Meshless-based hybrid field source signal localization method and system

Abstract

The present application relates to electronic communication signal positioning identification technical field, especially to a kind of hybrid field source signal positioning method and system based on meshless, for the target area in hybrid field source, construct four-order cumulant matrix that has eliminated distance parameter: generate four-order cumulant matrix equivalent to uniform array by interpolation operation on four-order cumulant matrix;Based on four-order cumulant matrix equivalent to uniform array and using atomic norm theory to construct hybrid field source direction of arrival estimation optimization problem;Hybrid field source direction of arrival estimation optimization problem is solved using the MUSIC matrix characteristic space decomposition method, and direction of arrival estimation value and distance estimation value of hybrid field source are obtained according to solving structure.The present application can realize high-precision hybrid field positioning, and positioning success rate is high, with good robustness, with good application prospect.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electronic communication signal positioning and identification, and particularly relates to a mixed field source signal positioning method and system based on a meshless method. BACKGROUND

[0002] Source positioning is one of the important topics in the fields of radar, sonar, wireless communication and speech recognition positioning. In the past few decades, researchers have developed various high-resolution algorithms, among which the most widely used are multiple signal classification (MUSIC) and estimation of signal parameters via rotational invariance techniques (ESPRIT). According to the definition of the Fresnel region, sources can be divided into far-field (FF) sources and near-field (NF) sources. For far-field sources, the incident wave of the source is assumed to be a plane wave, and the parameters to be estimated only contain angle information; while for near-field sources, the incident wave is assumed to be a spherical wave, and the position of the source is determined by the joint of the angle and distance parameters. In the mixed field where FF sources and NF sources coexist, the signal model is relatively more complex.

[0003] Current mixed field positioning algorithms based on fourth-order cumulants mainly include spatial smoothing algorithms and compressed sensing algorithms. Spatial smoothing algorithms can only use the continuous lag part of the virtual array, and the algorithm accuracy is low; most traditional compressed sensing algorithms are based on grids, and the grid accuracy will affect the algorithm performance; increasing the grid accuracy will increase the algorithm complexity; and the existing mixed field positioning algorithms based on meshless compressed sensing are implemented by interpolation on the physical array, which has large errors and low positioning success rate. The present application aims to realize mixed field positioning under fourth-order cumulants by using the meshless idea. At the same time, by combining the idea of virtual array interpolation, the high-order cumulant matrix is interpolated to realize high-precision mixed field positioning. SUMMARY

[0004] To this end, the present application provides a mixed field source signal positioning method and system based on a meshless method, which solves the problem of grid mismatch in existing electronic communication positioning.

[0005] According to the design scheme provided by the present application, a mixed field source signal positioning method based on a meshless method is provided, which comprises:

[0006] For mixed field sources in a target area, a fourth-order cumulant matrix with eliminated distance parameters is constructed:

[0007] An interpolation operation is performed on the fourth-order cumulant matrix to generate a fourth-order cumulant matrix equivalent to a uniform array;

[0008] Based on the fourth-order cumulant matrix equivalent to the uniform array, an atomic norm theory is used to construct a mixed field source direction of arrival estimation optimization problem;

[0009] The problem of mixed field source direction of arrival estimation optimization is solved by using a MUSIC matrix characteristic space decomposition method, and mixed field source direction of arrival estimation values and distance estimation values are obtained according to the solving structure.

[0010] As the mixed field source signal positioning method based on the meshless method of the application, further, for the mixed field source in the target area, a fourth-order cumulant matrix eliminating the distance parameter is constructed, which comprises: first, according to the symmetric array of the signal receiving sensor and the sensor propagation time delay phase shift, the mixed field source receiving signal representation is obtained; then, the symmetry of the fourth-order cumulant is used to eliminate the component affected by the distance parameter of the signal source in the phase of the mixed field source receiving signal, so as to construct the fourth-order cumulant matrix in the mixed field source.

[0011] As the mixed field source signal positioning method based on the meshless method of the application, further, the fourth-order cumulant matrix is represented as: C1=BC 4s B H , wherein, B is an array steering matrix, and K is the number of mixed field sources, 2M+1 is the number of receiving sensors, θ k represents the direction of arrival information of the kth field source, is the fourth-order cumulant matrix of the receiving signal s k (t), ωk is the receiving signal angle information, represents a real number set.

