Method and device for determining direction of arrival of co-prime array under non-uniform noise

Abstract

The invention discloses a method and a device for determining the direction of arrival of a co-prime array under non-uniform noise. The method comprises the following steps: acquiring an array signal received by a signal receiving module; the signal receiving module is used for determining an array covariance matrix of the array signals, and comprises a plurality of array elements and an array element co-prime array with spacing distances among the plurality of array elements; a second noise covariance matrix is used for replacing the first noise covariance matrix in the array covariance matrix, a reconstructed covariance matrix is obtained, the second noise covariance matrix is a diagonal matrix, and the diagonal element of the second noise covariance matrix is the minimum value of the diagonal element in the first noise covariance matrix; and performing spatial spectrum analysis on the reconstructed covariance matrix by using a spatial spectrum estimation algorithm to obtain the direction of arrival of each target signal in the array signals. According to the invention, the technical problem that the direction of arrival of the array signal cannot be accurately determined under the condition of non-uniform noise is solved.

Description

Technical Field

[0001] The present invention relates to the field of radio, and in particular to a method and a device for determining a direction of arrival of a mutual prime array under non-uniform noise. Background Art

[0002] Direction of Arrival (DOA) estimation is an important research area in spatial spectrum estimation. Traditional high-resolution DOA estimation methods, such as multiple signal classification (MUSIC) and rotation-invariant technique (ESPRIT), were originally proposed for uniform linear arrays. These methods have advantages in improving estimation accuracy and resolution, but usually require increasing the number of array elements to expand the array aperture, resulting in a significant increase in algorithm complexity. In underdetermined DOA estimation scenarios, the performance of these methods will degrade significantly.

[0003] In order to meet the above challenges, researchers have proposed a method to use coprime sampling data for DOA estimation. Compared with traditional uniform linear sampling, using an array containing coprime elements for data sampling can form a differential joint array, whose virtual uniform linear array (ULA) has greater degrees of freedom. In recent years, many scholars have conducted in-depth research on the application of coprime array sampling data in DOA estimation, and found that these methods can generate longer virtual ULAs while reducing mutual coupling effects, and achieve DOA estimation that is not limited by the number of physical array elements through subspace algorithms, showing good performance.

[0004] However, existing studies usually assume that the noise is independent Gaussian white noise, but the spatial distribution of noise in actual environments is often uneven. If the subspace algorithm based on eigendecomposition is continued to be used, subspace leakage may occur, thus affecting the performance of DOA estimation.

[0005] Although DOA estimation in non-uniform noise environments has been studied for many years, the commonly used method is to achieve robust DOA estimation by pre-whitening the non-uniform noise, but these methods usually require the number of array elements to be at least three times the number of signal sources. In addition, although DOA estimation methods based on maximum likelihood and subspace methods can iteratively estimate noise parameters, their high computational complexity limits their practicality.

[0006] In order to reduce the computational complexity and avoid convergence problems, some non-iterative methods have been proposed. However, these methods also require that the number of array elements is greater than the number of signal sources, which limits their application in underdetermined DOA estimation. The introduction of compressed sensing (CS) and low-rank matrix recovery theory provides new solutions, but some methods may also mistakenly remove some useful signals when removing noise, resulting in performance degradation.

[0007] Currently, no effective solution has been proposed to the problem that the direction of arrival of array signals cannot be accurately determined under the condition of non-uniform noise. Summary of the invention

[0008] The embodiments of the present invention provide a method and device for determining the direction of arrival of a coprime array under non-uniform noise, so as to at least solve the technical problem that the direction of arrival of an array signal cannot be accurately determined under the condition of non-uniform noise.

[0009] According to one aspect of an embodiment of the present invention, a method for determining a coprime array direction of arrival under non-uniform noise is provided, comprising: obtaining an array signal received by a signal receiving module, wherein the signal receiving module comprises: a plurality of array elements, a coprime array of array elements with a spacing distance between the plurality of array elements, the array signal being a signal to be analyzed received by the plurality of array elements, the signal to be analyzed comprising: a target signal and a noise signal that is mutually prime under non-uniform noise; determining an array covariance matrix of the array signal, wherein the array covariance matrix comprises: a signal covariance matrix corresponding to the target signal and a first noise covariance matrix corresponding to the noise signal, the matrix dimensions of the signal covariance matrix and the first noise covariance matrix being the same as the array The number of elements is the same, each covariance matrix element in the signal covariance matrix corresponds to the target signal with different wave path difference, the first noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the first noise covariance matrix are the sum of the target signal and the noise signal; the first noise covariance matrix in the array covariance matrix is ​​replaced by the second noise covariance matrix to obtain a reconstructed covariance matrix, wherein the second noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the second noise covariance matrix are the minimum values ​​of the diagonal elements in the first noise covariance matrix; the reconstructed covariance matrix is ​​subjected to spatial spectrum analysis using a spatial spectrum estimation algorithm to obtain the wave arrival direction of each target signal in the array signal.

