A method for amplitude and phase error self-correction and direction finding of a coprime array under impulsive noise

Abstract

The application discloses a kind of under impulse noise amplitude-phase error self-correction and direction finding method of coprime array, belong to array signal processing field.The application can realize amplitude-phase error correction and direction of arrival estimation without setting additional correction source, improve the real-time of practical application.The traditional WF self-correction method has higher requirement to initial direction finding accuracy, otherwise it is easy to fall into local optimal value, the method first adopts infinite norm weighting to combine fractional low-order correlation matrix to improve stability under impulse noise, and elite learning quantum sparrow search mechanism is used to search phase error, accurate phase error value can be searched in the case where initial direction finding accuracy is low, and phase error and amplitude error are independently searched and estimated, which can further improve the stability of self-correction method.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of array signal processing, and particularly relates to a method for amplitude-phase error self-correction and direction finding of a co-prime array under impulse noise. BACKGROUND

[0002] The direction of arrival estimation is a research focus in the field of array signal processing, and can be widely applied in battlefield communication, geological exploration and other fields. With the increasingly complex electromagnetic environment of modern civil and military communication, the technical requirements for the direction of arrival estimation are also increasingly high. In the traditional uniform linear array, only the number of signals smaller than the number of array elements can be accurately estimated. In view of this defect, scholars propose a special array, i.e. a co-prime array, which can effectively increase the array aperture to estimate the direction of arrival of signals greater than the number of array elements. However, in actual application, the array may not be in an ideal state, and there may be array position errors, array amplitude-phase errors, array mutual coupling errors and the like. Among them, the most common array amplitude-phase error will seriously affect the direction of arrival estimation accuracy, and even make the direction of arrival estimation algorithm invalid. In addition, the noise background in the actual communication scene is often impulsive, which will also cause the performance of the classical direction of arrival estimation algorithm to decline or even fail. Therefore, it is of great significance and value to study the amplitude-phase error correction method and direction finding method of the co-prime array under impulse noise.

[0003] The most classic amplitude-phase error correction method is the auxiliary source correction method, which can be extended to the amplitude-phase error correction of the co-prime array and can achieve high accuracy. However, the auxiliary source correction method requires the angle of the auxiliary source to be accurately known, and has poor real-time performance, which is not suitable for actual communication scenarios. The classical amplitude-phase error self-correction method proposed by Weiss and Friedlande, i.e. the WF algorithm, is commonly used for amplitude-phase error correction of uniform arrays. However, the algorithm needs to be iterated a large number of times, and only when the amplitude-phase error is small can accurate results be obtained. In the correction of the co-prime array, since the spatial smoothing algorithm is used, the performance of the WF self-correction algorithm will decrease more when the amplitude-phase error is large, and even will fail.

[0004] According to the existing literature, Sun Bing et al. published in System Engineering and Electronics (2020, ISSN 1001-506X, CN 11-2422 / TN) “Mutually prime array DOA estimation method under amplitude and phase error conditions” needs to set up additional mutually prime array elements that have been accurately corrected, which increases the difficulty of implementation in practical applications. Peng Wencan et al. published in Computer Simulation (2019, 1006-9348 (2019) 04-0205-04) “Array amplitude and phase error correction method based on IWO-PSO” needs to add auxiliary sources for correction, which is poor in real-time performance, and only discusses the case of uniform array and Gaussian noise, so the present application proposes an amplitude and phase error correction and direction finding method with good performance in a very low signal-to-noise ratio impact environment, which estimates the phase error and amplitude error independently to improve the estimation accuracy, uses infinite norm weighting combined with fractional low-order covariance to suppress the impact of impact noise, and uses the quantum sparrow search mechanism of elite learning mechanism to allow amplitude and phase error estimation when there is a large error. SUMMARY

[0005] The purpose of the present application is to provide an amplitude and phase error self-correction and direction finding method for mutually prime arrays under impact noise.

[0006] The purpose of the present application is achieved by the following technical solutions:

[0007] An amplitude and phase error self-correction and direction finding method for mutually prime arrays under impact noise, comprising the following steps:

[0008] Step 1: Establish a mathematical model of the mutually prime array receiving signal under impact noise with amplitude and phase errors; calculate the infinite norm normalized fractional low-order correlation matrix of the received signal;

[0009] Construct two uniform arrays A and B combined together to form a mutually prime array consisting of array elements; after K times of array snapping, the signal data matrix received by the array elements is X=[x(1),...,x(K)], and the column vector wherein, array A contains array elements, and array B contains array elements, (·) T represents the transpose operation of the matrix, k∈[1,K]; the data vector h=[h1,h2,..,h K ] where Then the infinite norm normalized array receiving signal matrix can be recorded as X′=[x′(1),...,x′(K)]=[x(1) / h1,...,x(K) / h K ];

[0010] Step 2: Calculate the magnitude error of the coprime matrix elements based on the fractional low-order correlation matrix normalized by the infinite norm;

[0011] Step 3: Initialize the elite quantum sparrow search mechanism population and construct the objective function and fitness function for direction-of-arrival estimation;

[0012] Initialize the elite quantum sparrow search mechanism population, with N individual quantum sparrows in the population. a The maximum number of iterations is T. a The iteration number is labeled t, and t∈[1,T] a ]; During the t-th iteration, the th The quantum position of a quantum sparrow is denoted as and Q is the dimension of the search space, which is equal to the number of information sources. When t=1, each element of the quantum sparrow quantum position is randomly initialized to a uniform random number between [0,1].

