A DOA estimation method for non-cooperative sources based on eigenvector

Abstract

The present invention discloses a non-cooperative source DOA estimation method based on eigenvectors, and the present invention aims to solve the problem of non-cooperative source DOA estimation when the number of sources is unknown, the coherent source situation is unknown, and the array aperture is avoided from being sacrificed. The present invention performs eigenvalue decomposition on the covariance matrix of the array received signal to obtain the eigenvector corresponding to the maximum eigenvalue of the covariance matrix, and then establishes a linear model based on the eigenvector and the steering matrix, and realizes the DOA estimation of the source by solving the linear model. Theoretical analysis proves that under the background of ideal white noise, the eigenvector corresponding to the maximum eigenvalue of the covariance matrix of the array received signal is a linear combination of the steering vectors of each source. Numerical simulation results show that the scheme can realize source DOA estimation in the absence of prior information on the source, and can provide a simpler and more reliable solution for array signal processing.

Description

Technical Field

[0001] The invention belongs to the technical field of array signal processing, and in particular relates to a non-cooperative source DOA estimation method based on characteristic vectors. Background Art

[0002] As an important part of array signal processing, the direction of arrival (DOA) estimation of the source is obtained by processing the array received signal to obtain the direction angle of the expected signal arriving at the array in space. When there are coherent sources in space, the dimension of the signal subspace is smaller than the number of sources because the covariance matrix of the received signal is not full rank, resulting in the "diffusion" of the signal subspace into the noise subspace. At this time, the steering vectors of some coherent sources are not orthogonal to the noise subspace, and traditional spatial spectrum estimation methods cannot correctly estimate the source DOA. The multi-target detection capability of the array is seriously affected.

[0003] Under the premise that the existence and number of coherent sources are known, the DOA of the coherent sources can be estimated by spatial smoothing and other methods. However, when estimating the DOA of non-cooperative signals, there is a lack of prior information on whether there are coherent sources in space and the number of coherent sources. Therefore, a non-cooperative signal DOA estimation method is urgently needed under the condition of unknown prior information. Summary of the invention

[0004] In order to overcome the difficulty of the above-mentioned existing array signal processing technology in estimating the DOA of non-cooperative signals in the absence of prior information of the source, the present invention provides a non-cooperative source DOA estimation method based on a characteristic vector.

[0005] The technical solution to realize the present invention is: a non-cooperative source DOA estimation method based on characteristic vector, the steps are as follows:

[0006] Step S1: Obtain received signal matrix :Each element in the antenna array receives the electromagnetic wave signal in the space. After the receiving channel completes the receiving sampling of the received signal, the intermediate frequency signal output by each channel is used to construct the receiving signal model to obtain the signal matrix output by the receiving array, that is, the receiving signal matrix .

[0007] Step S2: Calculate the received signal matrix The eigenvector corresponding to the maximum eigenvalue of the covariance matrix R : Using the received signal matrix ,calculate The covariance matrix R of the covariance matrix R is decomposed into eigenvalues ​​to obtain the eigenvalues ​​of R and their corresponding eigenvectors; the eigenvalues ​​of R are sorted to find the maximum eigenvalue, and the eigenvector corresponding to the maximum eigenvalue is obtained through the corresponding relationship. .

[0008] Step S3: Convert the source DOA estimation problem into a linear system solution problem: construct a linear system based on the eigenvector and a linear system of steering matrix dictionaries Adic.

[0009] Step S4: Solve the linear system constructed in step S3, and the solution result is the source DOA estimation result.

[0010] Compared with the prior art, the present invention has the following significant advantages:

[0011] (1) The present invention is applicable to DOA estimation of non-cooperative incoherent signal sources and coherent signal sources.

[0012] (2) The present invention can estimate the DOA of the information source when the number of information sources is unknown, that is, the present invention can achieve DOA estimation without special processing such as spatial smoothing for the coherent information sources.

[0013] (3) The solution method of the present invention has fast iteration speed and small amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is the simulation result of DOA estimation when there are two non-cooperative coherent sources in space.

[0015] Figure 2 It is the simulation result of DOA estimation when there are two non-cooperative and incoherent sources in space.

[0016] Figure 3 is the root mean square error of the DOA estimation of the present invention under different signal-to-noise ratios.