[0010] Optionally, after replacing the first noise covariance matrix in the array covariance matrix with the second noise covariance matrix to obtain a reconstructed covariance matrix, the method further includes: obtaining the coprime array of the array elements of the signal receiving module, wherein the multiple array elements in the signal receiving module include: a plurality of first array elements arranged according to a first spacing distance, and a plurality of second array elements arranged according to a second spacing distance, the first spacing distance and the second spacing distance are coprime integers, the first spacing distance is used to determine a first coprime array corresponding to the first array element, and the second spacing distance is used to determine a second coprime array corresponding to the second array element , the array element coprime matrix is ​​the union of a first coprime array and a second coprime array; performing virtual difference and difference on the array element coprime array to obtain an enhanced coprime array, wherein the enhanced coprime array represents the spacing distance between multiple virtual array elements, and the multiple virtual array elements include: a first virtual array element belonging to the first array element, and a second virtual array element belonging to the second array element; based on the enhanced coprime array, the reconstructed covariance matrix is ​​expanded to obtain an enhanced covariance matrix, wherein the enhanced covariance matrix is ​​used to represent the signals to be analyzed received by the multiple virtual array elements; and the enhanced covariance matrix is ​​used as the reconstructed covariance matrix.

[0011] Optionally, expanding the reconstructed covariance array based on the enhanced coprime array to obtain the enhanced covariance array includes: determining an element difference joint array based on the first coprime array and the second coprime array, wherein each element in the element difference joint array represents the difference in the interval distance between the first array element and the second array element, and there is a corresponding relationship between the elements in the element difference joint array and the elements in the reconstructed covariance matrix; after determining the enhanced coprime array based on the first coprime array and the second coprime array, expanding the element difference joint array to obtain the enhanced difference joint array, wherein the enhanced coprime array The matrix array includes: a first enhanced array corresponding to the first virtual array element, and a second enhanced array corresponding to the second virtual array element, each element in the enhanced difference joint array represents the difference in interval distance between the first virtual array element and the second virtual array element; according to the correspondence between the elements in the element difference joint array and the elements in the reconstructed covariance matrix, the reconstructed covariance matrix is ​​expanded in combination with the enhanced difference joint array determined according to the element difference joint array to obtain the enhanced covariance matrix, wherein the elements in the enhanced difference joint array and the elements in the enhanced covariance matrix have a corresponding relationship.

[0012] Optionally, using a spatial spectrum estimation algorithm to perform spatial spectrum analysis on the reconstructed covariance matrix to obtain the direction of arrival of each target signal in the array signal includes: using a preset parameter matrix to replace the signal covariance matrix in the reconstructed covariance matrix for fitting to obtain the preset parameter matrix after fitting, wherein the preset parameter matrix includes: signal parameters corresponding to each target signal in the array signal; using the spatial spectrum estimation algorithm to perform spatial spectrum analysis on the preset parameter matrix to obtain the direction of arrival of each target signal in the array signal.

[0013] Optionally, a preset parameter matrix is ​​used to replace the signal covariance matrix in the reconstructed covariance matrix for fitting, and obtaining the preset parameter matrix after fitting includes: detecting the singularity of the reconstructed covariance matrix; when the reconstructed covariance matrix is ​​non-singular, fitting the preset parameter matrix to the reconstructed covariance matrix based on a minimization criterion.

[0014] Optionally, the method further comprises: when the reconstructed covariance matrix is ​​singular, fitting the preset parameter matrix to the reconstructed covariance matrix using a preset criterion, wherein the preset criterion is: Z is a free variable matrix to be optimized, T(u) is the preset parameter matrix, is the reconstructed covariance matrix.

[0015] Optionally, when the reconstructed covariance matrix is ​​singular, fitting the preset parameter matrix to the reconstructed covariance matrix using a preset criterion includes: projecting the preset parameter matrix onto each preset matrix in a preset matrix set in turn, and updating alternately, wherein the preset matrices include: a first preset matrix, a second preset matrix and a third preset matrix, the rank number in the first preset matrix is ​​not greater than a preset rank threshold, the second preset matrix is ​​a constant diagonal matrix, and the target matrix formed by the third preset matrix and the free variable matrix is ​​a semi-positive definite matrix; when the projections of the preset parameter matrix on each of the preset matrices satisfy the convergence conditions, outputting the preset parameter matrix.

[0016] According to another aspect of an embodiment of the present invention, a device for determining the direction of arrival of a coprime array under non-uniform noise is also provided, comprising: an acquisition module, used to acquire an array signal received by a signal receiving module, wherein the signal receiving module comprises: a plurality of array elements, the array signal is a signal to be analyzed received by the plurality of array elements, and the signal to be analyzed comprises: a target signal and a noise signal; a determination module, used to determine an array covariance matrix of the array signal, wherein the array covariance matrix comprises: a signal covariance matrix corresponding to the target signal and a first noise covariance matrix corresponding to the noise signal, the matrix dimensions of the signal covariance matrix and the first noise covariance matrix are the same as the number of the array elements, and the signal covariance matrix is ​​a first noise covariance matrix corresponding to the noise signal. Each covariance matrix element in the matrix corresponds to the target signal with different wave path difference, the first noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the first noise covariance matrix are the sum of the target signal and the noise signal; a reconstruction module is used to replace the first noise covariance matrix in the array covariance matrix with a second noise covariance matrix to obtain a reconstructed covariance matrix, wherein the second noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the second noise covariance matrix are the minimum values ​​of the diagonal elements in the first noise covariance matrix; an analysis module is used to perform spatial spectrum analysis on the reconstructed covariance matrix using a spatial spectrum estimation algorithm to obtain the wave direction of each target signal in the array signal.

[0017] According to another aspect of an embodiment of the present invention, a non-volatile storage medium is further provided, in which a computer program is stored, wherein the device where the non-volatile storage medium is located executes the above-mentioned method for determining the direction of arrival of a coprime array under non-uniform noise by running the computer program.

[0018] According to another aspect of an embodiment of the present invention, a computer program product is provided, comprising computer instructions, which, when executed by a processor, implement the steps of the method for determining the direction of arrival of a coprime array under non-uniform noise.