[0013] The t-th iteration A quantum sparrow position can be represented as in, and Let $\frac{i}{i}$ be the lower bound and upper bound of the search boundary of the quantum sparrow when the self-calibration algorithm iterates to the $i$th iteration, and let $\frac{i}{i}$ be the lower bound and upper bound of the initial quantum sparrow in the $q$-th dimension when $i=1$. When i > 1, the update formulas for the upper and lower limits of the q-th dimension search boundary in Quantum Sparrow are as follows: Among them, C1, C2, and C3 are optional parameters. It is the direction angle of arrival of the q-th unknown signal source estimated before the i-th cycle self-calibration; it can generate the q-th unknown signal source direction angle. The guidance vector estimated by the quantum sparrow is Among them All It is the first The positions of the virtual uniform array elements involved in the calculation. The maximum likelihood equation can then be written as In the t-th iteration, the... The formula for calculating the fitness value of a quantum sparrow's position is:

[0014] Step 4: Execute the elite learning quantum sparrow search mechanism to estimate the direction of arrival;

[0015] Step 5: Check if the number of iterations t is equal to the maximum number of iterations T. a ;

[0016] Step 6: Perform phase error estimation and correction;

[0017] Step 7: judge whether the self-correcting cycle number reaches the set value.

[0018] The application can also include:

[0019] 1. The amplitude error vector estimated in step 2 is The estimated phase error vector is denoted as The estimated amplitude and phase error diagonal matrix is The maximum cycle number of self-correction is I, when i < I, the amplitude and phase error diagonal matrix estimated in the i-th cycle is used to compensate the amplitude and phase error of the fractional low-order correlation matrix, and the compensated fractional low-order correlation matrix is denoted as Where (·) -1 is the matrix inversion operation, (·) H is the matrix conjugate transpose operation;

[0020] When i = 1, is the unit matrix; after correction, the amplitude error value update formula of the m-th array element is Where sqrt(·) is the square root operation, γ n is the dispersion coefficient of the impact noise.

[0021] 1. In step 4, define the variable to store the quantum position corresponding to the optimal quantum sparrow in the i-th cycle until the t-th iteration, denoted as At the same time, define the variable and record the optimal fitness value, suboptimal fitness value and sub-suboptimal fitness value at this iteration, and the corresponding quantum positions are and

[0022] 2. Define the variable that rises nonlinearly with the rising of the iteration number t of the optimization algorithm Define the elite guide vector Where the weighting coefficient is defined as Integer f ∈ [1, 3]; calculate the fitness of all quantum sparrows and sort them, define the quantum sparrows with the top 20% fitness as producers, the quantum sparrows with the last 80% fitness as followers, and randomly select 20% of the quantum sparrows from all quantum sparrows as guards.

[0023] 3. In step 5, the maximum iteration number is T a , the optimal fitness position is output and the direction of arrival vector estimated in this cycle is updated Where, If not, let t = t + 1 and return to step 4 to continue iteration.

[0024] 2, the number of self-correcting cycles in step 6 , at this time the direction of arrival estimation error is larger, the elite learning quantum sparrow search mechanism with higher stability is used for phase error estimation;

[0025] The coprime array is divided into two uniform arrays A and B. Taking uniform array A as an example, it contains Array elements, the array element spacing is Its array position is The position set of the array element in the uniform array A in the original coprime array is Among them, the first The sub-array element in the first Array element in the original coprime array, The fractional low-order covariance matrix of the sub-array composed of the elements of the corresponding position extracted from the fractional low-order covariance matrix normalized by the infinity norm is denoted as The element in the first Row, the first Column of the fractional low-order covariance matrix of the sub-array is

