CN113341371A - DOA estimation method based on L array and two-dimensional ESPRIT algorithm - Google Patents

Abstract

The invention belongs to the technical field of radar signal processing, and in particular relates to a DOA estimation method based on an L-array and a two-dimensional ESPRIT algorithm. The invention proposes a DOA estimation method based on L-array and two-dimensional ESPRIT algorithm. After the array receives the radiation source signal, the array data is processed by using the array characteristics of the L-array to construct the data for the two-dimensional ESPRIT algorithm operation. matrix, obtain the estimated angle, and complete the direction measurement estimation of the signal source. The beneficial effects of the present invention are that the present invention utilizes the L array to construct a large matrix, and the obtained matrix has a simple form, maintains a low computational complexity in the subsequent direction finding process, effectively removes the influence of statistical independent noise sources, and improves the The resolving power and statistical performance in Gaussian noise environment are improved.

Description

A DOA Estimation Method Based on L-Array and Two-Dimensional ESPRIT Algorithm

technical field

The invention belongs to the technical field of radar signal processing, and in particular relates to a DOA estimation method based on an L-array and a two-dimensional ESPRIT algorithm.

Background technique

In radar signal processing, the estimation of the direction of arrival (DOA) of the target radar radiation source signal based on the L-array has always been the focus of research. With the application of high-power electronic equipment, the electromagnetic environment is becoming more and more complex. The traditional DOA estimation method based on the MUSIC algorithm faces the problems of low direction finding accuracy and large computational complexity. At the same time, most of these methods are only applicable to one-dimensional For DOA estimation, the direction finding ability for two-dimensional angles in real space is lacking, and it is still a big challenge to realize two-dimensional DOA estimation on L-array. Therefore, it is urgent to seek new technologies and means, and it is urgent to improve the signal processing capability and direction finding accuracy of the radar receiving array.

The principle of the ESPRIT algorithm is to use the rotation invariant characteristics of the signal subspace of the data covariance matrix to solve the information such as the incident angle of the signal. Since it does not need to search for spectral peaks, its complexity and calculation amount are greatly reduced compared with the MUSIC algorithm. In DOA has been widely used in estimation. For the two-dimensional direction finding based on the L-array, some two-dimensional ESPRIT methods have been proposed before, but these methods have the problems of complex structure and high calculation amount, and can not suppress the influence of noise well, and cannot be used in radar signal processing. With a good balance between performance and computational cost, there will always be large errors in the array direction finding results.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the above problems, and propose a DOA estimation method based on L-array and two-dimensional ESPRIT algorithm. Based on the data matrix operated by the two-dimensional ESPRIT algorithm, the estimated angle is obtained, and the direction measurement and estimation of the signal source is completed.

The technical scheme of the present invention is:

Divide the L array into four sub-arrays, and calculate the cross-covariance matrix between the three sub-arrays without shared array elements in the L-array by processing the received data of the target signal in the space, and use the three cross-covariance matrices to form a For the large matrix used for L-array subspace decomposition, two rotation matrices are obtained according to the rotation invariance, and the two matrices are processed based on the two-dimensional ESPRIT algorithm. Solve the azimuth and elevation of the obtained signal, and complete the two-dimensional DOA estimation.

表示：其中θ为方位角，范围为θ∈(-π,π)，定义为波达方向在xoy平面的投影与x正半轴的夹角，

为仰角，范围为

定义为波达方向在yoz平面的投影与z正半轴的夹角。相邻阵元之间的间距为d。The signal receiving model based on the L-array of the present invention is shown in Figure 1, and the direction of arrival (DOA) of the signal _si (t) uses a vector

Representation: where θ is the azimuth angle, the range is θ∈(-π,π), which is defined as the angle between the projection of the direction of arrival on the xoy plane and the positive semi-axis of x,

is the elevation angle, and the range is

It is defined as the angle between the projection of the direction of arrival on the yoz plane and the positive half-axis of z. The spacing between adjacent array elements is d.