[0019] In the above embodiment of the present application, an array signal received by a signal receiving module is obtained, wherein the signal receiving module includes: a plurality of array elements, an array of mutually prime array elements with a spacing distance between the plurality of array elements, the array signal is a signal to be analyzed received by the plurality of array elements, and the signal to be analyzed includes: a target signal and a noise signal mutually primed under non-uniform noise; an array covariance matrix of the array signal is determined, wherein the array covariance matrix includes: a signal covariance matrix and a first noise covariance matrix, the matrix dimensions of the signal covariance matrix and the first noise covariance matrix are the same as the number of array elements, each covariance matrix element in the signal covariance matrix corresponds to a target signal with a different wave path difference, the first noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the first noise covariance matrix are the sum of the target signal and the noise signal; the array covariance matrix is ​​replaced by the second noise covariance matrix The first noise covariance matrix in the array is used to obtain a reconstructed covariance matrix, wherein the second noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the second noise covariance matrix are the minimum values ​​of the diagonal elements in the first noise covariance matrix; the spatial spectrum estimation algorithm is used to perform spatial spectrum analysis on the reconstructed covariance matrix to obtain the wave direction of each target signal in the array signal, so that by replacing the first noise covariance matrix in the array covariance matrix with the second noise covariance matrix, the influence of non-uniform noise can be suppressed, and then the wave direction analysis is performed based on the reconstructed covariance matrix with the influence of non-uniform noise suppressed, so that the wave direction obtained by the analysis can be made more accurate, thereby achieving the technical effect of improving the accuracy of determining the wave direction, and solving the technical problem that the wave direction of the array signal cannot be accurately determined under the condition of non-uniform noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0021] Figure 1 is a flow chart of a method for determining a direction of arrival of a coprime array under non-uniform noise according to an embodiment of the present invention;

[0022] Figure 2 is a schematic diagram of an augmented coprime array of signals according to an embodiment of the present invention;

[0023] Figure 3 is a schematic diagram of an augmented coprime array structure consisting of two sparse uniform linear arrays according to an embodiment of the present invention;

[0024] Figure 4 is a schematic diagram of a weight coefficient according to an embodiment of the present invention;

[0025] Figure 5is a schematic diagram of a normalized spatial spectrum of a covariance sparse reconstruction (CSR) algorithm according to an embodiment of the present invention;

[0026] Figure 6 is a schematic diagram of a normalized spatial spectrum of a matrix-based MUSIC (MC-MUSIC) algorithm according to an embodiment of the present invention;

[0027] Figure 7 is a schematic diagram of a normalized spatial spectrum of a matrix completion based on linear prediction (MCLP) algorithm according to an embodiment of the present invention;

[0028] Figure 8 is a schematic diagram of a normalized spatial spectrum of an RGLS according to an embodiment of the present invention;

[0029] Fig. 9 is a schematic diagram of RMSE performance when an input SNR and the number of snapshots are 500 according to an embodiment of the present invention;

[0030] Fig.10 is a schematic diagram of a result when the number of input snapshots and the input SNR are 5 dB according to an embodiment of the present invention;

[0031] Fig.11 is a schematic diagram of a device for determining a direction of arrival of a coprime array under non-uniform noise according to an embodiment of the present invention;

[0032] Fig.12 It is a structural block diagram of a computer terminal according to an embodiment of the present invention. DETAILED DESCRIPTION

[0033] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0034] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0035] According to an embodiment of the present invention, an embodiment of a method for determining the direction of arrival of a coprime array under non-uniform noise is provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0036] Figure 1 FIG. 4 is a flow chart of a method for determining a direction of arrival of a coprime array under non-uniform noise according to an embodiment of the present invention. Figure 1 As shown, the method comprises the following steps:

[0037] Step S102, acquiring an array signal received by a signal receiving module, wherein the signal receiving module includes: a plurality of array elements, an array element coprime array with a spacing distance between the plurality of array elements, the array signal is a signal to be analyzed received by the plurality of array elements, and the signal to be analyzed includes: a target signal and a noise signal coprime under non-uniform noise;

[0038] Step S104, determining an array covariance matrix of the array signal, wherein the array covariance matrix includes: a signal covariance matrix corresponding to the target signal and a first noise covariance matrix corresponding to the noise signal, the matrix dimensions of the signal covariance matrix and the first noise covariance matrix are the same as the number of array elements, each covariance matrix element in the signal covariance matrix corresponds to a target signal with a different wave path difference, the first noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the first noise covariance matrix are the sum of the target signal and the noise signal;

[0039] Step S106, using the second noise covariance matrix to replace the first noise covariance matrix in the array covariance matrix to obtain a reconstructed covariance matrix, wherein the second noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the second noise covariance matrix are the minimum values ​​of the diagonal elements in the first noise covariance matrix;

[0040] Step S108, performing spatial spectrum analysis on the reconstructed covariance matrix using a spatial spectrum estimation algorithm to obtain the direction of arrival of each target signal in the array signal.

