CN102608565A - Direction-of-arrival estimation method on basis of uniform circular array - Google Patents

Abstract

The invention relates to a method for estimating a direction of arrival, in particular to a method for estimating a direction of arrival based on an independent signal and a coherent signal of a uniform circular array. The DOA estimation method based on a uniform circular array of the present invention includes: preprocessing DOA estimation parameters; removing pattern space noise; increasing the array aperture, performing DOA estimation on independent signals; eliminating independent signals, and performing DOA estimation on coherent signals Direction of arrival estimation. The invention has higher estimating precision, the array aperture is more fully utilized, the array aperture loss caused by the virtual array transformation is compensated, the estimation performance is further improved, the calculation is simple and the calculation amount is small.

Description

A Direction of Arrival Estimation Method Based on Uniform Circular Array

technical field

The present invention relates to a direction of arrival (Direction of Arrival, referred to as DOA) estimation method, in particular to a direction of arrival estimation method based on independent signals and coherent signals of a uniform circular array (Uniform Circular Array, referred to as UCA).

Background technique

In the actual signal environment, independent signals and coherent signals often exist at the same time. Most DOA estimation algorithms are mainly designed for independent signals or coherent signals. The characteristics of the signal and the coherent signal are used to estimate the DOA. In the literature: Ye Z F, Zhang Y F, LiuC.Direction-of-arrival estimation for uncorrelated and coherent signals with fewer sensors[J].IEEE Trans.on Microwaves, Antennas&Propagation, 2009, 3(3):473-482 , considering the DOA estimation of independent signals and coherent signals, but it is only applicable to the DOA estimation of Uniform Linear Array (ULA).

The UCA array is distributed on a plane, it can provide azimuth angle and elevation angle information at the same time, and the azimuth angle information it provides is 360° without ambiguity. However, because the UCA array steering vector does not have a Vandermonde structure, many direction finding algorithms based on ULA arrays cannot be used for UCA arrays, especially in the presence of coherent signals. In order to make the direction-finding algorithm based on ULA arrays suitable for UCA arrays or even arbitrary arrays, many scholars have proposed many methods to virtually transform non-ULA arrays into ULA arrays. Some of the more classic methods are: pattern space transformation for UCA arrays, interpolation transformation technology for arbitrary arrays and popular separation technology. Using the aforementioned array virtual transformation technology, any array can be virtualized as a ULA array, and then the DOA estimation algorithm based on the ULA array can be used to obtain the corresponding direction of arrival. However, the array after virtual transformation often has different degrees of array aperture loss, which reduces the estimation performance; and the noise may be nonlinearly amplified after virtual transformation, which will further deteriorate the estimation performance, especially in the signal When the noise ratio is small.

Contents of the invention

The purpose of the present invention is to propose a direction of arrival estimation method based on a uniform circular array with a simple estimation process and a small amount of calculation.

The purpose of the present invention is achieved like this:

The DOA estimation method based on the uniform circular array of the present invention comprises the following steps:

(1) Direction of arrival estimation parameter preprocessing:

a. According to the array output data matrix X: X=AS+Z, seek the received data covariance matrix R of the uniform circular array: R=E[XX ^H ]=AR _S A ^H +σ ² I;

D为相干信源组数，n_k为第k组相干信源的信号个数，S表示N×L维信号数据矩阵，L表示快拍数，Z表示M×L维高斯白噪声数据矩阵，X^H表示X的共轭转置，R_S为信号数据协方差矩阵，σ²为高斯白噪声的功率，I为与R相同维数的单位阵；Among them, A represents the M×N dimensional array flow pattern matrix of the uniform circular array, M represents the number of array elements, N represents the number of signals, and the numbers of independent signals and coherent signals in N are N _i and N _c , respectively.

