阅读说明：本技术 基于空域融合的压缩感知二维doa估计方法 (Compressed sensing two-dimensional DOA estimation method based on spatial domain fusion ) 是由 窦慧晶 肖子恒 杨帆 于 2020-11-30 设计创作，主要内容包括：本发明公开了一种基于空域融合的压缩感知二维DOA估计方法,属于阵列信号处理技术领域。由于二维DOA估计算法目前存在着计算复杂度过高,估计精度较低的问题,本发明主要在压缩感知模型的基础上研究二维DOA估计方法。首先利用L阵的空间合成角进行降维,采用一种等角度结合等余弦的空域划分方式构建性能更优的阵列流型矩阵,以得到压缩感知框架下的DOA估计模型。再分别采用OMP算法进行角度重构并按照信源幅值大小进行配对,得到目标的二维方向信息。该发明具有估计精度高、解相干、抗噪性能好的特点,促进了压缩感知与DOA估计的进一步融合。(The invention discloses a compressed sensing two-dimensional DOA estimation method based on spatial domain fusion, and belongs to the technical field of array signal processing. Because the two-dimensional DOA estimation algorithm has the problems of high computational complexity and low estimation precision at present, the two-dimensional DOA estimation method is mainly researched on the basis of a compressed sensing model. Firstly, reducing the dimension by using a spatial synthesis angle of an L array, and constructing an array flow matrix with better performance by adopting an equiangular and equicosine combined airspace division mode to obtain a DOA estimation model under a compressed sensing framework. And then, respectively adopting an OMP algorithm to carry out angle reconstruction and pairing according to the magnitude of the information source amplitude to obtain two-dimensional direction information of the target. The method has the characteristics of high estimation precision, coherent solution and good noise resistance, and promotes the further fusion of compressed sensing and DOA estimation.)

1. A compressed sensing two-dimensional DOA estimation method based on airspace fusion is characterized by comprising the following steps:

the first step is as follows: modeling and simulating the two-dimensional array signal model to obtain the direct relation between the output signal of each antenna array element and a target information source;

the second step is that: constructing a space synthetic angle by using the space geometric relationship of the L array, and reducing the dimension of the two-dimensional angle into two one-dimensional space angles for estimation;

the third step: according to the sparsity of a target signal in the whole spatial domain, all possible spatial angles of the signal are divided by adopting an equiangular division and equicosine division combined mode to obtain a discretized angular direction; after the division mode of the airspace is determined, an array steering matrix A (theta) containing signal characteristic information is expanded along with the division mode, so that a DOA estimation model based on compressed sensing is obtained;

the fourth step: respectively solving the sparse reconstruction problem by utilizing an OMP algorithm to obtain DOA estimation results of two groups of spatial synthetic angles;

the fifth step: corresponding two groups of angles to sparse coefficients h_xAnd h_ySorting according to the amplitude values, then pairing the amplitude values in groups, and finally obtaining the azimuth angle theta and the pitch angle of each information source according to the inverse solution of the pairing result

2. The method of claim 1, wherein:

the method comprises the following steps: an L-shaped uniform array is adopted, the L-shaped uniform array comprises two mutually perpendicular sub-arrays X, Y which are respectively positioned on an x axis and a y axis, an original point is shared by the two sub-arrays, and each sub-array comprises M array elements; assuming that there are K far-field narrowband signals incident on the array, K1, 2.. K denotes K sources; the distance between each array element is half wavelength, the included angles between the incident signal and the x-axis and the y-axis are respectively alpha, beta and the incident direction angle theta,the azimuth angle and the pitch angle of the signal are respectively, and the single snapshot vector model of the two subarrays receiving the signal at the moment t is as follows:

wherein s (t) ═ s₁(t)，s₂(t)…，s_k(t)]T represents a signal vector of K information sources at time T, x (T) x₁(t)，x₂(t)，...，x_M(t)]^TAnd y (t) ═ y₁(t)，y₂(t)，...，y_M(t)]^TThe arrays that are respectively sub-arrays X, Y receive the vectors,andare all variance equal toAdditive white Gaussian noise with the mean value of zero, wherein the noise signal is independent from the original received signal; the M × K order array flow pattern matrix is expressed as:

the m row and k column elements in the matrix represent the gain and phase delay information of the k far-field signal received by the m antenna element, wherein:

formula (5) and formula (6) represent the steering vectors of the k-th signal in subarray X and subarray Y,λ represents the wavelength of the signal, d represents the distance between two subarray elements;

step two: if the linear array's angular separation of airspace in one-dimensional DOA estimationThe discretization number is n, and when the plane array with the same precision estimates the azimuth angle and the pitch angle at the same time, the discretization number of the airspace angle is n²；