[0041] In the above embodiment of the present application, an array signal received by a signal receiving module is obtained, wherein the signal receiving module includes: a plurality of array elements, an array of mutually prime array elements with a spacing distance between the plurality of array elements, the array signal is a signal to be analyzed received by the plurality of array elements, and the signal to be analyzed includes: a target signal and a noise signal mutually primed under non-uniform noise; an array covariance matrix of the array signal is determined, wherein the array covariance matrix includes: a signal covariance matrix and a first noise covariance matrix, the matrix dimensions of the signal covariance matrix and the first noise covariance matrix are the same as the number of array elements, each covariance matrix element in the signal covariance matrix corresponds to a target signal with a different wave path difference, the first noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the first noise covariance matrix are the sum of the target signal and the noise signal; the array covariance matrix is ​​replaced by the second noise covariance matrix The first noise covariance matrix in the array is used to obtain a reconstructed covariance matrix, wherein the second noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the second noise covariance matrix are the minimum values ​​of the diagonal elements in the first noise covariance matrix; the spatial spectrum estimation algorithm is used to perform spatial spectrum analysis on the reconstructed covariance matrix to obtain the wave direction of each target signal in the array signal, so that by replacing the first noise covariance matrix in the array covariance matrix with the second noise covariance matrix, the influence of non-uniform noise can be suppressed, and then the wave direction analysis is performed based on the reconstructed covariance matrix with the influence of non-uniform noise suppressed, so that the wave direction obtained by the analysis can be made more accurate, thereby achieving the technical effect of improving the accuracy of determining the wave direction, and solving the technical problem that the wave direction of the array signal cannot be accurately determined under the condition of non-uniform noise.

[0042] In the above step S102, the signal receiving module may be an array antenna, on which a plurality of array elements are distributed, and each array element is a sensor in the array antenna.

[0043] In the above step S102, the array signal includes: a plurality of signals to be analyzed, each of which is received by a corresponding array element.

[0044] In the above step S102, the signal received by the array element is a signal to be analyzed, and the signal to be analyzed includes a target signal including valid information and a noise signal that interferes with the target signal.

[0045] In the above step S102, the arrangement of array elements in the signal receiving module can be represented by an augmented coprime array (ie, an array element coprime array).

[0046] It should be noted that the present application mainly studies a signal receiving module composed of two array elements with different spacing distances. In the signal receiving module, the distance between the array elements is an augmented coprime array composed of two coprime arrays (ie, a coprime array of array elements).

[0047] Figure 2 is a schematic diagram of an augmented coprime array of a signal according to an embodiment of the present invention, such as Figure 2 As shown, the augmented coprime array includes: two sparse uniform linear arrays (such as a first coprime array and a second coprime array), each sparse uniform linear array is a subarray of the augmented coprime array, wherein the first coprime array has 2M array elements, and the spacing distance between the array elements (i.e., the first spacing distance) is Nd, and the second coprime array has Nd array elements, and the spacing distance between the array elements (i.e., the second spacing distance) is Md, wherein M and N are coprime integers, and M<N, and d is half of the wavelength of the incident signal.

[0048] Figure 3 is a schematic diagram of an augmented coprime array structure composed of two sparse uniform linear arrays according to an embodiment of the present invention, such as Figure 3 As shown, the entire array of the augmented coprime array (i.e., the element difference joint array) has P = 2M + N-1 physical elements, and the element position is expressed as The set of integers It is expressed as:

[0049] Alternatively, if Figure 2 As shown, two sparse uniform linear enhanced conjugate arrays are constructed; Figure 3 As shown, an enhanced conjugate array is composed of two sparse uniform linear enhanced conjugate arrays.

[0050] Optionally, a pair of coprime integers M=3 and N=5 are selected to deploy an augmented coprime array, which results in a total number of physical sensors P=2M+N-1=10, where the physical sensors are used to receive signals.

[0051] Optionally, in order to intuitively analyze the array elements of the coprime array Given the concept of its difference union array, it is defined as the set in,

[0052] Figure 4 is a schematic diagram of a weight coefficient according to an embodiment of the present invention, such as Figure 4 As shown, the collection If there are identical element values, All the different element values ​​d in x The set formed is defined as d x exist The number of repetitions in the weight coefficient w(d x )express, Figure 4 The different element values ​​and corresponding weight coefficients of the element difference joint array are shown. According to the coprime array property, the position of the virtual array element in the element difference joint array is expressed as Among them, the set of integers It is expressed as: Among them, the number of non-negative elements is the array degree of freedom, which directly determines the maximum number of estimable signals of the coprime array.

[0053] In the above step S104, the array covariance matrix can represent the signals to be analyzed received by multiple array elements in the form of a matrix, and the matrix dimension of the array covariance matrix is ​​the same as the number of array elements in the signal receiving module; the signals to be analyzed include target signals and noise signals, so the array covariance matrix can be represented by a signal covariance matrix corresponding to the target signal and a first noise covariance matrix corresponding to the noise signal, and the matrix dimensions of the corresponding signal covariance matrix and the first noise covariance matrix are also the same as the number of array elements in the signal receiving module.

[0054] As an optional embodiment, assume that K far-field narrowband signals are incident on the coprime array (ie, signal receiving module) respectively, and the arrival angle (ie, wave arrival direction) is: θ = [θ1, θ2, ..., θ K ], the array output data (i.e., array signal) can be expressed as: in, is the output data of the array (i.e., array signal), S(t)=[s1(t),s2(t),...,s K (t)] T are K incident signal data vectors, N(t)=[n1(t),n2(t),...,n 2M+N-1 (t)] T is the noise vector, A=[a(θ1),a(θ2),...,a(θ K )] is the manifold matrix, is the orientation vector, l i d,i∈{2,3,…,P} represents the position of the i-th sensor in the coprime array.

[0055] It should be noted that the manifold matrix is ​​a matrix composed of the steering vectors of the signals received by each sensor in the array, wherein each column represents the response of a sensor to different arrival angles.

[0056] It should be noted that the steering vector is a key tool in array signal processing. It is used to describe the relationship between the array received signal and the signal source arrival angle, and is used to calculate the array response under different arrival angles (Direction of Arrival, DOA). Each column of the steering vector matrix represents a specific arrival angle, and each row represents an array element in the array. The steering vector matrix can be used to calculate the array response under different arrival angles.

