quantum position of the quantum lizard. but Then, the quantum lizards after the greedy selection are sorted in ascending order of fitness. The quantum lizard with the lowest fitness is found and its quantum position is recorded as the globally optimal quantum position up to generation ε+1. This position is then updated to... (3) Map the updated quantum lizard position to a position, calculate the fitness value of the new quantum position according to the fitness function, and then update the global optimal quantum position; (4) Determine whether the iterative model has reached its maximum number of iterations G; if not, return to step (2) and iterate again; otherwise, output the global optimal quantum position of the quantum lizard population. The globally optimal position obtained after mapping Then the amplitude and phase error matrix estimated in the t-th cycle is:

10. A self-correction and direction-finding system for amplitude and phase errors of nested arrays under impulse noise, characterized in that, The system has a program module corresponding to the steps of the method described in any one of claims 1 to 9, and executes the steps in the above-described method for amplitude and phase error self-correction and direction finding of nested arrays under impact noise when running.

Images