According to the spatial geometrical position relation:

reducing the two-dimensional space angle estimation into two one-dimensional space angle estimations through the space synthesis angle of the formula (7);

formula (7) is respectively brought into formula (5), and formula (6) obtains the guide quantity of the spatial synthetic angle:

step three: the spatial synthetic angle alpha defined by the formula (7)_kAnd beta_kThe information such as azimuth angle and pitch angle of the two-dimensional signal is contained, and sparseness exists in the whole space domain; therefore, all possible space angles theta of the signal are subjected to space domain division to obtain N discrete angle directions by using h_iRepresenting the signal in the ith direction, the spatial domain signal can be represented as h ═ h₁，h₂，...，h_N]^TIf K target information sources exist in the space, obviously, the K signals in the corresponding directions in h have nonzero elements, and the other directions are all zero;

according to the definition of the vector inner product, the orthogonality between any vectors in the array manifold matrix a is expressed by the following formula:

in the formula [ theta ]_p、θ_qRepresenting different angle values after spatial domain division, wherein p, q is 1, 2. Obviously, the orthogonality is the maximum when the two angles are the closest;

the observation space is divided into N angles according to equiangular and equichordal angles respectively

Suppose μ (A)₁) Represents the orthogonality of the equiangular-division downflow type matrix, then

Suppose μ (A)₂) Representing the orthogonality of the flow-type matrix under the isochordal division

Carrying out simulation comparison on the orthogonality of the two, adopting a uniform linear array with 16 array elements, and uniformly dividing the space into 180 parts according to equal chord division and equal angle division;

there is a critical angle that satisfies the same non-orthogonality of the equiangular and equichordal divisions, namely:

μ(A₁)＝μ(A₂) (13)

the formula (11) is simplified by substituting the formula (12) into the formula (13):

cosθ_P-cosθ_P-1＝2/N (14)

is pushed out by the upper way

The sum and difference products are added to the left side of the above formula to obtain

The above formula is related to theta_PCan be respectively expressed as theta_P1、θ_P2

I.e. at (-90 deg., theta)_P1) And (theta)_P2The 90 degree iso-chord division is more preferable at (theta)_P1，θ_P2) The equal angle division mode is more optimal; selecting a space domain division mode according to the angle range, and fusing the corresponding array flow pattern matrixes to obtain an optimal array flow pattern matrix; assuming that the total number of spatial grids is n, the number of equiangular division grids is (theta)_P2-θ_P1) N/180, the rest grid number is equal sine division grid number; the merged matrix can be represented as:

the DOA estimation data model of the sparse signal representation is then:

x, Y are the received signal vectors of subarrays X, Y, N_x、N_yRespectively representing the noise signal vectors of the two sub-arrays; the expanded sparse dictionary matrix is:

expression (20) and expression (21) are typical compressed sensing models, and expanded manifold matricesPlays the role of a measurement matrix phi; because of the target signal h_x、h_yIs sparse relative to the whole space domain, does not need a sparse base matrix to be sparsely represented, soBoth the observation matrix and the perception matrix; the DOA estimation model based on compressed sensing is constructed;

step three: by constructing the estimation model, the sparse reconstruction problem of equations (24) and (25) is solved to obtain two sets of spatial synthetic angles α_kAnd beta_k(ii) a Namely the known observed signal X, Y and the perception matrixReconstructing a target sparse signal h_x、h_yExpressed as:

wherein h_x||₀、||h_y||₀Is h_x、h_y0 norm of (1) represents h_x、h_yThe number of the medium nonzero elements, wherein epsilon is the energy of noise contained in the observation signal;