[0026] The elite learning quantum sparrow search mechanism is initialized, the number of quantum sparrows in the population is N b , the maximum number of iterations is T b , and the iteration index is The quantum position of the first Quantum sparrow in the first Iteration can be expressed as And Define the variable To store the position corresponding to the best quantum sparrow before the first Iteration, let the upper and lower limits of the known phase error be U1 and L1, respectively, and let The estimated phase error of the first Array element in the original coprime array before the first i self-correcting cycle, the value corresponds to the phase error of the first Array element in the first i self-correcting cycle in the uniform linear array A; when the amplitude and phase error self-correcting cycle number i = 1, the first Dimension of the lower and upper limits of the search boundary of the quantum sparrow is equal to the lower and upper limits of the phase error, i.e. When i > 1, the update formula of the first Dimension of the upper and lower limits of the quantum sparrow position is Where V1, V2 and V3 are self-selected parameters; the first The first Quantum sparrow output in the first Dimension position can be expressed as The amplitude error vector of the uniform subarray A is The first element of the amplitude error vector of the uniform subarray A is The second element of the amplitude error vector of the uniform subarray A is The third element of the amplitude error vector of the uniform subarray A is The fourth element of the amplitude error vector of the uniform subarray A is The fifth element of the amplitude error vector of the uniform subarray A is The sixth element of the amplitude error vector of the uniform subarray A is The seventh element of the amplitude error vector of the uniform subarray A is The eighth element of the amplitude error vector of the uniform subarray A is The ninth element of the amplitude error vector of the uniform subarray A is The phase error vector of the first quantum sparrow at the first iteration is The phase error vector of the first quantum sparrow at the second iteration is The steering vector matrix of the uniform subarray A is generated by the direction of arrival angle estimated in the previous step The maximum likelihood estimation equation is written according to the steering vector and the fractional low-order correlation matrix after amplitude and phase error correction The quantum position fitness function of the first quantum sparrow at the first iteration is The quantum position fitness function of the first quantum sparrow at the second iteration is The quantum position fitness function of the first quantum sparrow at the third iteration is The phase error of the uniform subarray A is estimated by the elite learning quantum sparrow search mechanism in step four, and the phase vector and the phase error vector are updated by the historical optimal position of the quantum sparrow search mechanism after the iteration number reaches the maximum iteration number T b The phase vector and the phase error vector are updated by the historical optimal position of the quantum sparrow search mechanism after the iteration number reaches the maximum iteration number T The phase vector and the phase error vector are updated by the historical optimal position of the quantum sparrow search mechanism after the iteration number reaches the maximum iteration number T The phase vector and the phase error vector are updated by the historical optimal position of the quantum sparrow search mechanism after the iteration number reaches the maximum iteration number T The phase vector and the phase error vector are updated by the historical optimal position of the quantum sparrow search mechanism after the iteration number reaches the maximum iteration number T The phase vector and the phase error vector are updated by the historical optimal position of the quantum sparrow search mechanism after the iteration number reaches the maximum iteration number T

[0027] The phase vector and the phase error vector are updated by the historical optimal position of the quantum sparrow search mechanism after the iteration number reaches the maximum iteration number T The uniform subarray B contains The position set of the array elements of the uniform subarray B in the original coprime array is The first uniform array B corresponds to the first array element in the original coprime array The second uniform array B corresponds to the second array element in the original coprime array The phase error vector set of the uniform subarray B is estimated according to the phase error estimation method of the subarray A, and is denoted as The phase error vector of the original coprime array is updated as The elements of each position are equal to the elements of the corresponding positions of the phase error vectors of the two uniform subarrays The phase vector and the phase error vector are updated by the historical optimal position of the quantum sparrow search mechanism after the iteration number reaches the maximum iteration number T The phase vector and the phase error vector are updated by the historical optimal position of the quantum sparrow search mechanism after the iteration number reaches the maximum iteration number T The phase vector and the phase error vector are updated by the historical optimal position of the quantum sparrow search mechanism after the iteration number reaches the maximum iteration number T

[0028] 4、When , set Perform eigenvalue decomposition on the fractional low-order covariance matrix, and select the characteristic vectors corresponding to the small eigenvalues to form the noise subspace E N , set Let w = [1, 0,..., 0] T For Cyclic vector, at this time, the phase error update formula is Where angle(·) represents the operation of taking the angle of a complex number, and the phase error vector can be generated according to the phase error value

[0029] 5、Step 7, the self-correcting cycle number reaches the set value, then output the arrival angle estimation Phase error vector And amplitude error vector If the set value is not reached, let i = i + 1 continue to execute step 2.

[0030] The beneficial effects of the present application are:

[0031] The present application is aimed at the shortcomings and deficiencies of the existing impact noise environment under the coprime array amplitude and phase error correction and direction of arrival estimation method, and the present application designs an amplitude and phase error correction and direction of arrival estimation method based on the elite quantum sparrow search mechanism under the impact noise environment. Through simulation, compared with the classical self-correcting estimation algorithm, the method proposed in the present application has higher effectiveness and reliability under the condition of impact noise and large amplitude and phase error.