[0017] Figure 4 The present invention is a flow chart of a non-cooperative source DOA estimation method based on characteristic vectors. DETAILED DESCRIPTION

[0018] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Combination Figure 4 , a non-cooperative source DOA estimation method based on characteristic vector, comprising the following steps:

[0020] Step S1: Obtaining a received signal matrix :

[0021] Each element in the antenna array receives the electromagnetic wave signal in the space. After the antenna front end and microwave channel complete the reception sampling of the received signal, the intermediate frequency signal output by each receiving channel is used to construct the received signal model to obtain the signal matrix output by the receiving array, that is, the received signal matrix , the specific process is:

[0022] Assume that the number of elements in the antenna array is N and the element numbers are ; There are K far-field narrowband sources, the source numbers are , from the direction Irradiating to each element in the array, the carrier frequency of each signal source is ; Taking array element 0 as the reference array element, the intermediate frequency signal received by array element n can be expressed as:

[0023] (1),

[0024] in represents the signal after the received narrowband source k radiation signal is converted to the intermediate frequency, c represents the propagation speed of electromagnetic waves in free space, j represents the imaginary unit, t represents time, represents the noise signal received by array element n, It represents the path difference between the signal radiated by source k reaching array element n and the signal radiated by source k reaching array element 0. , represents the wave path of the signal radiated by source k to array element 0, It represents the wave path of the signal radiated by source k to array element n. The array can be in the form of a uniform linear array, a non-uniform linear array, a circular array or other array forms.

[0025] The signal received by each array element in the array is written in matrix form, which can be expressed as:

[0026] (2),

[0027] in, is the signal received by N array elements at time t in matrix form, and its matrix dimension is , is the input signal of K sources at time t expressed in matrix form, and its matrix dimension is , represents the matrix transpose operation, is the noise signal received by the array at time t in matrix form, and its matrix dimension is , represents the steering matrix of the array for K signal sources, and its matrix dimension is ,in for Dimensional steering vector:

[0028] (3),

[0029] The array collects snapshot data at L moments, and equation (2) can be expressed as:

[0030] (4),

[0031] in is a signal containing L snapshot data received by the array in matrix form, is a signal of K sources with L snapshots expressed in matrix form, is a noise signal containing L snapshots represented in matrix form.

[0032] Step S2: Calculate the received signal matrix The eigenvector corresponding to the maximum eigenvalue of the covariance matrix R :

[0033] calculate The covariance matrix R of the covariance matrix R is decomposed into eigenvalues ​​to obtain the eigenvalues ​​of R and their corresponding eigenvectors; the eigenvalues ​​of R are sorted to find the maximum eigenvalue, and the eigenvector corresponding to the maximum eigenvalue is obtained through the corresponding relationship. .

[0034] For the received signal matrix X r , its covariance matrix R can be calculated as follows:

[0035] (5),

[0036] in represents the matrix conjugate operation, from which the received signal matrix is ​​obtained The covariance matrix R of is .

[0037] From the principal component analysis (PCA analysis), it can be seen that the eigenvector corresponding to the maximum eigenvalue of the covariance matrix R contains the information of all sources in the received signal. Therefore, the DOA of the source can be estimated based on the eigenvector corresponding to the maximum eigenvalue of the covariance matrix R.

[0038] The eigenvalue decomposition of the covariance matrix R can be expressed as

[0039] (6),

[0040] in, is the eigenvalue of the covariance matrix, e is the eigenvalue The corresponding eigenvectors, after solving all the eigenvalues ​​of the matrix R, are sorted from large to small as follows:

[0041]

[0042] The corresponding eigenvector is:

[0043]

[0044] This finds the maximum eigenvalue The corresponding feature vector .

[0045] Step S3: Convert the source DOA estimation problem into a linear system solution problem:

[0046] The source DOA estimation problem is transformed into a linear system solution problem, and a feature vector based and the guide matrix dictionary A dic The linear system.

[0047] When the noise received by each array element is uncorrelated, that is, the covariance matrix of the noise signal When full rank, we have:

[0048] (7),

[0049] in is the linear combination factor, for dimensional steering vector.

[0050] When the noise is ideal white noise, the characteristic vector The steering vectors of each source satisfy the following linear relationship:

[0051] (8)

[0052] According to formula (8), the linear system is constructed:

[0053] (9)

[0054] in A dictionary representing the steering matrix of an array, whose matrix dimensions are , P represents the number of sampling points covering the spatial domain of the array, for The coefficient vector of the linear combination factors of dimension, Only the vector corresponding to the source direction Factor is non-zero and the remaining factors are zero.

[0055] Considering that ideal white noise does not exist, when the covariance matrix of the noise signal is When full rank, we have:

[0056] (10)

[0057] That is:

[0058] (11)

[0059] Where I represents the identity matrix, is the modeling error caused by the non-idealization of noise, thus the source DOA estimation problem is transformed into the problem of solving the linear system shown in equation (11).