solving the DOA by adopting an OMP algorithm to obtain two groups of DOA estimation results;

step four: solving a group of included angles alpha and beta corresponding to the two sub-linear arrays by the reconstruction algorithm; if the number of the incoming wave signals is 1, directly converting the included angle alpha and the included angle beta according to a formula (19) to obtain a two-dimensional space angle of the information source;

if there are more incoming wave signals, h is the number_xAnd h_yThe size of the non-zero element in the equation corresponds to the amplitude of the signal, so the angle pairing is realized by adopting a signal amplitude sequencing method, namely the sparse coefficient h estimated by the equation (15) and the equation (16)_xAnd h_yThe non-zero elements in the information source are sorted according to the amplitude value and then are enabled to correspond one to one, and finally a group of paired angles are reversely solved according to a formula (26) to obtain the azimuth angle theta and the pitch angle of each information source

Technical Field

The invention relates to a direction of arrival (DOA) estimation algorithm, which is often applied to tasks such as radar detection, wireless communication, seismic exploration and the like, and can automatically estimate a two-dimensional direction of arrival angle. The invention belongs to the technical field of array signal processing.

Background art as a key problem in the field of array signal processing, direction of arrival estimation (DOA) is widely used in many fields such as radar, communication, earthquake, etc. Since the one-dimensional direction estimation cannot describe the spatial characteristics, and is not suitable for engineering practice in many aspects, the two-dimensional direction of arrival (2D-DOA) estimation has become a research hotspot. Among the estimation algorithms for two-dimensional signal subspace, the most classical estimation algorithm is the two-dimensional multiple signal classification (2D MUSIC) algorithm, which performs eigenvalue decomposition on a covariance matrix of received data to obtain a signal subspace and a noise subspace, and then constructs a spatial spectrum according to the orthogonality of the subspaces, however, the algorithm requires two-dimensional spectral peak search, which brings huge computation and is difficult to satisfy practical application. In order to solve the above-mentioned drawbacks, another scholart has proposed a two-dimensional rotation invariant subspace (2-D ESPRIT) algorithm without spectral peak search, but needs data with shift invariant characteristics and a special array flow pattern, and needs eigenvalue decomposition, and the computational complexity of the algorithm is still high. On the basis, a two-dimensional propagation operator (2D PM) algorithm without spectral peak search and eigenvalue decomposition is provided, the processing performance of array signals is greatly improved, and the method is suitable for multi-dimensional angle estimation under different arrays. However, the above algorithms cannot break through the limitation of subspace algorithms, and the direction of arrival cannot be accurately estimated usually when the signal-to-noise ratio is low, the snapshot is small, and the spatial distance between the signal sources is very small, so that the practicability is limited to a certain extent. The computational complexity of the two-dimensional direction of arrival estimation is influenced by the array geometry, and compared with other array structures such as a uniform rectangular array or a uniform circular array, the two-dimensional DOA estimation under the L-shaped array structure has higher estimation accuracy and lower computational complexity, and is simple in structure and easy to implement, so that the two-dimensional DOA estimation is widely applied to engineering application.

The theory of Compressive Sensing (CS) proposed by Donoho et al in recent years has brought a more efficient, accurate approach to modern signal processing by exploiting the sparsity of the signal by solving for l at a sampling rate much less than the nyquist frequency₀And obtaining a high-precision reconstruction signal by the minimum norm optimization problem. Compared with the whole space angle, the target signal in the actual space domain is few and has sparsity, so that the method is very suitable for angle division of the space domain to construct a DOA estimation model under the compressed sensing for solving. The DOA estimation method based on sparse representation effectively reduces the sampling number of signals, the cost of data transmission, storage and processing, improves the estimation performance of parameters, and is not influenced by phaseInterference sources. Therefore, the DOA estimation method is continuously explored on the basis of compressed sensing, and the practicability of the algorithm is further improved.