[0032] Compared with the existing coprime array amplitude and phase error correction technology under impact noise, the present application does not need to set an additional correction source, and can realize amplitude and phase error correction and direction of arrival estimation, and improves the real-time performance of practical application. The traditional WF self-correcting method has a higher requirement for the initial direction finding accuracy, otherwise it is easy to fall into local optimal value. The present method first adopts infinite norm weighting combined with fractional low-order correlation matrix enhancement algorithm to improve the stability under impact noise, and adopts elite learning quantum sparrow search mechanism to search for phase error, which can search for accurate phase error value under the condition of low initial direction finding accuracy, and independently searches and estimates the phase error and amplitude error, which can further improve the stability of the self-correcting method. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 The amplitude and phase error correction and direction finding method designed by the present application is shown in the figure;

[0034] Figure 2 The elite learning quantum sparrow search mechanism is shown in the figure;

[0035] Figure 3 The relationship curve between the direction finding angle root mean square error and the upper and lower limits of the phase error is shown in the figure;

[0036] Figure 4 The relationship curve between the direction finding angle root mean square error and the generalized signal-to-noise ratio is shown in the figure;

[0037] Figure 5 Fig. 3 is a spectrum peak search diagram before and after phase error correction. DETAILED DESCRIPTION

[0038] The application will be further described below with reference to the accompanying drawings.

[0039] Step one, establish the mathematical model of the coprime array receiving signal under the impact noise and the existing amplitude and phase error. And calculate the infinite norm normalized fraction low-order correlation matrix of the receiving signal.

[0040] The constructed coprime array is composed of two uniform sub-arrays A and B. It is assumed that the wavelength of the signal of the unknown signal source is λ, and the unit interval of the two array elements is Array A contains array elements, and the array element interval is The array element position of array A is Array B contains array elements, and the array element interval is The array element position is Wherein, and the two numbers are coprime.

[0041] Combining the two uniform arrays A and B together, the final coprime array is composed of array elements. It is assumed that there are Q unknown signal sources emitting signals, and the angles between the signal directions of the signal sources and the array normal are θ1, θ2,..., θ Q , the k-th snapshot data of the array x(k) = ΓA0(θ) s(k) + N(k), k ∈ [1, K], A0(θ) = [a1(θ1),...,a Q (θ Q )]. The amplitude and phase error diagonal matrix of the array is Wherein, m , is the amplitude error and phase error of the m-th sub-array element, and the amplitude and phase errors of the remaining array elements are normalized with the first array element as the reference array element. There are ρ m = 1, After K times of snapshots, the signal data matrix received by the array element is X = [x(1),...,x(K)], and the column vector Wherein (·) T represents the transpose operation of the matrix, and k ∈ [1, K]. Let the data vector h = [h1, h2,..., h K ], wherein The infinite norm normalized array receiving signal matrix can be recorded as X' = [x'(1),...,x'(K)] = [x(1) / h1,...,x(K) / h K ].

[0042] The mutually prime array receives the normalized fractional low-order correlation matrix C floc The element in the gth row and hth column of C can be expressed as Where (·) * is the conjugate operation, x′ g (k) and x′ h (k) are the values of the kth snapshot data received by the gth and hth array elements, respectively, after infinite norm normalization. g, p is an optional calculation constant, and 0 < p ≤ 1.

[0043] Step two, calculate the amplitude error of the mutually prime array elements according to the infinite norm normalized fractional low-order correlation matrix.

[0044] Let the estimated amplitude error vector of the amplitude-phase error self-correction cycle to the ith time be The estimated phase error vector is denoted as The estimated amplitude-phase error diagonal matrix is Let the maximum cycle number of the self-correction be I. When i < I, use the amplitude-phase error diagonal matrix estimated by the ith cycle to compensate the fractional low-order covariance matrix, and denote the compensated fractional low-order correlation matrix as Where (·) -1 is the matrix inversion operation, (·) H is the matrix conjugate transpose operation. When i = 1, is the unit matrix. After correction, the mth array element amplitude error value update formula is Where sqrt(·) is the square root operation, γ n is the dispersion coefficient of the impulse noise.

[0045] Step three, initialize the elite quantum sparrow search mechanism population, and construct the target function and fitness function of the direction of arrival estimation.

[0046] Let the estimated phase error vector of the amplitude-phase error self-correction algorithm at the ith cycle be When i = 1, the initial phase error vector can be denoted as The amplitude error vector updated in step two is The diagonal matrix can be obtained ⊙ is the vector dot product operation, which is used to compensate the fractional low-order covariance matrix, and let the compensated fractional low-order covariance matrix be Vectorize the compensated fractional low-order covariance matrix to obtain a column vector of dimension n Then generate a virtual array from the original mutually prime array, and denote the array element position vector of the virtual array as Where, η s =d s -v, Vector ν is the position vector of the original coprime array. After removing redundancy from vector η and sorting it, continuous vectors are extracted. The set of positions of elements that make up a uniform virtual linear array element. Use it to extract column vectors Obtain the received signal vector of the virtual uniform array element Then, a spatial smoothing algorithm is used to divide the virtual array into... There are overlapping subarrays, each containing A uniform virtual array element is used to stitch together the virtual received data vectors of the subarray into a single array. dimensional matrix Wherein, the l-th column vector The elements correspond to the virtual uniform array received signal vector. The Okay. At this time. It can be regarded as a The signal reception matrix of the next snapshot, then its covariance matrix R i It can be estimated from the column vectors of the matrix. in