[0060] Step S4: Solve the linear system constructed in step S3, and the solution is the source DOA estimation result:

[0061] When the noise is ideal white noise, the coefficient vector of the linear combination factor is Estimated value of ; When the noise is non-ideal white noise but the noise signals received by each array element are uncorrelated, the solution to equation (11) can be expressed as:

[0062] (12),

[0063] in is the regularization parameter and , express norm, express norm; thus, by solving equation (12), we can get ,Depend on The non-zero value of can obtain the corresponding source steering vector , from which we can get This is the DOA estimation result of the source.

[0064] The iterative solution process of equation (12) is as follows:

[0065] (13),

[0066] In formula (13), , is the number of iterations, is the upper limit of the number of iterations, represents the iteration vector, represents the iteration parameter, The coefficient vector representing the linear combination factor Estimated value of , Representation Matrix The Lipschitz constant.

[0067] The initial values ​​of the iteration are as follows: , Right now is the zero vector, ,when After convergence, or when the number of iterations reaches the upper limit, the estimated value can be obtained ,Depend on The non-zero value of can obtain the corresponding source steering vector , from which we can get This is the DOA estimation result of the source.

[0068] For example, for a uniform linear array with 10 elements, the antenna units are evenly arranged with a half wavelength of 10 GHz as the element spacing. When there are two non-cooperative coherent sources in space, the signal carrier frequency of the two sources is 10 GHz, and they have the same intermediate frequency signal and Doppler characteristics. The intermediate frequency signal bandwidth is 10 MHz. The two sources are located at -2° and 4° directions of the array respectively. The signal-to-noise ratio of the array receiving the two sources is -5 dB. The numerical simulation results of the DOA estimation method proposed in the present invention are as follows: Figure 1 shown.

[0069] When there are two non-cooperative and incoherent signal sources in space, the signal carrier frequency of the two signal sources is 10 GHz, but they have different intermediate frequency signals and different Doppler characteristics. The intermediate frequency signal bandwidths are 10 MHz and 8 MHz respectively. The two signal sources are located at -5° and 10° directions of the array respectively. The signal-to-noise ratio of the signal radiated by the two signal sources received by the array is -5 dB. The numerical simulation results of the DOA estimation method proposed by the present invention are as follows: Figure 2 shown.

[0070] When the signal-to-noise ratio of the source in the array receiving space is improved, the root mean square error RMSE of the DOA estimation result of the method proposed in the present invention will decrease. The signal-to-noise ratio is changed from -20dB to 0dB, with a step of 1dB, and the number of Monte Carlo simulations is 100. The simulation results show Figure 1 The root mean square error curve of DOA estimation of the array under different signal-to-noise ratio conditions corresponding to the simulation case is as follows Figure 3 shown.

Claims

1. A non-cooperative source DOA estimation method based on eigenvector, characterized in that: Here are the steps: Step S1: Obtain received signal matrix X r : Each element in the antenna array receives the electromagnetic wave signal in the space, samples and converts the frequency to obtain the intermediate frequency signal, and uses the intermediate frequency signal to build the receiving signal model to obtain the signal matrix output by the receiving array, that is, the receiving signal matrix X r ; Step S2: Calculate the received signal matrix X r The eigenvector e1 corresponding to the maximum eigenvalue of the covariance matrix R is: Calculate X r The covariance matrix R of is obtained, and the eigenvalue decomposition of the covariance matrix R is performed to obtain the eigenvalues ​​of R and their corresponding eigenvectors; the eigenvalues ​​of R are sorted, the maximum eigenvalue is found, and the eigenvector e1 corresponding to the maximum eigenvalue is obtained through the corresponding relationship; Step S3: Convert the source DOA estimation problem into a linear system solution problem: Construct a dictionary A based on the feature vector e1 and the guiding matrix dic Linear system of Steering Matrix Dictionary A dic =[a(θ1),a(θ2),…,a(θ P )], the matrix dimension is N×P, P represents the number of sampling points in the array coverage space, N represents the number of elements in the antenna array, a(θ P ) is the source steering vector; Step S4: Solve the linear system constructed in step S3, and the solution result is the source DOA estimation result.