Disclosure of Invention

The traditional two-dimensional DOA estimation algorithm has the problems of high computational complexity and low estimation precision at present, and is difficult to meet the requirements of the modern signal processing on real-time performance and accuracy. In order to solve the defects, two-dimensional DOA estimation is carried out under a compressed sensing model, a sparse division mode of a space domain is researched, and finally a compressed sensing two-dimensional DOA estimation algorithm based on space domain fusion division is provided, so that the calculation amount of the algorithm is greatly reduced, and the DOA estimation precision is improved.

In order to achieve the above object, the present invention comprises the steps of:

the first step is as follows: and modeling and simulating the two-dimensional array signal model to obtain the direct relation between the output signals on each antenna array element and the target information source.

The second step is that: and constructing a space synthesis angle by using the space geometric relationship of the L array, and reducing the dimension of the two-dimensional angle into two one-dimensional space angles for estimation.

The third step: according to the sparsity of the target signal in the whole space domain, all possible space angles of the signal are divided by adopting an equiangular division and equicosine division combined mode to obtain a large number of discretized angle directions. After the division mode of the space domain is determined, the array steering matrix A (theta) containing the signal characteristic information is expanded, and therefore the DOA estimation model based on the compressed sensing is obtained.

The fourth step: and respectively solving the sparse reconstruction problem by using a classical OMP algorithm to obtain DOA estimation results of two groups of spatial synthetic angles.

The fifth step: corresponding two groups of angles to sparse coefficients h_xAnd h_ySorting according to the amplitude values, then pairing the amplitude values in groups, and finally obtaining the azimuth angle theta and the pitch angle of each information source according to the inverse solution of the pairing result

And a sixth step: experiments verify the effectiveness of the compressed sensing two-dimensional DOA estimation method based on airspace fusion, and the mean square error is used as an index to verify the performance of the algorithm.

Compared with the prior art, the invention has the following beneficial effects:

(1) the two-dimensional signals are reduced into two one-dimensional signals by using the spatial synthesis angle of the L-array model, so that the dimensionality of the array flow pattern matrix is greatly reduced, and further the computational complexity and the spatial complexity of the two-dimensional DOA estimation are effectively reduced.

(2) A sparse reconstruction model is constructed by utilizing a compressed sensing theory, so that the algorithm can restore two-dimensional angle information of signals with high precision under the condition of few snapshots and low signal-to-noise ratio, matrix eigenvalue decomposition is not involved, and the method has the excellent characteristic of natural solution coherence.

(3) By analyzing the orthogonality of the equiangular division and the equichord division, the angle space which is dominated by each division mode is found, and the equiangular division and the equichord division are combined to form a new space division mode, so that the method has higher estimation performance compared with the equiangular division and the equichord division.

Drawings

FIG. 1 shows an L-shaped array receiving model

FIG. 2 is a schematic view of spatial sparsification of an incident signal

FIG. 3 is an orthogonality curve of an array flow matrix varying with the number of grids under two division modes

FIG. 4 shows a root mean square error curve of two division modes varying with signal-to-noise ratio

FIG. 5 shows the root mean square error curve of the second two division modes with the change of signal-to-noise ratio

FIG. 62D-DOA estimate scatter plot of the MUSIC algorithm

FIG. 72D-PM Algorithm DOA estimate scatter plot

FIG. 8 DOA estimation scatter plot of the algorithm herein

FIG. 9 shows the RMS error curves for each algorithm as the SNR changes

Detailed Description

The present invention will be described in further detail below with reference to specific embodiments and with reference to the attached drawings.

The method comprises the following steps: the L-shaped uniform array is adopted, the model comprises two mutually perpendicular sub-arrays X, Y which are respectively positioned on an x axis and a y axis, an origin is shared by the two sub-arrays, and each sub-array comprises M array elements. Assuming that K far-field narrow-band signals (K1, 2.., K) are incident on the array, the distance between each array element is half a wavelength, the angles between the incident signals and the x-axis and the y-axis are respectively alpha and beta, the incident direction angle theta,a schematic diagram of the array received signal, shown in figure 1, is the azimuth and elevation of the signal, respectively. The single snapshot vector model of the two subarrays receiving signals at time t is:

wherein s (t) ═ s₁(t)，s₂(t)…，s_k(t)]^TRepresenting the signal vector at time t of the K sources, x (t) ═ x₁(t)，x₂(t)，…，x_M(t)]^TAnd y (t) ═ y₁(t)，y₂(t)，…，y_M(t)]^TThe arrays that are respectively sub-arrays X, Y receive the vectors,andare all variance equal toAnd the noise signal is independent from the original received signal. The M × K order array flow pattern matrix can be expressed as:

the m row and k column elements in the matrix represent the gain and phase delay information of the k far-field signal received by the m antenna element, wherein:

formula (5) and formula (6) represent the steering vectors of the k-th signal in subarray X and subarray Y, λ represents the wavelength of the signal and d represents the distance between two subarray elements.