In order to simplify the analysis process and ensure the rationality of the constructed mathematical model, the signal receiving model based on the L-array in the present invention is based on the following assumptions: (1) the amplitude and phase errors of the array element channels of the receiving antenna array are not considered; (2) the array receives The signals are all narrowband signals from far-field point sources, the center frequencies of the signals are the same and known, and the signal wavelength λ is greater than twice the array element spacing d, that is, λ≥2d; (3) The phase of the received signal is random, not Consider the special case under the prior information of known signal parts such as strictly non-circular signals.

As shown in Figure 2, a uniform L-array can be divided into four sub-arrays: the first M array elements on the x-axis form a sub-array X ₁ , the last M array elements form a sub-array X ₂ ; the first M array elements on the y-axis form a sub-array X 2 ; The elements form a sub-array Y ₁ , and the last M array elements form a sub-array Y ₂ .

The data matrices received by the sub-arrays X ₁ , X ₂ and Y ₁ , Y ₂ are:

Wherein, x _l and y _l respectively represent the data received by the array elements of the array X and the array Y whose labels are l (l=0, 1, 2, . . . , M, M+1).

The DOA estimation method based on L-array and two-dimensional ESPRIT mainly includes the following steps:

S1. Three cross-covariance matrices are obtained by constructing the data matrices received by the sub-arrays X ₁ , X ₂ and Y ₁ , Y ₂ :

Since the sub-arrays X ₁ and Y ₂ , the sub-arrays X ₂ and Y ₁ , and the sub-arrays X ₂ and Y ₂ do not share array elements, and the noises received by each array element are independent of each other, the obtained three cross-covariances There are no noise terms in the matrix.

S2. Stack the three cross-covariance matrices in step S1 into a large matrix _CL , and the structure of the matrix is as follows

S3. Perform singular value decomposition on the large matrix _CL constructed in step S2, and use the matrix formed by the eigenvectors corresponding to the first N large eigenvalues as the estimation of the signal subspace to obtain the estimation E _S of the signal subspace.

Wherein, E ₁ , E ₂ and _{E 3} are three M×M-dimensional block matrices that form the matrix ES;

S4. Calculate two rotation matrices Ψ _X and Ψ _Y , the calculation formula is

Eigen decomposition of these two rotation matrices, we get

where λ ₁ ,…,λ _N and γ ₁ ,…,γ _N are the eigenvalues of the rotation matrices Ψ _X and Ψ _Y respectively, Φ _X and Φ _Y are the eigenvalue matrices, T ₁ and T ₂ are the rotation matrices Ψ Orthogonal matrix of eigenvectors of _X and Ψ _Y.

S5. Perform two-dimensional angle parameter pairing based on the two-dimensional ESPRIT algorithm to determine the correspondence between the eigenvalues of the two rotation matrices Ψ _X and Ψ _Y. The specific steps are:

构造形式为：S51. Construct an estimation matrix

The construction form is:

的对角元素u₁,…,u_N，并对这些元素取复数相角，并按照相角大小，从大到小对对角元素进行排序，得到排序后的对角元素

取矩阵Ψ_Y特征值γ₁,…,γ_N的相角，并按照相角的大小按从大到小对γ₁,…,γ_N进行排序，得到排序后的特征值顺序

按照排序后的序号得到配对关系S52, take out the matrix

The diagonal elements u ₁ ,…,u _N of , take complex phase angles for these elements, and sort the diagonal elements according to the size of the phase angles, from large to small, to obtain the sorted diagonal elements

Take the phase angles of the eigenvalues γ ₁ ,…,γ _N of the matrix Ψ _Y , and sort γ ₁ ,…,γ _N according to the size of the phase angles in descending order to obtain the sorted eigenvalue order

Get the pairing relationship according to the sorted sequence number

与矩阵T₁中特征向量的对应关系，调整Ψ_X的特征值顺序(若

在矩阵

中的行序为j，那么其对应特征向量为矩阵T₁的第j个列向量，对应的Ψ_X的特征值为λ_j)，得到调整之后矩阵Ψ_X的特征值

以及配对关系为S53, according to the diagonal elements in step S52

The corresponding relationship with the eigenvectors in the matrix T1, _adjust the eigenvalue order of _ΨX (if

in the matrix

The row order in is j, then its corresponding eigenvector is the jth column vector of the matrix T ₁ , and the corresponding eigenvalue of Ψ _X is λ _j ), and the eigenvalue of the matrix Ψ _X after adjustment is obtained.

