Off-lattice DOA estimation method based on covariance vectorization processing and compressed sensing

Abstract

The invention provides an off-lattice DOA (direction of arrival) estimation method based on covariance vectorization processing and compressed sensing, which aims to realize DOA estimation of a one-dimensional plane signal, especially a coherent signal under a small array element with a higher resolution ratio through a covariance matrix model of deformation array receiving data, and comprises the following steps of: calculating a covariance matrix according to the received data; and constructing a dictionary matrix of a virtual signal steering vector according to the covariance matrix, obtaining OMP estimation angles of all the information sources by using an orthogonal matching pursuit (OMP) algorithm, and obtaining DPL accurate angle estimation values of all the information sources as final output DOA estimation values by using a gradient descent iteration DPL algorithm based on the OMP estimation angles. According to the method, an array receiving data model is deformed, and receiving data of a virtual signal is obtained through a rearrangement operation; through combination of OMP and DPL algorithms, meshless DOA estimation is realized. The method not only can effectively decouple coherent signals, but also can effectively overcome the problems of low precision and poor estimation effect under the condition of low signal-to-noise ratio.

Description

Technical Field

[0001] The present invention relates to radar communication and array signal processing technology, and in particular to a grid-free direction of arrival estimation technology based on covariance vector processing and compressed sensing. Background Art

[0002] Direction of Arrival (DOA) estimation is widely used in array signal processing applications such as radar, sonar, and wireless communications. Classic DOA estimation methods include the Multiple Signal Classification (MUSIC) algorithm proposed by Schmidt R.O. et al. and the Estimation of Signal Parameters by Rotational Invariant Techniques (ESPRIT) method proposed by Roy R. and Kailath T. However, these methods require preprocessing for angle estimation when the signals are coherent. In 2006, Donoho formally proposed the theory of compressed sensing, and subsequently Malioutov et al. proposed the L1-SVD algorithm based on this theory. Cotter et al. proposed the Orthogonal Matching Pursuit (OMP) algorithm based on the Matching Pursuit (MP) algorithm. In 2013, American scholars Tang et al. first introduced atomic norm theory to the single-snapshot DOA estimation problem and proposed an estimation method based on semi-positive definite programming.

[0003] The forward-backward smoothing method smoothes the angles through forward and backward signal processing, effectively reducing noise and fluctuations in the estimation. Specifically, this method performs signal correction during both the forward and backward estimation processes to reduce errors caused by signal coherence, thereby improving the stability and accuracy of DOA estimation. Especially when the signal exhibits temporal or spatial coherence, forward-backward smoothing can effectively suppress error propagation and significantly improve estimation accuracy. However, smoothing requires sub-array division, which reduces the system's degrees of freedom, thereby reducing the number of estimable sources. Furthermore, due to the reduced subspace dimensionality, the algorithm's estimation performance degrades.

[0004] The atomic norm theory effectively addresses several challenges in the signal reconstruction process by introducing a sparsity measure, showing particular advantages when dealing with the DOA estimation problem of coherent signals. In DOA estimation, the atomic norm is regarded as a new sparsity measure that can model and estimate coherent signals without relying on a grid, thus overcoming the problem of traditional methods with significantly reduced estimation performance when the signals are highly correlated. However, although the atomic norm method has good robustness in theory, its estimation accuracy still has certain limitations. In particular, in low signal-to-noise ratio or small sample conditions, the estimation results may not be accurate enough, which limits its promotion and use in high-precision application scenarios.

[0005] Later, a proposal combined compressed sensing theory and proposed the L1-SVD algorithm based on L1 norm optimization. This method not only effectively estimates coherent signals but also reduces the bias seen in peak search methods. The L1-SVD method is suitable for estimating incoherent signals and can also effectively address issues with estimating coherent signals. However, many current peak search algorithms assume that the signal's incident angle is located at a precise grid location. In practice, however, the signal's angle typically does not fall precisely on the preset grid points. In this case, using these methods for angle estimation may introduce bias. To reduce this bias, a common approach is to divide the grid very finely. However, this approach inevitably increases the computational effort, placing higher requirements on the length of the dictionary matrix, which in turn increases the computational complexity of the sparse reconstruction algorithm and makes its implementation more difficult.

[0006] The applicant analyzed some existing DOA estimation schemes based on one-dimensional plane signals, especially coherent signals, such as the algorithm based on atomic norm minimization. This algorithm requires the use of the CVX toolbox to reconstruct a dual Toeplitz matrix during the signal reconstruction process. However, the matrix structure is complex and the computational complexity is huge. At the same time, many spectral peak search algorithms based on forward and backward smoothing preprocessing all assume that the angle of the incident signal is exactly at the precise position of the grid. When the incident angle deviates from the grid division point, the direction-finding error always exists. At the same time, conventional DOA estimation methods often require a trade-off between accuracy and performance, usually at the expense of accuracy, thereby affecting the accuracy of the final estimate. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a one-dimensional gridless coherent signal source DOA estimation method that takes into account both estimation accuracy and performance requirements under low signal-to-noise ratio conditions, in order to address the problem that the existing direction of arrival (DOA) estimation method has large deviations in coherent signal estimation due to grid mismatch under poor conditions.