Step two: if the discretization number of the airspace angles of the linear arrays in the one-dimensional DOA estimation is n, the discretization number of the airspace angles is n when the plane arrays with the same precision estimate the azimuth angle and the pitch angle simultaneously². This greatly increases the temporal and spatial complexity of the algorithm, and therefore we choose to use L-matrix dimensionality reduction to solve this problem. The L array is composed of two linear arrays with spatial relationship.

As can be seen from the spatial geometric relationship of fig. 1:

the two-dimensional spatial angle estimate is reduced to two one-dimensional spatial angle estimates by the spatial synthetic angle of equation (7).

Formula (7) is respectively brought into formula (5), and formula (6) obtains the guide quantity of the spatial synthetic angle:

step three: the spatial synthetic angle alpha defined by the formula (7)_kAnd beta_kThe information of azimuth angle and pitch angle of the two-dimensional signal is contained, and the sparseness exists in the whole space domain. Therefore, all possible space angles theta of the signal can be subjected to space domain division to obtain N discrete angle directions by using h_iRepresenting the signal in the ith direction, the spatial domain signal can be represented as h ═ h₁，h₂，…，h_N]^TIf there are K target sources in the space, it is obvious that the K signals corresponding to the directions in h have non-zero elements, and the remaining directions are all zero. At present, two common space division modes are equiangular division and equiangular division, and array manifold matrixes obtained by different division methods are different, which directly influence the performance of sparse reconstruction and further influence the DOA estimation performance. Therefore, in order to select a good spatial domain partition method, RIP (finite isometry) conditions of the array flow matrix a under two partition methods need to be analyzed.

However, directly verifying the RIP condition for a given matrix is an NP-hard problem, and the learner Candes gives an equivalent description of the RIP condition: if the 2K column vectors are arbitrarily extracted from the sensing matrix to be almost orthogonal, the accurate reconstruction of sparse signals can be ensured. Therefore, the orthogonality among columns in the array manifold matrix under different division methods determines whether the signal can be accurately recovered or not, and an accurate information source DOA estimation value is obtained. According to the definition of the vector inner product, the orthogonality between any vectors in the array manifold matrix a can be represented by the following formula:

in the formula [ theta ]_p、θ_qAnd (3) representing different angle values after spatial domain division, wherein p, q is 1, 2, … and N. It is clear that the orthogonality is greatest when the two angles are the closest.

The observation space is divided into N angles according to equiangular and equichordal angles respectively

Suppose μ (A)₁) Represents the orthogonality of the equiangular-division downflow type matrix, then

Suppose μ (A)₂) Representing the orthogonality of the flow-type matrix under the isochordal division

And performing simulation comparison on the orthogonality of the two, adopting a uniform linear array with 16 array elements, and uniformly dividing the space by 180 parts according to equal chord division and equal angle division. The graph is a result graph of the orthogonality of the two division modes along with the change of grids. It can be seen that when the target angle is at two ends, the array manifold matrix has better approximate orthogonality under the equal sine method, and the RIP condition is easier to meet; and when the angle is in the middle range, the approximate orthogonality of the array manifold matrix under the equal-angle division method is better, and the RIP property is more remarkable. Then there must be a critical angle that satisfies the same non-orthogonality of the equiangular and equiangular divisions, namely:

μ(A₁)＝μ(A₂) (13)

the formula (11) is simplified by substituting the formula (12) into the formula (13):

cosθ_P-cosθ_P-1＝2/N (14)

can be pushed out from the above way

The sum and difference products are added to the left side of the above formula to obtain