[0057] Optionally, assuming that the incident signals are independent and uncorrelated, the covariance matrix of the coprime array received data (ie, the array covariance matrix) can be obtained as: Where E{·} represents the expectation operation, H represents the conjugate transpose, and R S =E{S(t)S H (t)} represents the signal covariance matrix and Q = E{N(t)N H (t)} respectively the noise covariance matrix (ie the first noise covariance matrix).

[0058] Optionally, let the noise power vector be Under ideal conditions, when the background noise is uniform white noise, At this time, Q = σI; when the background noise is non-uniform white noise, the noise powers are not equal, and the noise covariance matrix (that is, the first noise covariance matrix) is expressed as: Where diag{·} represents a diagonal matrix. In practical applications, the number of snapshots T is limited. The sampling covariance matrix is ​​equivalent to:

[0059] As an optional example, for The array covariance matrix in Expand it and you get the following:

[0060]

[0061] in, Represents the kth incident signal power, B = πMsinθ k , C=π(2M-1)Nsinθ k , D = π((2M-1)NN)sinθ k .

[0062] Optionally, each element of the array covariance matrix is ​​further analyzed to reveal the signal characteristics corresponding to each path difference, thereby providing necessary detailed information for accurate signal source positioning. It can also be expressed as follows:

[0063]

[0064] in, Represents the covariance matrix elements corresponding to different path differences.

[0065] In the above step S104, the signal covariance matrix is:

[0066]

[0067] In the above step S104, the first noise covariance matrix is:

[0068]

[0069] It should be noted that non-uniform noise mainly affects the diagonal elements of the covariance matrix, and the diagonal elements are the sum of the signal and noise power and are all real numbers. In order to suppress the influence of non-uniform noise, the minimum value of the diagonal elements is selected to replace other diagonal elements to complete the reconstruction of the covariance matrix (that is, to generate a reconstructed covariance matrix), which can be expressed as follows: Where I represents the identity matrix. Further, the integer set of virtual element positions of the difference joint array (such as the element difference joint array) is and the covariance matrix of the coprime array receiving data (such as the array covariance matrix) It can be seen that there is a corresponding relationship between the virtual array element positions of the difference joint array (such as the array element difference joint array) and the elements in the reconstructed received data covariance matrix (such as the array covariance matrix) R′.

[0070] Optionally, considering the influence of background noise, multiple covariance matrix elements corresponding to the same virtual array element are not equal. To improve the robustness of the estimation result, an average operation is performed on each element in the reconstructed covariance matrix to obtain:

[0071]

[0072] Among them, R′ i (d x ) represents the i-th covariance matrix element in the reconstructed covariance matrix R′ corresponding to the same path difference.

[0073] In the above step S106, the diagonal elements in the second noise covariance matrix are The minimum value in .

[0074] As an optional embodiment, after replacing the first noise covariance matrix in the array covariance matrix with the second noise covariance matrix to obtain the reconstructed covariance matrix, the method further includes: obtaining a coprime array of array elements of the signal receiving module, wherein the multiple array elements in the signal receiving module include: a plurality of first array elements arranged according to a first spacing distance, and a plurality of second array elements arranged according to a second spacing distance, the first spacing distance and the second spacing distance are coprime integers, the first spacing distance is used to determine a first coprime array corresponding to the first array element, and the second spacing distance is used to determine a second coprime array corresponding to the second array element. A coprime array is provided, wherein the array element coprime matrix is ​​the union of the first coprime array and the second coprime array; virtual differences and differences are performed on the array element coprime array to obtain an enhanced coprime array, wherein the enhanced coprime array represents the spacing distance between multiple virtual array elements, and the multiple virtual array elements include: a first virtual array element belonging to the first array element, and a second virtual array element belonging to the second array element; based on the enhanced coprime array, a reconstructed covariance matrix is ​​expanded to obtain an enhanced covariance matrix, wherein the enhanced covariance matrix is ​​used to represent the signals to be analyzed received by the multiple virtual array elements; and the enhanced covariance matrix is ​​used as the reconstructed covariance matrix.

[0075] In the above-mentioned embodiment of the present application, the spacing distance between multiple array elements in the signal receiving module can be represented by an array element coprime array. By performing virtual differentiation and difference on the array element coprime array, the expansion of the array element coprime array can be realized to obtain an enhanced coprime array. The enhanced coprime array can represent the spacing distance between multiple virtual array elements obtained after the virtual expansion of the array elements in the signal receiving module, and then the virtual array elements can simulate the reception of the signal to be analyzed. Therefore, based on the enhanced coprime array, the reconstructed covariance matrix can be expanded to obtain an enhanced covariance matrix, and then the enhanced covariance matrix is ​​used as the reconstructed covariance matrix, and then the spatial spectrum estimation algorithm is used to perform spatial spectrum analysis on the expanded reconstructed covariance matrix to obtain the wave direction of each target signal in the array signal, thereby obtaining a high-precision DOA estimation while achieving an improvement in the degree of freedom.