D is the number of coherent source groups, _nk is the number of signals of the kth coherent source group, S represents the N×L dimensional signal data matrix, L represents the number of snapshots, Z represents the M×L dimensional Gaussian white noise data matrix, X ^H represents the conjugate transpose of X, _RS is the signal data covariance matrix, σ ² is the power of Gaussian white noise, and I is the identity matrix with the same dimension as R;

对均匀圆阵列的接收数据R进行变换，得到模式空间中均匀线阵列的接收数据协方差矩阵R₁： b. Use the pattern space transformation matrix T:

Transform the received data R of the uniform circular array to obtain the received data covariance matrix R ₁ of the uniform linear array in the pattern space:

q＝-K，…，K；A₁为虚拟均匀线阵的(2K+1)×N维流型矩阵，A₁＝[a₁ a₂…a_N]，

i＝1，…，N；Among them, J ₀ is a 2K+1-dimensional diagonal matrix, and the elements on the diagonal position of J ₀ are J ₀ (k, k)=j ^(k-1-K) B _(k-1-K) (-β ), B _(k-1-K) ( ) is the Bessel function of the first kind of k-1-K order, k=1,..., 2K+1; F is the discrete Fourier transform matrix, F=[w _-K w _-K+1 ...w _K ], w _q =[1e ^-jp ...e ^-jp(M-1) ] ^H ,

q=-K,...,K; A ₁ is the (2K+1)×N-dimensional manifold matrix of the virtual uniform linear array, A ₁ =[a ₁ a ₂ ... a _N ],

i=1,...,N;

(2) Remove pattern space noise:

噪声功率σ²通过对R进行特征值分解，并对其M-(N_i+D)个小特征值求平均得到；Find the data covariance matrix R ₂ without noise components:

The noise power σ ² is obtained by decomposing the eigenvalues of R and averaging its M-(N _i +D) small eigenvalues;

(3) Improve the array aperture and estimate the direction of arrival for independent signals:

Use the multiple signal split spectrum peak search method to estimate the direction of arrival, search out the spectral peaks corresponding to N _i + D large eigenvalues, and the corresponding estimated angles include the direction of arrival angles corresponding to N _i independent signals and D groups The direction of arrival angle corresponding to the coherent signal, select the direction of arrival angle corresponding to the N _i spectral peak amplitudes with the largest amplitude as the direction of arrival estimation result of the independent signal;

(4) Eliminate independent signals and estimate direction of arrival for coherent signals:

其中，J为与R₂同维数的反对角单位矩阵，A_1c表示由相干信号的导向矢量组成的流型矩阵，R_Sc表示相干信号的信号协方差矩阵，

表示R_Sc的转置，利用前后向矢量重构算法进行解相干，得到没有秩亏损的相干信号数据矩阵，并利用总体最小二乘-旋转不变子空间算法求解相干信号的波达方向。The data covariance matrix R ₃ of the coherent signal:

Among them, J is the anti-diagonal identity matrix with the same dimension as R ₂ , A _1c represents the flow pattern matrix composed of the steering vector of the coherent signal, R _Sc represents the signal covariance matrix of the coherent signal,

Represent the transpose of R _Sc , use forward-backward vector reconstruction algorithm to decoherence, obtain the coherent signal data matrix without rank deficit, and use the total least squares-rotation invariant subspace algorithm to solve the direction of arrival of the coherent signal.

The beneficial effects of the present invention are:

Compared with the existing direction-finding algorithm based on the uniform circular array, the present invention is not affected by noise in the DOA estimation process, and has higher estimation accuracy, especially when the signal-to-noise ratio is small, the estimation performance is greatly improved; The independent signal and the coherent signal are estimated separately, the array aperture is more fully utilized, and the loss of the array aperture caused by the virtual array transformation is compensated, and the estimation performance is further improved; Based on the uniform linear array algorithm, the calculation is simple and the amount of calculation is small.

Description of drawings

Fig. 1 is the flow chart of the method for estimating the direction of arrival based on the uniform circular array of the present invention;

Fig. 2 is under the same condition, when the incident signal is an independent signal, the comparison schematic diagram of the root mean square error estimated by the method of the present invention and the model space MUSIC algorithm without denoising;

Fig. 3 is a schematic diagram of the estimated root mean square error comparison between the method of the present invention and the TLS-ESPRIT algorithm based on the Toeplitz decoherence method when the incident signal is a mixture of independent signals and coherent signals under the same conditions.