2. The non-cooperative source DOA estimation method based on characteristic vector according to claim 1, characterized in that: Step S1 is specifically implemented as follows: Assume that the number of antenna array elements is N, and the element numbers are n = 0, 1, ..., N-1; there are K far-field narrowband sources, and the source numbers are k = 1, 2, ..., K, from the directions θ1, θ2, ..., θ K The carrier frequency of each signal source is f0, and the intermediate frequency signal x received by element n is n (t) is expressed as: Among them, s k (t) represents the signal after the received source k radiation signal is converted to the intermediate frequency, c represents the propagation speed of electromagnetic waves in free space, j represents the imaginary unit, t represents time, Δr k,n The difference between the path length of the signal radiated by source k reaching array element n and that reaching array element 0, δ n (t) represents the noise signal received by array element n; The signal received by each array element is written in matrix form, expressed as x(t): x(t)=AS(t)+δ(t) (2), Among them, the input matrix S(t) composed of K information sources is [s1(t), s2(t),…, s K (t)] T , whose matrix dimension is K×1, [·] T represents the matrix transpose operation, the noise signal matrix δ(t) received by the array = [δ0(t),δ1(t),…,δ N-1 (t)] T , whose matrix dimension is N×1, and the array steering matrix for K sources is A=[a(θ1),a(θ2),…,a(θ K )], whose matrix dimension is N×K, a(θ k ) is the N×1-dimensional steering vector: By collecting snapshot data at L moments, the received signal matrix X r It is expressed as: X r =AS t +δ r (4), Where X r =[x(t1),x(t2),…,x(t L )], source signal matrix S t =[S(t1),S(t2),…,S(t L )], the noise signal matrix δ r =[δ(t1),δ(t2),…,δ(t L )],t L represents the Lth moment, thus obtaining the signal matrix output by the receiving array containing L snapshot data, that is, the received signal matrix X r , whose matrix dimension is N×L.

3. The non-cooperative source DOA estimation method based on characteristic vector according to claim 2, characterized in that: Step S2 is specifically implemented as follows: Received signal matrix X r The covariance matrix R of is calculated by the following formula: in[·] H Represents the matrix conjugate operation, thereby obtaining the received signal matrix X r The covariance matrix R of , the dimension of matrix R is N×N; The eigenvalue decomposition of the covariance matrix R is expressed as Re=λe (6), Among them, λ is the eigenvalue of the covariance matrix, e is the eigenvector corresponding to the eigenvalue λ, and after solving all the eigenvalues ​​of the matrix R, the eigenvalues ​​are sorted from large to small as follows: λ1>λ2>…>λ N , The corresponding eigenvector is: e1,e2,…,e N , In this way, the eigenvector e1 corresponding to the maximum eigenvalue λ1 is found.

4. The non-cooperative source DOA estimation method based on characteristic vector according to claim 3 is characterized in that: Step S3 is specifically implemented as follows: When the noise received by each array element is uncorrelated, that is, the covariance matrix of the noise signal When full rank, we have: where α k is the linear combination factor, a(θ k ) is a N×1-dimensional steering vector; When the noise is ideal white noise, the characteristic vector e1 and the steering vector of each source satisfy the following linear relationship: According to formula (8), a linear system is constructed: e1=A dic a (9), Among them, P represents the number of sampling points covering the spatial domain of the array, and the coefficient vector α of the P×1-dimensional linear combination factor is α=[α1,α2,…,α P ] T , only the source-directed vector a(θ k ) factor α k is non-zero, and the remaining factors are zero; Considering that ideal white noise does not exist, when the covariance matrix R of the noise signal N When full rank, we have: A dic α=R N e1 (10), =(R N -I+I)e1 =(R N -I)e1+e1 =-σ+e1 That is: e1=A dic a+s (11), Where I represents the unit matrix, and the modeling error σ caused by the non-idealization of noise is (IR N )e1, thus the source DOA estimation problem is converted into the problem of solving the linear system shown in equation (11).

5. The non-cooperative source DOA estimation method based on characteristic vector according to claim 4, characterized in that: Step S4 is specifically implemented as follows: When the noise is ideal white noise, the estimated value of the coefficient vector α of the linear combination factor is When the noise is non-ideal white noise but the noise signals received by each array element are uncorrelated, the solution to equation (11) is expressed as: Where γ is the regularization parameter, and γ>0, ||·||1 represents the l1 norm, and ||·||2 represents the l2 norm. Thus, by solving equation (12), we can obtain Depend on The non-zero value of can obtain the corresponding source steering vector From this we get That is the DOA estimation result of the source; The iterative solution process of formula (12) is as follows: In formula (13), the number of iterations m = 1, 2…M, M is the upper limit of the number of iterations, q m represents the iteration vector, v m represents the iteration parameter, r m Represents the estimated value of the coefficient vector α composed of linear combination factors Lf represents the matrix A dic The Lipschitz constant; The initial values ​​of the iteration are as follows: v1 = 1, q0 = 0, that is, q0 is the zero vector, r1 = q0, when r m After convergence, or when the number of iterations reaches the upper limit, the estimated value is obtained Depend on The non-zero value of can obtain the corresponding source steering vector From this we get This is the DOA estimation result of the source.

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