and the pairing relationship is

S54. According to the two groups of pairing relationships obtained in steps S52 and S53, the pairing relationship between the eigenvalues of the matrices Ψ _X and Ψ _Y is obtained as

完成二维DOA估计：S6, using the eigenvalues paired in step S5 to calculate the numerical solution of the two-dimensional direction of arrival of the target radiation source signal

Complete the 2D DOA estimation:

in,

为第i个信号的方位角估值，

为第i个信号的仰角估值，函数“arctan(·)”和“arcsin(·)”分别表示反正切函数和反正弦函数。

is an estimate of the azimuth angle of the ith signal,

For the elevation angle estimation of the ith signal, the functions "arctan(·)" and "arcsin(·)" represent the arc tangent function and the arc sine function, respectively.

The beneficial effects of the present invention are that the present invention utilizes the L array to construct a large matrix, and the obtained matrix has a simple form, maintains a low computational complexity in the subsequent direction finding process, effectively removes the influence of statistical independent noise sources, and improves the The resolving power and statistical performance in Gaussian noise environment are improved.

Description of drawings

Figure 1 is a schematic diagram of L-array signal reception;

Fig. 2 is a schematic diagram of L-array sub-array division;

Figure 3 is the curve of RMSE versus SNR;

Fig. 4 is the change curve of RMSE with the number of sub-array elements;

Figure 5 shows the variation curve of the simulation running time with the number of sub-array elements.

Detailed ways

The performance of the present invention will be described below with reference to the accompanying drawings and simulations.

The method proposed in the present invention is simulated and verified by using Matlab. Computer simulation environment: Microsoft Windows 10 operating system, Matlab 2020a software, AMD R7-4800U processor (supporting AVX instruction set), 16GBDDR4-3200 memory.

(1) DOA direction finding estimation performance of the method of the present invention

Simulation 1: The direction accuracy of the method varies with the signal-to-noise ratio

The total number of L-array elements in the space is 13, the number of elements of the four sub-arrays is 7, the length of the simulated signal data is 500 snapshots, and the direction of arrival of the signal is (60°, 60°). 1000 times of Monte-Carlo experiments are carried out under different signal-to-noise ratios, and the curve of the angle estimated RMSE of the method of the present invention as a function of SNR is obtained as shown in Fig. 3 .

Conclusion analysis: From the simulation results, the new L-array ESPRIT method of the present invention has high DOA estimation accuracy, less performance loss, and good direction finding effect.

Simulation 2: The direction accuracy of the method varies with the number of sub-array elements of the receiving array

In the L-shaped array in space, the number of array elements of the four sub-arrays are all M, the length of the simulated data is 200 snapshots, the signal-to-noise ratio is -10dB, the direction of arrival of the signal is (60°, 60°), and the different sub-arrays are 500 times of Monte-Carlo experiments are performed under the array number M to obtain the variation curve of the RMSE of the ESPRIT algorithm of the present invention with the number M of sub-array elements as shown in FIG. 4 .

Conclusion analysis: The results in Figure 4 show that the statistical performance of the method of the present invention increases with the increase of the number of sub-array elements.

(2) the running time of the method of the present invention

Simulation 1: Simulation time of the method

For the L-shaped array in space, the number of array elements of the four sub-arrays is M, the direction of arrival of the signal is (30°, 30°), the length of the simulated data is 500 snapshots, and the signal-to-noise ratio is 0dB. The method of the present invention is simulated to obtain the simulation duration of 1000 Monte-Carlo experiments performed by the algorithm under different numbers of sub-array elements.

The simulation duration data is drawn into a curve graph to obtain the variation curve of the simulation duration of the algorithm with the number of sub-array elements, as shown in Figure 5.

Conclusion analysis: From the results of Figure 5, with the increase of the number of sub-array elements, the duration of the algorithm of the present invention also increases, but the increase is small, which shows that the present invention has a small computational cost and low computational complexity. , has a computational advantage.

Based on the above simulation results, the method proposed in the present invention achieves a better balance between computational cost and estimation performance.