[0012] As the mixed field source signal positioning method based on the meshless method of the application, further, the fourth-order cumulant matrix is generated by interpolation operation on the fourth-order cumulant matrix, which is equivalent to a uniform array, comprising: first, the fourth-order cumulant matrix is vectorized by using the array steering matrix to obtain a vector representation; then, the repeated items in the vector are removed, and a preset selection matrix is used to obtain an intermediate vector representation, and a Toeplitz matrix is constructed by using the intermediate vector representation; then, the Toeplitz matrix is interpolated by using the interpolation signal vector to construct the fourth-order cumulant matrix equivalent to the uniform array.

[0013] As the mixed field source signal positioning method based on the meshless method of the application, further, the process of obtaining the intermediate vector representation by using the preset selection matrix is represented as: c G =Gc L =A G C' 4s , wherein, A G is a co-array manifold matrix, G is a selection matrix, c L is a vector representation obtained by vectorizing the fourth-order cumulant matrix, c G is an intermediate vector representation, K is the number of mixed field sources.

[0014] As the mixed field source signal positioning method based on the meshless of the application, further, the mixed field source direction of arrival estimation optimization problem is represented based on the fourth-order cumulant matrix equivalent to the uniform array and by using the atomic norm theory: Wherein, T(u) is the Toeplitz matrix with u as the first column, F is the selection matrix containing 0 and 1 values, and the selection matrix corresponds to the zero value and the non-zero value of the fourth-order cumulant matrix C I The fourth-order cumulant matrix equivalent to the uniform array, and ε is the fitting error, tr[] represents the trace function, C and W are the convex optimization solution values.

[0015] As the mixed field source signal positioning method based on the meshless of the application, further, in the solution of the mixed field source direction of arrival estimation optimization problem by using the MUSIC matrix characteristic space decomposition method, first, the direction of arrival estimation information in the mixed field source is obtained by solving, then the eigenvalue decomposition is carried out on the covariance matrix of the received signal, and the distance estimation value in the mixed field source is obtained in combination with the direction of arrival estimation information.

[0016] Further, the application further provides a mixed field source signal positioning system based on the meshless, comprising: a signal processing module and a signal estimation module, wherein,

[0017] The signal processing module is used for constructing the fourth-order cumulant matrix with the distance parameter eliminated for the mixed field source in the target area: the fourth-order cumulant matrix equivalent to the uniform array is generated by the interpolation operation on the fourth-order cumulant matrix;

[0018] The signal estimation module is used for constructing the mixed field source direction of arrival estimation optimization problem based on the fourth-order cumulant matrix equivalent to the uniform array and by using the atomic norm theory; and the mixed field source direction of arrival estimation optimization problem is solved by using the MUSIC matrix characteristic space decomposition method, and the mixed field source direction of arrival estimation value and the distance estimation value are obtained according to the solution structure.

[0019] The beneficial effects of the application are as follows:

[0020] The application combines the virtual array interpolation idea and the atomic norm minimization method, constructs the fourth-order cumulant matrix equivalent to the uniform linear array by realizing the interpolation operation on the fourth-order cumulant matrix with the distance parameter eliminated, and then performs the positioning of the mixed field based on the matrix, so that the high-precision mixed field positioning can be realized, the positioning success rate is high, the robustness is good, and the application prospect is good. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 It is the flowchart of the mixed field source signal positioning method based on the meshless in the embodiment;

[0022] Figure 2 This is a schematic diagram of the algorithm principle in the embodiment;

[0023] Figure 3 This is a schematic diagram illustrating the algorithm simulation performance in the example. Detailed implementation method:

[0024] To make the objectives, technical solutions, and advantages of this invention clearer and more understandable, the invention will be further described in detail below with reference to the accompanying drawings and technical solutions.

[0025] This invention, see Figure 1 As shown, a method for locating hybrid field source signals based on a meshless system is provided, comprising:

[0026] S101. For the mixed field sources in the target region, construct a fourth-order cumulant matrix with the distance parameter eliminated:

[0027] S102. A fourth-order cumulant matrix equivalent to a uniform array is generated by performing interpolation on the fourth-order cumulant matrix.

[0028] S103. Based on the fourth-order cumulant matrix equivalent to a uniform array and using atomic norm theory, construct the optimization problem of direction-of-arrival estimation for hybrid field sources.

[0029] S104. Solve the optimization problem of direction-of-arrival estimation of mixed field sources using the MUSIC matrix eigenspace decomposition method, and obtain the estimated values ​​of direction-of-arrival and distance of mixed field sources based on the solution structure.