Detailed ways

The core idea of the present invention is to use the characteristics of the data structure in the process of mode space transformation to eliminate the influence of uniform Gaussian white noise on DOA estimation and improve the estimation performance; The effect of the noise after the UCA array is increased after the mode space transformation of the effective array aperture.

The UCA array has great advantages because it can provide unambiguous azimuth information and two-dimensional angle information. However, due to the particularity of the position of its array elements, many traditional direction-finding algorithms based on ULA arrays are not suitable for UCA arrays, especially in the presence of coherent signals. With the introduction of the mode space transformation method, the UCA array can be virtually converted into a ULA array, but there is an array aperture loss after conversion, and the noise power will be amplified in the mode space, which will affect the accuracy of DOA estimation.

When independent signals and coherent signals exist at the same time, if the characteristics of the two signals are used to separate them for DOA estimation, the array aperture will be effectively improved. According to the data structure in the estimation process, designing a reasonable method to eliminate noise will greatly improve the accuracy of DOA estimation.

The method for estimating the direction of arrival of the present invention will be described in detail below with reference to the accompanying drawings.

Fig. 1 is a flow chart of the method for estimating the direction of arrival based on the UCA array in the present invention. As shown in Figure 1, the method includes the following steps:

(1) Direction of arrival estimation parameter preprocessing:

D为相干信源组数，n_k为第k组相干信源的信号个数)；Z表示N×L维信号数据矩阵，L表示快拍数；N表示M×L维高斯白噪声数据矩阵。由X求出UCA阵列的接收数据协方差矩阵R：1. From the snapshot data received by each array element, the array output data matrix X is obtained, X=AS+Z, where A represents the M×N-dimensional array flow matrix of the UCA array, M represents the number of array elements, and N represents The number of signals, where the numbers of independent signals and coherent signals are N _i and

D is the number of coherent information source groups, n _k is the number of signals of the kth coherent information source); Z represents the N×L dimensional signal data matrix, L represents the number of snapshots; N represents the M×L dimensional Gaussian white noise data matrix . Find the received data covariance matrix R of the UCA array from X:

R＝E[XX ^H ]＝AR _S A ^H +σ ² I

Among them, X ^H represents the conjugate transpose of X, _RS is the signal data covariance matrix, σ ² is the power of Gaussian white noise, and I is the identity matrix with the same dimension as R.

2. Construct the pattern space transformation matrix T as follows:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}{{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

q＝-K，…，K。Wherein, J ₀ is a 2K+1-dimensional diagonal array, and the elements on the diagonal position of J ₀ are J ₀ (k, k)=j ^(k-1-K) B _(k-1-K) (- β), B _(k-1-K) (.) is the Bessel function of the first kind of k-1-K order, k=1,..., 2K+1; F is the discrete Fourier transform matrix, F=[ w _-K w _-K+1 ...w _K ], w _q =[1e ^-jp ...e ^-jp(M-1) ] ^H ,

q=-K, . . . , K.

The pattern space transformation is performed on R to obtain the data covariance matrix R ₁ in the pattern space:

${\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA0000146190930000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_1={\mathrm{TRT}}^h=A_1{R}_S{A}_1^h+{\mathrm{\&sigma;}}^2{\mathrm{TT}}^h$ (Formula 5)

i＝1，…，N。Among them, A ₁ is the (2K+1)×N-dimensional manifold matrix of the virtual uniform linear array, A ₁ =[a ₁ a ₂ ... a _N ],

i=1,...,N.

(2) Remove pattern space noise:

From Equation 5 in Step 3, it can be seen that the original spatial white noise is still white noise in the mode space, but the noise power will become larger and uneven, which seriously affects the estimation performance. Calculate the data covariance matrix R ₂ without noise components from R ₁ :

${\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000146190930000012.png,HDA0000146190930000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_2=R_1-{\mathrm{\&sigma;}}^2{\mathrm{TT}}^h=A_1{R}_S{A}_1^h$ (Formula 6)

It can be known from formula 6 that as long as the noise power σ ² and T are known, the noise-free data covariance matrix R ₂ can be obtained. The noise power σ ² can be obtained by decomposing the eigenvalues of R and averaging its M-(N _i +D) small eigenvalues; and T has been obtained in step two.