Claims (1)

1. A DOA estimation method based on L-array and two-dimensional ESPRIT algorithm, establish a signal receiving model based on L-array, and the direction of arrival (DOA) of the signal s _i (t) uses a vector

represents, where θ is the azimuth angle and the range is θ∈(-π,π), which is defined as the angle between the projection of the direction of arrival on the xoy plane and the positive semi-axis of x,

is the elevation angle, and the range is

Defined as the angle between the projection of the direction of arrival on the yoz plane and the positive half-axis of z, the distance between adjacent array elements is d; the uniform L array is divided into four sub-arrays: the first M array elements on the x-axis form sub-arrays Array X ₁ , the last M array elements form a sub-array X ₂ ; the first M array elements on the y-axis form a sub-array Y ₁ , and the last M array elements form a sub-array Y ₂ ; the sub-arrays X ₁ , X ₂ and Y The data matrices received by ₁ and Y ₂ are:

where x _l and y _l respectively represent the data received by the array element labeled l in array X and array Y, and l=0,1,2,...,M,M+1; It is characterized in that, the DOA estimation method comprises the following steps: S1. Three cross-covariance matrices are obtained by constructing the data matrices received by the sub-arrays X ₁ , X ₂ and Y ₁ , Y ₂ :

Since the sub-arrays X ₁ and Y ₂ , the sub-arrays X ₂ and Y ₁ , and the sub-arrays X ₂ and Y ₂ do not share array elements, and the noises received by each array element are independent of each other, the obtained three cross-covariances There are no noise terms in the matrix; S2. Stack the three cross-covariance matrices in step S1 into a matrix _CL , and the structure of the matrix is as follows

S3. Perform singular value decomposition on the matrix _CL constructed in step S2, and use the matrix composed of the eigenvectors corresponding to the first N eigenvalues as the estimation of the signal subspace to obtain the estimation of the signal subspace E _S :

Wherein, E ₁ , E ₂ and _{E 3} are three M×M-dimensional block matrices that form the matrix ES; S4. Calculate two rotation matrices Ψ _X and Ψ _Y , the calculation formula is

Eigen decomposition of these two rotation matrices, we get

where λ ₁ ,…,λ _N and γ ₁ ,…,γ _N are the eigenvalues of the rotation matrices Ψ _X and Ψ _Y respectively, Φ _X and Φ _Y are the eigenvalue matrices, T ₁ and T ₂ are the rotation matrices Ψ Orthogonal matrix composed of eigenvectors of _X and Ψ _Y ; S5. Perform two-dimensional angle parameter pairing based on the two-dimensional ESPRIT algorithm to determine the correspondence between the eigenvalues of the two rotation matrices Ψ _X and Ψ _Y. The specific steps are: S51. Construct an estimation matrix

The construction form is:

S52, take out the matrix

The diagonal elements u ₁ ,…,u _N of , take complex phase angles for these elements, and sort the diagonal elements according to the size of the phase angles, from large to small, to obtain the sorted diagonal elements

Take the phase angles of the eigenvalues γ ₁ ,…,γ _N of the matrix Ψ _Y , and sort γ ₁ ,…,γ _N according to the size of the phase angles in descending order to obtain the sorted eigenvalue order

Get the pairing relationship according to the sorted sequence number

S53, according to the diagonal elements in step S52

Corresponding relationship with the eigenvectors in the matrix T1, _adjust the eigenvalue order of _ΨX , the adjustment method is, if

in the matrix

The row order in is j, then its corresponding eigenvector is the jth column vector of matrix T ₁ , and the corresponding eigenvalue of Ψ _X is λ _j , and the eigenvalue of matrix Ψ _X after adjustment is obtained.

and the pairing relationship is

S54. According to the two groups of pairing relationships obtained in steps S52 and S53, the pairing relationship between the eigenvalues of the matrices Ψ _X and Ψ _Y is obtained as

S6, using the eigenvalues paired in step S5 to calculate the numerical solution of the two-dimensional direction of arrival of the target radiation source signal

Complete the 2D DOA estimation:

in,

is an estimate of the azimuth angle of the ith signal,

For the elevation angle estimation of the ith signal, the functions "arctan(·)" and "arcsin(·)" represent the arc tangent function and the arc sine function, respectively.

Images