The above formula is related to theta_PCan be respectively expressed as theta_P1、θ_P2

I.e. at (-90 deg., theta)_P1) And (theta)_P2The 90 degree iso-chord division is more preferable at (theta)_P1，θ_P2) The equal angle division mode is more preferable. Therefore, the division mode of the airspace can be selected according to the angle range, and the corresponding array flow matrix is fused to obtain the optimal array flow matrix. Assuming that the total number of spatial grids is n, the number of equiangular division grids is (theta)_P2-θ_P1) N/180, the remaining grid number is the equal sine division grid number. The merged matrix can be represented as:

the DOA estimation data model of the sparse signal representation is then:

x, Y are the received signal vectors of subarrays X, Y, N_x、N_yRepresenting the noise signal vectors of the two sub-arrays, respectively. The expanded sparse dictionary matrix is:

expression (20) and expression (21) are typical compressed sensing models, and expanded manifold matricesPlays the role of the measurement matrix phi. Because of the target signal h_x、h_yIs sparse relative to the whole space domain, does not need a sparse base matrix to be sparsely represented, soBoth the observation matrix and the perception matrix. Up to this point, the DOA estimation model based on compressed sensing is constructed.

Step three: by constructing the estimation model, the sparse reconstruction problem of the equations (24) and (25) is solved to obtain two groups of spatial synthetic angles alpha_kAnd beta_k. Namely the known observed signal X, Y and the perception matrixReconstructing a target sparse signal h_x、h_yIt can be expressed as:

wherein h_x||₀、||h_y||₀Is h_x、h_y0 norm of (1) represents h_x、h_yThe number of non-zero elements in (a), epsilon is the energy of the noise contained in the observed signal, and the equations (24) and (25) are essentially optimization problems with non-convex sparsity constraints. The invention adopts the most classical OMP algorithm to solve the DOA to obtain two groups of DOA estimation results. The algorithm flow of OMP is as follows:

inputting: measure matrix of M × N dimensionA measurement value X of M dimensions; sparsity K

Outputting; nx 1-dimensional sparse signalK x 1 dimensional DOA estimation result

(1) And (5) initializing. Residual r₀X, supporting setSupport matrixThe iteration time t is 1;

(2) the candidate set is extended. Calculating a measurement matrixOf atoms and the current residual r_t-1The correlation of (a):

and selecting a sum r from the measurement matrix_t-1The atom with the greatest relevance;

(3) and updating the support set. Current support set Λ_iSupport set Λ from last iteration_t-1And a union set of the atom subscripts selected in the previous step;

(4) and updating the support matrix. Current support matrixBy adding a selected atom to the support matrix of the last iterationObtaining the compound;

(5) the update signal approaches. To findLeast squares solution of (c):

(6) and updating the residual value.

(7) Judging iteration termination conditions, stopping iteration and outputting K sparse estimation of signals if the termination conditions t is more than or equal to KOtherwise, updating the iteration time t to t +1 and turning to the step (2).

The sparsity and number of preceding sources should be equal, using K.

Step four: a group of included angles alpha and beta corresponding to the two sub-linear arrays can be obtained through the reconstruction algorithm. If the number of incoming wave signals is 1, the two-dimensional space angle of the information source can be obtained by directly converting the included angle alpha and the included angle beta according to the formula (19), but in practical application, a plurality of signal sources often exist in a space, how angle results respectively estimated by two sub-line arrays are paired, and determining which two included angles belong to the same information source is a problem which needs to be solved.

Because of h_xAnd h_yIs non-zero inThe element size corresponds to the amplitude of the signal, so the angle pairing can be realized by adopting a signal amplitude ordering method, namely, the sparse coefficient h estimated by the formula (15) and the formula (16)_xAnd h_yThe non-zero elements in the method are sorted according to the amplitude and then are enabled to correspond one to one, and the angular pairing scheme is provided that the amplitudes of all signals have certain difference. Finally, reversely solving the paired angles according to the formula (26) to obtain the azimuth angle theta and the pitch angle of each information source