(3) Improve the array aperture and estimate the direction of arrival for independent signals:

Singular value decomposition is performed on R ₂ to obtain the noise subspace U _N corresponding to M-(N _i +D) small eigenvalues. Using the MUSIC peak search method for DOA estimation:

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; MUSIC</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; .</span>$

Spectrum peaks corresponding to N _i +D large eigenvalues can be searched out, and the corresponding estimated angles include DOA angles corresponding to N _i independent signals and DOA angles corresponding to D groups of coherent signals. Since the steering vector corresponding to a group of coherent signals is not in the standard form, its orthogonality with the noise subspace is not as good as that of independent signals, and the corresponding spectral peak amplitude is smaller. The DOA angles corresponding to the Ni spectral peak amplitudes with the largest amplitudes can be selected as the DOA estimation results of the independent signals.

(4) Eliminate independent signals and estimate direction of arrival for coherent signals:

In step five, DOA estimation has been performed on independent signals. In order to avoid repeated estimation and improve array utilization, it is necessary to remove information of all independent signals. According to Equation 6, and using the Toeplitz feature of the independent signal and noise data covariance matrix, the data covariance matrix R ₃ of the coherent signal is obtained:

${\mathrm{<figure-callout\; id="3"\; label="R"\; filenames="HDA0000146190930000021.png"\; state="\{\{state\}\}">R</figure-callout>}}_3=R_2-{\mathrm{JR}}_2^{T}J=A_{1c}(R_{\mathrm{sc}}-R_{\mathrm{sc}}^T)A_{1c}^h$ (Formula 7)

表示R_Sc的转置。显然，R₃中不含有任何的独立信号和噪声的信息。Among them, J is the anti-diagonal identity matrix with the same dimension as R ₂ , A _1c represents the flow pattern matrix composed of the steering vector of the coherent signal, R _Sc represents the signal covariance matrix of the coherent signal,

Indicates the transpose of R _Sc . Obviously, _R3 does not contain any independent signal and noise information.

对R₄进行奇异值分解，取D个大特征值对应的信号子空间U_S1＝[u₁，u₂，…，u_D]，构造列满秩的相干信号数据矩阵：The forward and backward vector reconstruction algorithm is used for decoherence, and the singular value decomposition is performed on R ₃ to obtain the signal subspace U _S corresponding to 2D large eigenvalues.

Singular value decomposition is performed on R ₄ , and the signal subspace U _S1 =[u ₁ , u ₂ ,...,u _D ] corresponding to D large eigenvalues is taken to construct a full-rank coherent signal data matrix:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="R"\; filenames="HDA0000146190930000021.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; fb</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="R"\; filenames="HDA0000146190930000012.png,HDA0000146190930000021.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; fb</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; fb</span>}}<span\; class="notranslate">\; ]</span>$

k＝1，…，D。

为由u_k构成的M₀×L_fk维数据矩阵，M₀＝M+1-max{L_fk}，

为由

构成的M₀×L_fk维数据矩阵，L_fb＝n_k-L_fk。in,

k=1,...,D.

is a M ₀ ×L _fk dimensional data matrix composed of u _k , M ₀ =M+1-max{L _fk },

for the reason

The formed M ₀ ×L _fk dimensional data matrix, L _fb =n _k -L _fk .

Use the total least squares-rotation invariant subspace algorithm (TLS-ESPRIT) to solve the direction of arrival of the coherent signal: R ₅₁ and R ₅₂ correspond to the front M ₀ -1 line and the back M ₀ -1 line of R ₅ respectively matrix, R ₆ =[R ₅₁ , R ₅₂ ]. Singular value decomposition is performed on R ₆ , Q is the eigenvector matrix corresponding to N _c small eigenvalues in the right singular matrix, the dimension is 2N×N, and Q=[Q ₁ ; Q ₂ ], Q ₁ and Q ₂ Both are N×N matrices, according to the TLS-ESPRIT principle

$\mathrm{<span\; class="notranslate">\; \&Psi;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}$

Perform eigendecomposition on Ψ, and obtain the direction of arrival of the coherent signal according to its eigenvalues

In the formula, i=1, ..., N _c , γ _i (Ψ) represents the ith eigenvalue of the matrix Ψ.