[0047] Initialize the elite quantum sparrow search mechanism population, setting the number of individual quantum sparrows in the population to N. a The maximum number of iterations is T. a The iteration number is labeled t, and t∈[1,T] a In the t-th iteration, the... The quantum position of a quantum sparrow is denoted as and Q is the dimension of the search space, which is equal to the number of information sources. When t=1, each element of the quantum sparrow quantum position is randomly initialized to a uniform random number between [0,1].

[0048] In this iteration, the t-th iteration... A quantum sparrow position can be represented as in, and Let $\frac{i}{i}$ be the lower bound and upper bound of the search boundary of the quantum sparrow when the self-calibration algorithm iterates to the $i$th iteration, and let $\frac{i}{i}$ be the lower bound and upper bound of the initial quantum sparrow in the $q$-th dimension when $i=1$. When i > 1, the update formulas for the upper and lower limits of the q-th dimension search boundary in Quantum Sparrow are as follows: Among them, C1, C2, and C3 are optional parameters. It is the direction angle of arrival of the q-th unknown signal source estimated before the i-th cycle of self-calibration. The q-th unknown signal source can be generated. The steering vector estimated by the quantum sparrow only is Where All have The first The virtual uniform array position participating in the calculation, The maximum likelihood equation can be written as At the tth iteration, the first The fitness value calculation formula of the quantum sparrow position only is

[0049] Step four, execute the elite learning quantum sparrow search mechanism to estimate the direction of arrival.

[0050] Define the variable Store the quantum position corresponding to the best quantum sparrow from the i th cycle to the t th iteration, denoted as At the same time, define the variable And Record the optimal fitness value, suboptimal fitness value and sub-suboptimal fitness value at this iteration, and the corresponding quantum position is And

[0051] Define the variable Define the elite steering vector Where the weighting coefficient is defined as Integer f ∈ [1,3]. Calculate the fitness of all quantum sparrows and sort them. Define the top 20% of the quantum sparrows as producers, the last 80% of the quantum sparrows as followers, and randomly select 20% of the quantum sparrows from all quantum sparrows as sentinels.

[0052] (1) The update formula of the qth dimensional quantum rotation angle of the first The producer is

[0053]

[0054] Where, Is a random number between 0 and 1, Is a random number between 0 and 1, S t Is a constant between 0.5 and 1 set by the user, Is a standard normal distribution random number.

[0055] (2) The update formula of the qth dimensional quantum rotation angle of the first The follower is

[0056]

[0057] Where, is a standard normal distribution random number, is a Q-dimensional column vector of all 1s, let ζ be a Q-dimensional random column vector whose elements are 1 or -1, ζ + = ζ T (ζζ T ) -1 , is the coordinate of the qth-dimensional quantum position of the elite guide vector at the tth iteration. is the coordinate of the qth-dimensional quantum position of the sparrow with the worst fitness at the tth iteration.

[0058] (3) The update formula of the qth-dimensional quantum rotation angle of the jth guard is

[0059]

[0060] where, is the fitness of the jth quantum sparrow at the tth generation, is a Gaussian random number, is a uniform random number between [-1, 1], is the worst fitness value at the current iteration, and ε is a positive number as small as possible, usually ε = 10 -50 to prevent the denominator from being 0 in the calculation.

[0061] Subsequently, the quantum position of the sparrow is updated according to the quantum rotation angle, and the update formula of the qth-dimensional quantum position of the jth quantum sparrow is Step five, detect whether the iteration number t is equal to the maximum iteration number T a , if yes, output the best fitness position

[0062] and update the direction-of-arrival vector at this cycle estimation where, if not, let t = t + 1 return to step four to continue iteration. Step six, phase error estimation and correction.

[0063] When the self-correcting cycle number

[0064] is greater than or equal to 2, the phase error estimation is performed using the elite learning quantum sparrow search mechanism with higher stability.