[0030] This paper utilizes the concept of meshless localization to achieve mixed-field localization based on fourth-order cumulants. Simultaneously, it incorporates virtual array interpolation to interpolate higher-order cumulant matrices, achieving high-precision mixed-field localization. Furthermore, for mixed-field sources in the target region, a fourth-order cumulant matrix with distance parameters eliminated is constructed. This involves: first, obtaining the received signal representation of the mixed-field source based on the symmetric array of the signal receiving sensor and the phase shift of the sensor propagation delay; then, utilizing the symmetry of the fourth-order cumulants to eliminate the component in the phase of the received signal of the mixed-field source affected by the source distance parameter, thus constructing the fourth-order cumulant matrix for the mixed-field source.

[0031] Assume a hybrid FF and NF narrowband source is incident on a symmetrical array with 2M+1 sensors. The element spacing is λ / 4, where λ is the signal wavelength, as shown below. Figure 1 As shown. The sensor is centrally symmetric, and the index of the array sensor is denoted as Ω. M ={-M,-M+1,…-1,0,1,…M-1,M}, the signal received by the m-th sensor can be represented as

[0032]

[0033] where s k (t) provides the kth received signal, n m (t) provides additive white Gaussian noise of the mth sensor, τ mk is the propagation delay phase shift of the kth s source between the mth sensor and the sensor reference point. For NF sources, τ mk The expression of τ

[0034] τ mk = mω k + m 2 φ k (2)

[0035] where

[0036]

[0037]

[0038] θ k represents the DOA information of the kth source, r k respectively represent the distance of the kth NF source. The NF sources are located in the Fresnel region, i.e., r k ∈ [0.62 (D 3 / λ) 1 / 2 , 2D 2 / λ], where D = 2Md is the array aperture. If the kth source is located in the FF region, i.e., r k is greater than 2D 2 / λ, the expression of τ mk is

[0039] τ mk = mω k (5)

[0040] Suppose there are a total of K sources, the first K1 are FF sources, and the remaining K - K1 are NF sources. The matrix form of formula (1) can be expressed as

[0041] x(t) = A F s F (t) + A N s N + n(t) (6)

[0042] where

[0043] x(t) = [x -M (t), …, x0(t), …, x M (t) (7)

[0044]

[0045]

[0046]

[0047]

[0048] n(t) = [n -M (t),…,n0(t),…,n M (t)] (12)

[0049]

[0050] is an array received signal, is a noise matrix, a(θ k ,r k ) is a steering vector.

[0051] As a preferred embodiment, further, the fourth-order cumulant matrix equivalent to the uniform array is generated by performing interpolation operation on the fourth-order cumulant matrix, comprising: first, the fourth-order cumulant matrix is vectorized by using the array steering matrix to obtain a vector representation; then, the repeated items in the vector are removed, and a preset selection matrix is used to obtain an intermediate vector representation, and a Toeplitz matrix is constructed by using the intermediate vector representation; then, the Toeplitz matrix is interpolated by using the interpolation signal vector to construct the fourth-order cumulant matrix equivalent to the uniform array. In solving the mixed field source direction of arrival estimation optimization problem by using the MUSIC matrix eigenvalue space decomposition method, first, the direction of arrival estimation information in the mixed field source is obtained by solving, then the eigenvalue decomposition of the covariance matrix of the received signal is performed, and the distance estimation value in the mixed field source is obtained by combining the direction of arrival estimation information.

[0052] Referring to Figure 2 , a fourth-order cumulant matrix is constructed, and the influence of the distance parameter is eliminated. The fourth-order cumulant matrix is

[0053]

[0054] where (·) * represents the conjugate operation of the matrix, assuming that n = -m and q = -p, then formula (14) can be re-expressed as

[0055]

[0056] Let and obtain the cumulant matrix C1, wherein the first element of C1 is expressed as

[0057]

[0058] In matrix form, C1 can be represented as

[0059] C1 = BC 4s B H (17)

[0060] in, It can be viewed as a special type of parameter r without a range. k steering matrix

[0061]

[0062] Then, by vectorizing matrix C1, we obtain vector c. L

[0063] c L =vec(C1)=(B * ×B)C' 4s (19)

[0064] in,

[0065] c L It can be viewed as a new noiseless array receiving data, while matrix B * ⊙B is a new array steering matrix whose sensor positions are determined by the set Sure:

[0066]

[0067] Remove c L We extract the duplicates from the vector and rearrange them to obtain a new vector c. G :