[0076] As an alternative example, by Figure 4 The weight coefficients shown in Figure 2 show that There are holes in the matrix. In order to facilitate the use of the least squares method GLS, virtual differences can be performed on the coprime arrays and interpolated to generate a matrix consisting of The enhanced virtual ULA (i.e., uniform linear array, which is a collection of sensor elements equidistantly distributed along a straight line) represented by (that is, the enhanced coprime array) is: Correspondingly, the sample covariance matrix (also known as the reconstructed covariance matrix) Expanded to the enhanced covariance matrix

[0077] Specifically, combined with the virtual interpolation technique, the single snapshot vector z is obtained by vectorizing R′ (i.e. reconstructing the covariance matrix) to construct the Toeplitz matrix (That is, the enhanced covariance matrix). Similarly, the enhanced covariance matrix can be It is regarded as the sum of the target signal and the noise signal and is expressed as: Where I is the identity matrix, is the noise power (ie, the noise signal), and the noise-free signal part (such as the signal covariance matrix corresponding to the target signal) is: Among them, c k =||s k: ||2>0, ||φ k: ||2=1.

[0078] It should be noted that the Toeplitz matrix is ​​a constant diagonal matrix, which is characterized by the same elements on each diagonal line from the upper left to the lower right.

[0079] As an optional embodiment, expanding the reconstructed covariance array based on the enhanced coprime array to obtain the enhanced covariance array includes: determining an element difference joint array based on the first coprime array and the second coprime array, wherein each element in the element difference joint array represents the difference in the spacing distance between the first element and the second element, and there is a corresponding relationship between the elements in the element difference joint array and the elements in the reconstructed covariance matrix; after determining the enhanced coprime array based on the first coprime array and the second coprime array, expanding the element difference joint array to obtain the enhanced difference joint array, wherein the enhanced coprime array includes: a first enhanced array corresponding to the first virtual element, and a second enhanced array corresponding to the second virtual element, and each element in the enhanced difference joint array represents the difference in the spacing distance between the first virtual element and the second virtual element; according to the corresponding relationship between the elements in the element difference joint array and the elements in the reconstructed covariance matrix, combining the enhanced difference joint array determined according to the element difference joint array, expanding the reconstructed covariance matrix to obtain the enhanced covariance matrix, wherein there is a corresponding relationship between the elements in the enhanced difference joint array and the elements in the enhanced covariance matrix.

[0080] In the above-mentioned embodiment of the present application, based on the first coprime array and the second coprime array, an array element difference joint array can be obtained, and there is a corresponding relationship between the elements in the array element difference joint array and the elements in the reconstructed covariance matrix. Then, when the array element coprime array is expanded to an enhanced coprime array, the first coprime array and the second coprime array are also expanded to obtain a first enhanced array after the expansion of the first coprime array and a second enhanced array after the expansion of the second coprime array. Based on the first enhanced array and the second enhanced array, an enhanced difference joint array can be obtained, and the enhanced difference joint array also inherits the corresponding relationship between the elements in the array element difference joint array and the elements in the reconstructed covariance matrix. Therefore, there is a corresponding relationship between the elements in the enhanced difference joint array and the elements in the enhanced covariance matrix. Based on the corresponding relationship, the reconstructed covariance matrix can be expanded to obtain an enhanced covariance matrix, thereby realizing the expansion of the reconstructed covariance array.

[0081] It should be noted that the difference joint array, also called the differential array, is a set of differences between the actual array element positions of coprime arrays, and is symmetric about the origin.

[0082] As an optional embodiment, using a spatial spectrum estimation algorithm to perform spatial spectrum analysis on the reconstructed covariance matrix to obtain the wave direction of each target signal in the array signal includes: using a preset parameter matrix to replace the signal covariance matrix in the reconstructed covariance matrix for fitting to obtain a fitted preset parameter matrix, wherein the preset parameter matrix includes: signal parameters corresponding to each target signal in the array signal; using a spatial spectrum estimation algorithm to perform spatial spectrum analysis on the preset parameter matrix to obtain the wave direction of each target signal in the array signal.

[0083] In the above embodiments of the present application, the signal covariance matrix corresponds to the target signal. In order to accurately determine the arrival direction of the target signal, the signal covariance matrix can be analyzed. Then, in order to determine the signal covariance matrix from the reconstructed covariance matrix, the preset parameter matrix of the signal covariance matrix can be fitted to the reconstructed covariance matrix, so that the preset parameter matrix can replace the signal covariance matrix. Then, based on the fact that the preset parameter matrix can fit the reconstructed covariance matrix, the preset parameter matrix can represent the target signal, and then the spatial spectrum analysis is performed on the preset parameter matrix using the spatial spectrum estimation algorithm to obtain the arrival direction of each target signal.

[0084] As an optional example, the least squares method GLS is a gridless DOA estimation method based on covariance fitting. Specifically, it converts the relevant parameter matrix (that is, the preset parameter matrix) of the signal covariance matrix R0 into Fit to the sample covariance matrix (ie reconstruct the covariance matrix) Among them, the preset parameter matrix R can be expressed as:

[0085]

[0086] It should be noted that is a PSD Toeplitz matrix of rank K (i.e., a semi-positive constant diagonal matrix) that is the same as R0. The least squares method GLS uses the Hermitian Toeplitz property of R to establish This avoids the highly nonlinear function formed by directly using DOA as a parameter.

[0087] As an optional embodiment, a preset parameter matrix is ​​used to replace the signal covariance matrix in the reconstructed covariance matrix for fitting, and the preset parameter matrix after fitting is obtained, including: detecting the singularity of the reconstructed covariance matrix; when the reconstructed covariance matrix is ​​non-singular, fitting the preset parameter matrix into the reconstructed covariance matrix based on a minimization criterion.