[0065] The coprime array is divided into two uniform arrays A and B. Taking the uniform array A as an example, it contains array elements, and the array element spacing is its array position is ​​​Let the set of positions of the array elements in the uniform array A in the original coprime array be . Among them, the The subarray element in the uniform array A corresponds to the first element in the original coprime array. Each array element, The fractional low-order covariance matrix formed by extracting elements at corresponding positions from the infinite norm normalized fractional low-order covariance matrix is ​​denoted as . its first line, number The elements of the column are

[0066] The elite learning quantum sparrow search mechanism is initialized, with the number of quantum sparrow individuals in the population being N. b The maximum number of iterations is T. b The iteration label is No. During the nth iteration, the 1st The quantum position of a quantum sparrow can be represented as and Define variables Used to store the first The position corresponding to the best quantum sparrow up to the nth iteration, assuming the known upper and lower limits of the phase error are U1 and L1 respectively, let... It is the first in the original coprime array The phase error estimated by the i-th array element before the i-th cycle, whose value corresponds to the i-th phase error in the uniform linear array A. The phase error of each element in the i-th self-calibration cycle. When the number of amplitude and phase error self-calibration cycles i = 1, the lower and upper bounds of the quantum sparrow's search boundary are... The dimensions are equal to the lower and upper limits of the phase error, respectively. When i > 1, the upper and lower limits of the quantum sparrow's position are... The update formula for dimension is: Among them, V1, V2, and V3 are optional parameters. Let the first... During the nth iteration, the 1st The first output of the quantum sparrow Dimensional position can be represented as Let the amplitude error vector of the uniform subarray A be... its first element in It is the first coprime array estimated in step two. The amplitude error of each array element No. In the next iteration, the amplitude and phase error estimation matrix ⊙ represents the dot product of vectors. It is the first During the nth iteration, the 1st The phase error vector generated by the quantum sparrow is used. The amplitude and phase error are corrected on the fractional low-order correlation matrix of the subarray using the amplitude and phase error estimation matrix, resulting in the matrix. Based on the direction-of-arrival angle estimated in the previous step, the steering vector matrix of the uniform subarray A can be generated as follows: Based on the steering vector and the fractional low-order correlation matrix after amplitude and phase error correction, the maximum likelihood estimation equation can be written as follows: The first can be obtained During the nth iteration, the 1st The quantum position fitness function of a quantum sparrow is: Subsequently, the phase error of the uniform subarray A is estimated using the elite learning quantum sparrow search mechanism in step four, until the maximum number of iterations T is reached. b Then, the phase vector is updated by the historical optimal position of the quantum sparrow search mechanism. and phase error vector in

[0067] For a uniform subarray B, it contains There are 1 array elements, and let the set of their positions in the original coprime array be . Among them, the The subarray element in the uniform array B corresponds to the first element in the original coprime array. Each array element, Following the phase error estimation method for subarray A, the set of phase error vectors for subarray B can be estimated and denoted as... Let the updated phase error vector of the original coprime array be... The elements at each position are respectively equal to the elements at the corresponding positions of the phase error vectors of the two uniform subarrays. in

[0068] when At that time, set Perform eigenvalue decomposition on the fractional low-order covariance matrix and select the eigenvalues ​​corresponding to the smallest eigenvalues. The noise subspace E is composed of 1 eigenvector. N ,set up Let w = [1, 0, ..., 0] T for With a column vector of dimension, the phase error update formula is as follows: Here, angle(·) represents the operation of taking an angle from a complex number, and a phase error vector can be generated from the phase error value.

[0069] Step 7: Determine if the number of self-calibration cycles has reached the set value. If so, output the estimated angle of arrival. Phase error vector And amplitude error vector If not, let i = i + 1 continue to perform step two.

[0070] According to Figure 3 And Figure 4 , the direction of arrival of the three unknown signals is-20°, 0° and 20° respectively, the amplitude error is set to a random number between 0.8 and 1.2, I is set to 6, and the number of Monte Carlo experiments is 100. And set And The direction of arrival of the three unknown signals is-20°, 0° and 20° respectively, the amplitude error is set to a random number between 0.8 and 1.2, I is set to 6, and the number of Monte Carlo experiments is 100.

[0071] In addition, in Figure 3 , the phase error is set to a random number between [-o, o], o is 5°, 10°, 15°, 25° and 35° respectively, the generalized signal-to-noise ratio is set to 10dB, parameters C1=30, C2=2.2, C3=1.5, V1=1.4o, V2=1.8 and V3=1.5, in Figure 4 , the generalized signal-to-noise ratio is set to 1dB, 4dB, 6dB, 9dB, 12dB and 15dB, the phase error is set to a random number between [-20°, 20°], parameters C1=30, C2=2.2, C3=1.5, V1=28, V2=1.8 and V3=1.5, and from the final result, it can be known that the performance of WF appears a large decline under a larger phase error and impact noise background, and estimation failure is prone to occur, the amplitude and phase error self-correction method proposed in the patent has good stability under different phase error conditions. Under the condition of 20° phase error, the WF self-correction method almost fails, the self-correction method proposed in the patent has poor effect at very low signal-to-noise ratio, and the performance is improved obviously when the signal-to-noise ratio becomes larger.