Step five: simulation verification of the effectiveness of the invention

Experiment one: verifying the effectiveness of the spatial domain fusion algorithm on DOA estimation, and comparing DOA estimation performances under two angle division modes under different signal-to-noise ratios in a simulation mode. The number of array elements is set to be 16 in an experiment, the number of discrete grids is 360, the signal-to-noise ratio is gradually increased to 10dB from minus 10dB by taking 2dB as an interval, the number of the information source is 16, the test angle is divided into two schemes according to a critical value obtained by the theoretical analysis, and the (1) information source grid numbers of 160, 200 and 230 and the (2) information source grid numbers of 10, 20 and 30 are set. In the experiment, the root mean square error is used as an index for measuring the performance of the DOA estimation algorithm, and the root mean square error of the DOA estimation is defined as:

wherein K is the number of sources, N is 100 is the number of Monte Carlo experiments,angle estimate, θ, for the nth trial of the kth source_kThe true angle of arrival of the kth source. FIG. 4 and FIG. 5 are diagrams illustrating the RMS error as a function of SNR for two partitioning schemes of a first scheme and a second scheme, respectivelyAnd (5) fruit.

It can be seen that, as the signal-to-noise ratio is improved, the root mean square error is gradually reduced, the root mean square error of the equiangular partition under the scheme is lower than that of the equiangular partition, it can be known that the equiangular partition performance in the middle angular region is better, and the root mean square error of the equiangular partition under the scheme is lower than that of the equiangular partition, it can be known that the DOA estimation obtained by equichord partition in the two end regions is more accurate. The experimental result shows that the suitable angle division modes of different angle spaces are different, and the feasibility of the spatial domain fusion method is also described.

Experiment two: compare the 2-D MUSIC algorithm, the 2-D PM algorithm, and the 2-dimensional DOA estimation performance of the algorithms herein. Assuming that there are 3 uncorrelated far-field signals, they are incident on the L-array with a total number of array elements of 16 from directions of (60 °, 120 °), (100 ° ), and (140 °, 80 °). The number of snapshots in the simulation test is set equal to 100, the signal-to-noise ratio is-10 dB, and the angular grid of the algorithm is 0.5 degrees. And respectively carrying out simulation tests on the classic 2-D MUSIC algorithm, the 2-D PM algorithm and the text algorithm, and repeatedly drawing 100 times of scatter points. The simulation results obtained are shown in fig. 6-8.

The MUSIC algorithm and the PM algorithm are compared, as well as the estimated performance of the algorithm herein in a noisy environment. In the experiment, the root mean square error is used as an index for measuring the performance of the DOA estimation algorithm, and the root mean square error of the two-dimensional DOA estimation is defined as:

and representing the azimuth angle and the pitch angle of the Kth information source obtained by the mth Monte Carlo simulation experiment. (alpha_k，β_k) And K is the number of the information sources, and N is set as 100, which is the number of Monte Carlo experiments. Gaussian white noise interference is added in simulation, the signal-to-noise ratio is gradually improved from-10 dB to 10dB, and other simulation parameters are the same as those in the previous experiment. The 2-D MUSIC algorithm, the 2-D PM algorithm and the book are compared in the experimentThe root mean square error of the text algorithm is plotted as a function of the signal-to-noise ratio, and the simulation result is shown in fig. 9:

as can be seen from fig. 9, as the SNR increases, the root mean square error of the 3 algorithms gradually decreases, and the estimation accuracy increases. The root mean square error of the algorithm is lower than that of the other two algorithms when the SNR is in the range of-10 dB to 2dB, and the root mean square errors of the three algorithms are almost the same when the SNR is over 2 dB. In a whole view, the root mean square error of the algorithm is in a lower position, and the estimation precision is higher, because the algorithm utilizes a compressed sensing theory to obtain more signal information, the utilization rate of array signals is improved, and the estimation performance under the conditions of less snapshots and low signal-to-noise ratio is greatly improved. Therefore, the improved algorithm has higher estimation precision under the same simulation condition and has more obvious advantages compared with other algorithms under the condition of low signal-to-noise ratio.

The above embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and the scope of the present invention is defined by the claims. Various modifications and equivalents may be made by those skilled in the art within the spirit and scope of the present invention, and such modifications and equivalents should also be considered as falling within the scope of the present invention.