[0068] c G =Gc L =A G C' 4s (twenty one)

[0069] in G is a coarray manifold matrix, and G is a selection matrix defined as follows:

[0070]

[0071] The set Includes each pair (n p -n q It contributes to the coarray index n. i It is

[0072]

[0073] From vector c GA new Toeplitz matrix can be constructed as:

[0074]

[0075] The interpolated signal vector c is defined as I and initialized as

[0076]

[0077] The vector c I contains the only lagged measurements of the vector c G , which is initialized to zero. represents that i is in but not in . After interpolation, the vector c I can be regarded as the signal received by a ULA with sensor positions being the integer set :

[0078]

[0079] A Toeplitz matrix T(u) is constructed according to the vector c I :

[0080]

[0081] According to the atomic norm theory, an optimization problem is constructed as

[0082]

[0083] where T(u) is the Toeplitz matrix with u as the first column. F is a selection matrix containing 0 and 1 values corresponding to the zero and non-zero values of the matrix C I , respectively, and ε is the fitting error. Based on the matrix T(u) solved in the above equation, the DOA estimation value of the mixed field source is solved by using the MUSIC algorithm.

[0084] The eigenvalue decomposition of the covariance matrix of the data received by the array is obtained as

[0085] R xx = U s Λ s U s + U n Λ n U n (29)

[0086] The DOA estimation value solved is substituted into b(θ k ,r), and the distance estimation value can be solved by the following equation

[0087]

[0088] The positioning problem of the mixed field is solved by using the idea of meshless, which has higher precision than existing algorithms. Compared with the spatial smoothing algorithm, the algorithm can use more virtual arrays and expand the virtual array aperture to estimate more sources. Compared with the traditional compressed sensing algorithm, the method overcomes the grid mismatch problem and improves the estimation accuracy. Moreover, the interpolation operation is performed on the high-order cumulative matrix, compared with the existing meshless algorithm which interpolates on the physical array. Even with a small fitting error ε, the method can recover the covariance matrix T(u), avoiding the problem that the interpolation on the physical array cannot recover the matrix T(u).

[0089] Further, based on the above method, the embodiment of the present application also provides a mixed field source signal positioning system based on meshless, comprising: a signal processing module and a signal estimation module, wherein,

[0090] The signal processing module is used for constructing a fourth-order cumulative quantity matrix with eliminated distance parameters for the mixed field source in the target area: generating a fourth-order cumulative quantity matrix equivalent to a uniform array by performing an interpolation operation on the fourth-order cumulative quantity matrix;

[0091] The signal estimation module is used for constructing a mixed field source direction of arrival estimation optimization problem based on the fourth-order cumulative quantity matrix equivalent to the uniform array and using the atomic norm theory; and solving the mixed field source direction of arrival estimation optimization problem by using a MUSIC matrix eigenvalue space decomposition method, and obtaining a mixed field source direction of arrival estimation value and a distance estimation value according to the solving structure.

[0092] To verify the effectiveness of the scheme, the following further explains and describes in combination with simulation data:

[0093] Referring to Figure 3 Fig. 2 shows the performance of the method proposed in the present application simulated by the MATLAB 2020a simulation platform, taking a 9-element symmetric uniform linear array as an example, the element position index is Ω M =-9,-6,-3,-2,0,2,3,6,9, the number of snapshots is 2000, and the signal-to-noise ratio is-5-30dB. Fig. a is a comparison of the DOA estimation accuracy of the proposed algorithm with the classical spatial smoothing algorithm and the LASSO algorithm, and Fig. b is a comparison of the distance estimation accuracy. It can be seen that the RMSE curve of the proposed algorithm is significantly lower than the above two algorithms, and the angle and distance estimation performance of the proposed algorithm is significantly better than other algorithms.

[0094] Unless specifically stated otherwise, the relative steps, numerical expressions and numerical values of the components and steps set forth in these embodiments do not limit the scope of the present application.

[0095] The various embodiments are described in the specification in a progressive manner, each embodiment focusing on different aspects of the other embodiments, and the same or similar parts between the embodiments can be mutually referred to. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method.

[0096] The units and method steps of each example described in combination with the embodiments disclosed herein can be realized in electronic hardware, computer software or a combination of both. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been described in the above description in general terms. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation does not exceed the scope of the present application.