[0072] According to Figure 5 , the spectral peak search diagram of the amplitude and phase error self-correction method based on the elite learning quantum sparrow search mechanism proposed in the application is set, the impact noise parameter is α=1.6, the calculation parameter p=0.75, and the array is set as Figure 3The experiments are the same. The directions of arrival of the three signals are set to-15°, 0° and 15° respectively, the generalized signal-to-noise ratio is 15dB, the amplitude error is set to a random number between 0.8 and 1.2, the phase error is set to a random number between [-25°, 25°], and the parameters I=6, C1=30, C2=2.2, C3=1.5, V1=35, V2=1.8 and V3=1.5 are set, the search interval is set to 0.01°, and the method of directly performing spectral peak searching without amplitude and phase error correction is marked as FLOC-MUSIC. It can be seen that, in the uncorrected case, the FLOC-MUSIC spectral peak appears to be offset, the offset is reduced after correction, and a more accurate direction of arrival angle can be estimated.

[0073] The above only describes preferred embodiments of the present application and is not intended to limit the present application. The present application can be variously changed and modified by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for self-correction of amplitude and phase error and direction finding of a coprime array under impulse noise, characterized in that: Includes the following steps: Step 1: Establish a mathematical model for the received signal of a coprime array under impulse noise and amplitude-phase error; calculate the low-order correlation matrix of the received signal with normalized fractional infinity norm. Construct two uniform arrays A and B, and combine them to form a coprime array consisting of [number of arrays]. The array consists of several array elements; after K snapshots, the signal data matrix received by the array elements is X = [x(1),...,x(K)], and the column vectors are... Among them, array A contains Array B contains array elements, and array B contains array elements. Each array element, (·) T This represents the operation of transposing a matrix, k∈[1,K]; the data vector h=[h1,h2,..,h K ],in The array received signal matrix after normalization by the infinite norm is denoted as X′=[x′(1),...,x′(K)]=[x(1) / h1,...,x(K) / h K ]; Step 2: Calculate the magnitude error of the coprime matrix elements based on the fractional low-order correlation matrix normalized by the infinite norm; Step 3: Initialize the elite quantum sparrow search mechanism population and construct the objective function and fitness function for direction-of-arrival estimation; Initialize the elite quantum sparrow search mechanism population, with N individual quantum sparrows in the population. a The maximum number of iterations is T. a The iteration number is labeled t, and t∈[1,T] a ]; During the t-th iteration, the th The quantum position of a quantum sparrow is denoted as and Q is the dimension of the search space, which is equal to the number of information sources. When t=1, each element of the quantum sparrow quantum position is randomly initialized to a uniform random number between [0,1]. The t-th iteration The quantum sparrow positions are represented as in, and Let $\frac{i}{i}$ be the lower bound and upper bound of the search boundary of the quantum sparrow when the self-calibration algorithm iterates to the $i$th iteration, and let $\frac{i}{i}$ be the lower bound and upper bound of the initial quantum sparrow in the $q$-th dimension when $i=1$. When i > 1, the update formulas for the upper and lower limits of the q-th dimension search boundary in Quantum Sparrow are as follows: Among them, C1, C2, and C3 are optional parameters. It is the estimated direction angle of arrival of the q-th unknown signal source before the i-th cycle self-calibration; generating the q-th unknown signal source direction angle before the i-th cycle self-calibration; The guidance vector estimated by the quantum sparrow is Among them All It is the first The positions of the virtual uniform array elements involved in the calculation. The maximum likelihood equation can then be written as In the t-th iteration, the... The formula for calculating the fitness value of a quantum sparrow's position is: Step 4: Execute the elite learning quantum sparrow search mechanism to estimate the direction of arrival; Step 5: Check if the number of iterations t is equal to the maximum number of iterations T. a ; Step 6: Perform phase error estimation and correction; Step 7: Determine whether the number of self-calibration cycles has reached the set value.

2. The method for self-correction of amplitude and phase error and direction finding of a coprime array under impulse noise as described in claim 1, characterized in that: In step 2, the amplitude error vector estimated at the i-th iteration of the amplitude and phase error self-correction cycle is: The estimated phase error vector is denoted as The estimated amplitude and phase error diagonal matrix is ​​as follows The maximum number of self-calibration cycles is I. When i < I, the amplitude and phase error diagonal matrix estimated in the i-th cycle is used to compensate for the amplitude and phase error of the fractional low-order covariance matrix, and the compensated fractional low-order correlation matrix is ​​denoted as . in(·) -1 It's the matrix inversion operation, (·) H It is the matrix conjugate transpose operation; When i = 1 It is a unit array; After correction, the formula for updating the amplitude error value of the m-th array element is: Here, sqrt(·) is the operation for finding the root mean square. γ n It is the dispersion factor of the impact noise.