[0088] In the above-mentioned embodiments of the present application, when a preset parameter matrix is ​​used to replace the signal covariance matrix in the reconstructed covariance matrix for fitting, different fitting criteria can be selected for fitting according to the singularity of the reconstructed covariance matrix. For example, when the reconstructed covariance matrix is ​​non-singular, the preset parameter matrix can be fitted to the reconstructed covariance matrix based on the minimization criterion, and the preset parameter matrix can be obtained according to the fitting result.

[0089] Optionally, the minimization criterion is In reconstructing the covariance matrix When is non-singular, covariance fitting is achieved by minimizing the criterion formula.

[0090] As an optional embodiment, the method further includes: when the reconstructed covariance matrix is ​​singular, fitting the preset parameter matrix to the reconstructed covariance matrix using a preset criterion, wherein the preset criterion is: Z is a free variable matrix to be optimized, T(u) is a preset parameter matrix, is the reconstructed covariance matrix.

[0091] In the above embodiments of the present application, when the reconstructed covariance matrix is ​​singular, the preset parameter matrix can be fitted to the reconstructed covariance matrix based on a preset criterion, and the preset parameter matrix can be obtained according to the fitting result.

[0092] Optionally, the preset criteria is In reconstructing the covariance matrix When is singular, covariance fitting is achieved through the preset criterion formula.

[0093] Optionally, the preset parameter matrix R=T(u) is substituted into the preset criterion to obtain the adjusted preset criterion:

[0094]

[0095] Where T(u)≥0 represents a positive semi-definite (PSD) matrix, is a free variable matrix to be optimized. When R=R0=T(u), we have definition Divide the target in the preset criteria by Then we have:

[0096] It should be noted that, from the minimization of atomic norm, we can know that minimizing This is equivalent to minimizing the atomic norm:

[0097]

[0098] The atomic norm is the convex relaxation of the atomic l0 norm:

[0099]

[0100] Therefore, minimizing the atomic l0 norm is equivalent to minimizing rank(R). This means that rank(R) and are related, and the latter is a compact version of the former, so The convex optimization problem in is reduced to the following non-convex optimization problem, and the final preset criterion is obtained:

[0101]

[0102] As an optional embodiment, when the reconstructed covariance matrix is ​​singular, fitting the preset parameter matrix to the reconstructed covariance matrix using a preset criterion includes: projecting the preset parameter matrix onto each preset matrix in a preset matrix set in turn, and updating alternately, wherein the preset matrices include: a first preset matrix, a second preset matrix, and a third preset matrix, the rank in the first preset matrix is ​​not greater than a preset rank threshold, the second preset matrix is ​​a constant diagonal matrix, and the target matrix formed by the third preset matrix and the free variable matrix is ​​a semi-positive definite matrix; when the projection of the preset parameter matrix on each preset matrix satisfies the convergence condition, the preset parameter matrix is ​​output.

[0103] In the above-mentioned embodiments of the present application, the preset parameter matrix is ​​determined by using the alternating projection technology, which can significantly reduce the computational burden caused by the complex iterative process.

[0104] It should be noted that the rank minimization problem is an NP-hard problem. Even if it is converted into a convex optimization problem, it still requires a lot of calculations. The AP method shows the advantages of efficiency and accuracy based on non-convex matrix completion technology. Therefore, when solving the rank minimization problem, convex relaxation is no longer required. Instead, the preset parameter matrix R that satisfies the following conditions is found: the preset parameter matrix R is a low-rank matrix; the preset parameter matrix R is a Toeplitz matrix; the target matrix F composed of the preset parameter matrix R and the free variable matrix Z (as shown in the constraints in the above non-convex optimization problem) is a semi-positive definite (PSD) matrix.

Claims

1. A method for determining the direction of arrival of a coprime array under non-uniform noise, characterized in that: include: Acquire an array signal received by a signal receiving module, wherein the signal receiving module comprises: a plurality of array elements, a mutually prime array of array elements with a spacing distance between the plurality of array elements, the array signal is a signal to be analyzed received by the plurality of array elements, and the signal to be analyzed comprises: a target signal and a mutually prime noise signal under non-uniform noise; Determine an array covariance matrix of the array signal, wherein the array covariance matrix includes: a signal covariance matrix corresponding to the target signal and a first noise covariance matrix corresponding to the noise signal, the matrix dimensions of the signal covariance matrix and the first noise covariance matrix are the same as the number of the array elements, each covariance matrix element in the signal covariance matrix corresponds to the target signal with different wave path difference, the first noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the first noise covariance matrix are the sum of the target signal and the noise signal; Replacing the first noise covariance matrix in the array covariance matrix with a second noise covariance matrix to obtain a reconstructed covariance matrix, wherein the second noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the second noise covariance matrix are the minimum values ​​of the diagonal elements in the first noise covariance matrix; A spatial spectrum estimation algorithm is used to perform spatial spectrum analysis on the reconstructed covariance matrix to obtain the direction of arrival of each target signal in the array signal.

2. The method according to claim 1, characterized in that: After replacing the first noise covariance matrix in the array covariance matrix with the second noise covariance matrix to obtain a reconstructed covariance matrix, the method further includes: Acquire the coprime array of the array elements of the signal receiving module, wherein the plurality of the array elements in the signal receiving module include: a plurality of first array elements arranged according to a first spacing distance, and a plurality of second array elements arranged according to a second spacing distance, the first spacing distance and the second spacing distance are coprime integers, the first spacing distance is used to determine a first coprime array corresponding to the first array element, the second spacing distance is used to determine a second coprime array corresponding to the second array element, and the array element coprime matrix is ​​a union of the first coprime array and the second coprime array; Performing virtual differentiation and difference on the coprime array of array elements to obtain an enhanced coprime array, wherein the enhanced coprime array represents the spacing distance between a plurality of virtual array elements, and the plurality of virtual array elements include: a first virtual array element belonging to the first array element, and a second virtual array element belonging to the second array element; Expanding the reconstructed covariance matrix based on an enhanced coprime array to obtain an enhanced covariance matrix, wherein the enhanced covariance matrix is ​​used to represent the signals to be analyzed received by the plurality of virtual array elements; The enhanced covariance matrix is ​​used as the reconstructed covariance matrix.