The DOA estimation method proposed by the invention is not affected by the pattern space noise, and greatly improves the estimation performance of the direction finding algorithm. By separately estimating the independent signal and the coherent signal, the array aperture is effectively utilized, which makes up for the shortage of the array aperture loss caused by the mode space transformation. The implementation of the above two points effectively solves the two defects of the UCA array in DOA estimation, and greatly expands the application field of the UCA array.

Claims (1)

1. A direction of arrival estimation method based on a uniform circular array is characterized by comprising the following steps:

(1) preprocessing the estimation parameters of the direction of arrival:

a. output data matrix X from array: and (3) solving a covariance matrix R of the received data of the uniform circular array when X is AS + Z: r ═ E [ XX ]^H]＝AR_SA^H+σ²I；

Wherein, A represents the M multiplied by N dimension array flow pattern matrix of the uniform circular array, M represents the number of array elements, N represents the number of signals, and N is an independent signal and a coherent signalThe number of each is N_iAnd N_c，

D is the number of coherent source groups, n_kThe number of the signals of the kth group of coherent information sources is S represents an NxL dimensional signal data matrix, L represents a fast beat number, Z represents an MxL dimensional Gaussian white noise data matrix, and X represents^HDenotes the conjugate transpose of X, R_SAs a covariance matrix, σ, of the signal data²Is the power of Gaussian white noise, and I is a unit array with the same dimension as R;

b. using the pattern space transformation matrix T:

transforming the received data R of the uniform circular array to obtain a covariance matrix R of the received data of the uniform linear array in the mode space₁：

Wherein, J₀Is a 2K +1 dimensional diagonal matrix, J₀The element in the diagonal position is J₀(k，k)＝j^(k-1-K)B_(k-1-K)(-β)，B_(k-1-K)(. cndot.) is a first class of Bessel function of order K-1-K, K being 1, …, 2K + 1; f is a discrete Fourier transform matrix, and [ w ]_-K w_-K+1…w_K]，w_q＝[1 e^-jp … e^-jp(M-1)]^H，q＝-K，…，K；A₁(2K +1) xN dimensional flow pattern matrix as virtual uniform linear array, A₁＝[a₁ a₂ … a_N]，i＝1，…，N；

(2) Removing mode spatial noise:

method for obtaining data association without noise componentVariance matrix R₂：

Noise power σ²Decomposing the characteristic value of R and carrying out M- (N) on R_i+ D) averaging small characteristic values to obtain;

(3) increasing the aperture of the array, and estimating the direction of arrival of the independent signals:

estimating direction of arrival by using multi-signal spectral peak searching method, and searching out N_iThe corresponding estimated angles of the spectrum peaks corresponding to the + D large eigenvalues comprise N_iThe direction of arrival angle corresponding to the independent signals and the direction of arrival angle corresponding to the D groups of coherent signals are selected, and N with the maximum amplitude is selected_iThe direction of arrival angle corresponding to the amplitude of each spectral peak is used as the estimation result of the direction of arrival of the independent signal;

(4) eliminating independent signals, and carrying out direction-of-arrival estimation on coherent signals:

data covariance matrix R of coherent signal₃：

Wherein J is and R₂Co-dimensional inverse diagonal identity matrix, A_1cRepresenting a flow pattern matrix consisting of steering vectors of coherent signals, R_ScA signal covariance matrix representing the coherent signal,

represents R_ScAnd performing decorrelation by using a forward and backward vector reconstruction algorithm to obtain a coherent signal data matrix without rank loss, and solving the direction of arrival of a coherent signal by using a total least square-rotation invariant subspace algorithm.

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