[0097] Those skilled in the art can understand that all or part of the steps in the above method can be instructed by a program to complete the relevant hardware, and the program can be stored in a computer readable storage medium, such as a read-only memory, a magnetic disk or an optical disk, etc. Alternatively, all or part of the steps of the above embodiments can also be implemented using one or more integrated circuits, and accordingly, each module / unit in the above embodiments can be implemented in the form of hardware or in the form of a software function module. The present application is not limited to any specific form of combination of hardware and software.

[0098] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present application, which are used to illustrate the technical solutions of the present application, and are not limiting. The protection scope of the present application is not limited thereto, although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily think of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed by the present application, or make equivalent replacements to some of the technical features; and these modifications, changes or replacements do not make the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for locating hybrid field source signals based on a meshless system, characterized in that, Include: For the mixed field sources in the target region, construct a fourth-order cumulant matrix with the distance parameter eliminated: The fourth-order cumulant matrix is ​​vectorized using the array turning matrix to obtain a vector representation; duplicate terms in the vector are removed, and an intermediate vector representation is obtained using a preset selection matrix. A Toeplitz matrix is ​​constructed using this intermediate vector representation; the Toeplitz matrix is ​​interpolated using an interpolation signal vector to generate a fourth-order cumulant matrix equivalent to a uniform array by interpolating the fourth-order cumulant matrix; the process of obtaining the intermediate vector representation using the preset selection matrix is ​​expressed as: c G =Gc L =A G C' 4s A G Let G be the coarray manifold matrix, G be the selection matrix, and c be the coarray matrix. L The vector representation obtained by vectorizing the fourth-order cumulant matrix, c G This is represented by an intermediate vector. To receive signal s k The fourth-order cumulant matrix of (t); Based on a fourth-order cumulant matrix equivalent to a uniform array and utilizing atomic norm theory, an optimization problem for estimating the direction of arrival (DOA) of a hybrid field source is constructed. The optimization problem is expressed as follows: Where T(u) is the Toeplitz matrix with u as the first column, F is the selection matrix containing 0 and 1 values, and this selection matrix is ​​equivalent to the fourth-order cumulant matrix C of a uniform array. I The zero and non-zero values ​​correspond to each other, ε is the fitting error, tr[] represents the trace function, and C and W are the values ​​of the convex optimization solution; By solving for the direction-of-arrival (DOA) estimation information of the mixed field source, the covariance matrix of the received signal is decomposed into eigenvalues, and the DOA estimation information is combined to obtain the distance estimation value of the mixed field source. The MUSIC matrix eigenspace decomposition method is used to solve the optimization problem of DOA estimation of the mixed field source, and the DOA estimation value and distance estimation value of the mixed field source are obtained based on the solution results.

2. The method for locating hybrid field source signals based on a meshless system according to claim 1, characterized in that, For the mixed field sources in the target region, a fourth-order cumulant matrix with the distance parameter eliminated is constructed, which includes: First, obtaining the received signal representation of the mixed field source based on the symmetrical array of the signal receiving sensor and the phase shift of the sensor propagation delay; Then, the symmetry of the fourth-order cumulants is used to eliminate the components in the phase of the received signal from the mixed field source that are affected by the source distance parameter, so as to construct the fourth-order cumulant matrix in the mixed field source.

3. The method for locating hybrid field source signals based on a meshless system according to claim 2, characterized in that, The fourth-order cumulant matrix is ​​represented as: C1 = BC 4s B H ,in, B is the array turning matrix, and K is the number of mixed field sources, 2M+1 is the number of receiving sensors, and θ k This represents the direction of arrival information of the k-th source. To receive signal s k The fourth-order cumulant matrix of (t), ω k In order to receive signal angle information, It represents the set of real numbers.

4. A meshless hybrid field source signal localization system, characterized in that, Based on the method described in claim 1, it comprises: a signal processing module and a signal estimation module, wherein... The signal processing module is used to construct a fourth-order cumulant matrix with the distance parameter eliminated for mixed field sources in the target region: by performing interpolation operations on the fourth-order cumulant matrix to generate a fourth-order cumulant matrix equivalent to a uniform array. The signal estimation module is used to construct an optimization problem for the direction-of-arrival (DOA) estimation of a mixed-field source based on a fourth-order cumulant matrix equivalent to a uniform array and using atomic norm theory. The module then uses the MUSIC matrix eigenspace decomposition method to solve the DOA estimation optimization problem and obtains the DOA and distance estimates of the mixed-field source based on the solution structure.

5. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor is configured to execute a program stored in memory and, when the program is executed, implement the method described in any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method described in any one of claims 1 to 3.

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