3. The method according to claim 2, characterized in that The reconstructed covariance array is expanded based on the enhanced coprime array to obtain the enhanced covariance array, including: Determine an element difference joint array based on the first coprime array and the second coprime array, wherein each element in the element difference joint array represents a difference in spacing distance between the first array element and the second array element, and there is a corresponding relationship between the elements in the element difference joint array and the elements in the reconstructed covariance matrix; After determining the enhanced coprime array based on the first coprime array and the second coprime array, expanding the element difference joint array to obtain an enhanced difference joint array, wherein the enhanced coprime array includes: a first enhanced array corresponding to the first virtual array element, and a second enhanced array corresponding to the second virtual array element, and each element in the enhanced difference joint array represents a difference in spacing distance between the first virtual array element and the second virtual array element; According to the correspondence between the elements in the element difference joint array and the elements in the reconstructed covariance matrix, combined with the enhanced difference joint array determined according to the element difference joint array, the reconstructed covariance matrix is ​​expanded to obtain the enhanced covariance matrix, wherein the elements in the enhanced difference joint array and the elements in the enhanced covariance matrix have a corresponding relationship.

4. The method according to claim 1, characterized in that: Performing spatial spectrum analysis on the reconstructed covariance matrix using a spatial spectrum estimation algorithm to obtain the direction of arrival of each target signal in the array signal includes: Using a preset parameter matrix to replace the signal covariance matrix in the reconstructed covariance matrix for fitting, to obtain the preset parameter matrix after fitting, wherein the preset parameter matrix includes: signal parameters corresponding to each of the target signals in the array signal; The spatial spectrum estimation algorithm is used to perform spatial spectrum analysis on the preset parameter matrix to obtain the direction of arrival of each target signal in the array signal.

5. The method according to claim 4, characterized in that Using a preset parameter matrix to replace the signal covariance matrix in the reconstructed covariance matrix for fitting, and obtaining the preset parameter matrix after fitting includes: detecting singularity of the reconstructed covariance matrix; In the case that the reconstructed covariance matrix is ​​non-singular, the preset parameter matrix is ​​fitted to the reconstructed covariance matrix based on a minimization criterion.

6. The method according to claim 5, characterized in that The method further comprises: In the case where the reconstructed covariance matrix is ​​singular, the preset parameter matrix is ​​fitted to the reconstructed covariance matrix using a preset criterion, wherein the preset criterion is: Z is a matrix of free variables to be optimized, T(u) 为所述预设参数矩阵 ， 为所述重构协方差矩阵 。 7. The method according to claim 6, characterized in that In the case where the reconstructed covariance matrix is ​​singular, fitting the preset parameter matrix to the reconstructed covariance matrix using a preset criterion comprises: The preset parameter matrix is ​​sequentially projected onto each preset matrix in a preset matrix set, and is updated alternately, wherein the preset matrix includes: a first preset matrix, a second preset matrix, and a third preset matrix, the rank number in the first preset matrix is ​​not greater than a preset rank number threshold, the second preset matrix is ​​a constant diagonal matrix, and the target matrix formed by the third preset matrix and the free variable matrix is ​​a semi-positive definite matrix; When the projection of each of the preset matrixes satisfies a convergence condition, the preset parameter matrix is ​​output.

8. A device for determining the direction of arrival of a coprime array under non-uniform noise, characterized in that: include: An acquisition module is used to acquire an array signal received by a signal receiving module, wherein the signal receiving module comprises: a plurality of array elements, a mutually prime array of array elements with a spacing distance between the plurality of array elements, the array signal is a signal to be analyzed received by the plurality of array elements, and the signal to be analyzed comprises: a target signal and a mutually prime noise signal under non-uniform noise; A determination module, used to determine an array covariance matrix of the array signal, wherein the array covariance matrix includes: a signal covariance matrix and a first noise covariance matrix, the matrix dimensions of the signal covariance matrix and the first noise covariance matrix are the same as the number of the array elements, each covariance matrix element in the signal covariance matrix corresponds to the target signal with different wave path difference, the first noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the first noise covariance matrix are the sum of the target signal and the noise signal; A reconstruction module, used for replacing the first noise covariance matrix in the array covariance matrix with a second noise covariance matrix to obtain a reconstructed covariance matrix, wherein the second noise covariance matrix is ​​a diagonal matrix, and the diagonal elements of the second noise covariance matrix are the minimum values ​​of the diagonal elements in the first noise covariance matrix; The analysis module is used to perform spatial spectrum analysis on the reconstructed covariance matrix using a spatial spectrum estimation algorithm to obtain the direction of arrival of each target signal in the array signal.

9. A non-volatile storage medium, characterized in that: A computer program is stored in the non-volatile storage medium, wherein the method for determining the direction of arrival of a mutual prime array under non-uniform noise as claimed in any one of claims 1 to 7 is executed by running the computer program in the device where the non-volatile storage medium is located.

10. A computer program product comprising computer instructions, characterized in that: When the computer instructions are executed by a processor, the steps of the method for determining the direction of arrival of a coprime array under non-uniform noise described in any one of claims 1 to 7 are implemented.

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