3. The method for self-correction of amplitude and phase error and direction finding of a coprime array under impulse noise as described in claim 1, characterized in that: Define variables in step 4 The quantum position corresponding to the best quantum sparrow from the i-th iteration up to the t-th iteration is denoted as . At the same time, define variables and Record the optimal fitness value, the second-best fitness value, and the second-best fitness value in this iteration, respectively, with the corresponding quantum positions as follows: and Define a variable that increases nonlinearly with the number of iterations t of the optimization algorithm. Define elite guiding vector The weighting coefficient is defined as follows: Integer f∈[1,3]; calculate and sort the fitness of all quantum sparrows, define the top 20% of quantum sparrows as producers, the bottom 80% as followers, and then randomly select 20% of all quantum sparrows as vigilants.

4. The method for self-correction of amplitude and phase error and direction finding of a coprime array under impulse noise as described in claim 1, characterized in that: The maximum number of iterations in step 5 is T. a Then output the optimal fitness position. And update the direction-of-arrival vector during the current iteration estimation. in, If not, then let t = t + 1 and return to step 4 to continue the iteration.

5. The method for self-correction of amplitude and phase error and direction finding of a coprime array under impulse noise as described in claim 1, characterized in that: Step 6 Self-calibration loop count At this time, the direction of arrival estimation error is relatively large, so the more stable elite learning quantum sparrow search mechanism is used to estimate the phase error. Divide the coprime array into two uniform arrays A and B. Taking uniform array A as an example, it contains... There are array elements, and the spacing between the array elements is... Its array position is The set of positions of the array elements in the uniform array A in the original coprime array is: Among them, the The subarray element in the uniform array A corresponds to the first element in the original coprime array. Each array element, The fractional low-order covariance matrix formed by extracting elements at corresponding positions from the infinite norm normalized fractional low-order covariance matrix is ​​denoted as . Its first line, the first The elements of the column are The elite learning quantum sparrow search mechanism is initialized, with N individual quantum sparrows in the population. b The maximum number of iterations is T. b The iteration label is No. During the nth iteration, the 1st The quantum position of a quantum sparrow is represented as and Define variables Used to store the first The position corresponding to the best quantum sparrow up to the nth iteration, assuming the known upper and lower limits of the phase error are U1 and L1 respectively, let... It is the first in the original coprime array The phase error estimated by the i-th array element before the i-th cycle, whose value corresponds to the i-th phase error in the uniform linear array A. The phase error of each element in the i-th self-calibration cycle; when the number of amplitude and phase error self-calibration cycles is i=1, the lower and upper bounds of the quantum sparrow's search boundary are... The dimensions are equal to the lower and upper limits of the phase error, respectively. When i > 1, the first of the upper and lower limits of the quantum sparrow's position. The update formula for dimension is: Among them, V1, V2, and V3 are optional parameters; the first During the nth iteration, the 1st The first output of the quantum sparrow Dimensional position is represented as The amplitude error vector of the uniform subarray A is its first element in It is the first coprime array estimated in step two. The amplitude error of each array element No. In the next iteration, the amplitude and phase error estimation matrix ⊙ represents the dot product of vectors. It is the first During the nth iteration, the 1st A phase error vector is generated by a quantum sparrow; the amplitude and phase error are corrected by applying the amplitude and phase error estimation matrix to the fractional low-order correlation matrix of the subarray, resulting in the matrix. Based on the direction-of-arrival angle estimated in the previous step, the steering vector matrix for generating the uniform subarray A is: Based on the steering vector and the fractional low-order correlation matrix after amplitude and phase error correction, the maximum likelihood estimation equation is written as follows: Dedi During the nth iteration, the 1st The quantum position fitness function of a quantum sparrow is: Subsequently, the phase error of the uniform subarray A is estimated using the elite learning quantum sparrow search mechanism in step four, until the maximum number of iterations T is reached. b Then, the phase vector is updated by the historical optimal position of the quantum sparrow search mechanism. and phase error vector in For a uniform subarray B, it contains There are 1 array elements, and let the set of their positions in the original coprime array be . Among them, the The subarray element in the uniform array B corresponds to the first element in the original coprime array. Each array element, Following the phase error estimation method for subarray A, the set of phase error vectors for subarray B is estimated and denoted as... Let the updated phase error vector of the original coprime array be... The elements at each position are respectively equal to the elements at the corresponding positions of the phase error vectors of the two uniform subarrays. in when At that time, set Perform eigenvalue decomposition on the fractional low-order covariance matrix and select the eigenvalues ​​corresponding to the smallest eigenvalues. The noise subspace E is composed of 1 eigenvector. N ,set up Let w = [1, 0, ..., 0] T for With a column vector of dimension, the phase error update formula is as follows: Where angle(·) represents the operation of taking an angle from a complex number, generating a phase error vector based on the phase error value.

6. The method for self-correction of amplitude and phase error and direction finding of a coprime array under impulse noise as described in claim 1, characterized in that: If the number of self-calibration cycles in step 7 reaches the set value, then the estimated angle of arrival will be output. Phase error vector and amplitude error vector If the set value is not reached, set i = i + 1 and continue to execute step 2.

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