[0008] The technical solution adopted by the present invention to solve the above technical problems is to use a grid-based DOA estimation method based on covariance vector processing and compressed sensing. By using the covariance matrix model of the deformed array received data, the present invention aims to achieve DOA estimation of one-dimensional planar coherent signals under small array elements with higher resolution. The method specifically includes the following steps:

[0009] Step 1) Calculate the covariance matrix of the received data;

[0010] Step 2) First, the covariance matrix is ​​vectorized into a covariance vector. Then, a difference coordination vector is obtained by performing element-by-element difference between the position of each array element in the array and the reference array element position. Then, each element in the difference coordination vector is sorted from small to large and duplicate elements are removed to obtain an integrated vector. A de-redundancy matrix is ​​constructed using the difference coordination vector and the integrated vector. Finally, the de-redundancy matrix is ​​multiplied by the covariance vector to obtain the received vector of the virtual signal, and a dictionary matrix of the virtual signal steering vector is constructed.

[0011] The number of rows in the de-redundancy matrix is ​​the same as the number of elements in the integration vector, and the t-th row in the de-redundancy matrix reflects the position and number of occurrences of the t-th element of the integration vector in the difference synergy vector.

[0012] Step 3) Orthogonal Matching Pursuit (OMP) algorithm:

[0013] Initialize the OMP residual using the received vector of the virtual signal, and initialize the OMP dictionary matrix using the dictionary matrix of the virtual signal steering vector;

[0014] During the iteration process, the grid angle corresponding to the steering vector with the highest matching degree with the OMP residual in the OMP dictionary matrix is ​​used as the OMP estimated angle of the signal source corresponding to the current iteration. The OMP residual and the OMP dictionary matrix are then updated until the OMP estimated angles of all signal sources are obtained.

[0015] Step 4) Gradient descent iterative DPL algorithm:

[0016] The OMP estimated angles of all sources are used to initialize the DPL accurate angle estimation value, and the DPL accurate angle estimation value of all sources is obtained through DPL iteration as the final output direction of arrival (DOA) estimation value.

[0017] Specifically, the DPL iteration is a two-layer nested iteration;

[0018] During the outer iteration, the precise DPL angle estimate is first used to obtain the steering vector matrix of the real element receiving signal. This is then transformed using a de-redundancy matrix and vectorization operations to obtain the steering vector matrix of the virtual element receiving signal. The virtual element receiving signal steering vector matrix and the virtual signal receiving vector are then used to obtain the virtual original signal and the DPL residual, thereby constructing a function of the steering angle and starting the inner iteration.

[0019] During the inner iteration process, the function of the arrival angle of the DPL precise angle estimate of the signal source corresponding to the current inner iteration is first derived, and then the DPL precise angle estimate is updated according to the step size and the derivative of the function of the arrival angle until the DPL precise angle estimate of all signal sources is updated. After the inner iteration is completed, it is determined whether the outer iteration has reached the stopping condition. If not, the outer iteration process is returned to. If so, the latest DPL precise angle estimate of all signal sources is used as the final output DOA estimate.

[0020] Preferably, the specific form of the t-th row in the redundancy removal matrix reflecting the position and number of occurrences of the t-th element of the integration vector in the difference coordination vector is:

[0021] When the integration vector D c The position set of the t-th element in the difference coordination vector D is {D q}; There are v elements in the difference coordination vector D, of which c are non-repeated elements; for the redundancy removal matrix F, row D q The elements of the column are assigned the integrated vector D c The reciprocal of the number of times w that the tth element appears in the difference coordination vector D The elements in other positions of row t are assigned 0. t=1,2,…c,D q ∈{1,2,…v}.

[0022] The present invention achieves the beneficial effect of deforming the array received data model and obtaining virtual signal received data through rearrangement. By combining the OMP and DPL algorithms, gridless DOA estimation is achieved. This method not only effectively decouples coherent signals but also effectively overcomes the low accuracy and poor estimation performance of traditional estimation methods under low signal-to-noise ratio conditions, small array elements, and single-snapshot data. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Flowchart of the present invention;

[0024] Figure 2 Comparison chart of array element performance curves;

[0025] Figure 3 Signal-to-noise ratio performance curve comparison chart;

[0026] Figure 4 Comparison chart of snapshot performance curves; DETAILED DESCRIPTION

[0027] In order to further illustrate the purpose, technical solution and advantages of the present invention, the present invention is described in detail below with reference to experiments and drawings. In a linear array with M elements, it is assumed that there are L signals coming from different directions, and their incident angles are θ l ,l=1,2,...,L. Figure 1 As shown in FIG, the off-grid DOA estimation algorithm based on covariance vectorization processing and compressed sensing specifically includes the following steps:

[0028] Step 1) Calculate the covariance matrix R of the received data y based on the known received data y x :

[0029]

[0030] Among them, N s Indicates the number of snapshots.

[0031] Step 2) Obtain the received data of the virtual signal through rearrangement operation and increase the number of array elements:

[0032] 2-1) First, the covariance matrix R x Vectorized into a covariance vector z:

[0033] z=vec(R x )

[0034] 2-2) For an array with a total of M elements, the array position set is The position q of each element in the array m With the reference element position q n Perform element-by-element difference to obtain a size of 1×M 2 The difference coordination vector D, m is the array element position number in the array, n is the array reference element position number, m=1,...,M, n=1,...,M;

[0035]

[0036] Among them, {q m} represents the set of all element positions in the array, It means any;

[0037] Taking an array of 4 elements as an example, the positions of the 4 elements in the array (q1, q2, q3, q4) are (1, 2, 3, 4). The element-by-element difference between the positions of each element in the array (q1, q2, q3, q4) and the reference element position is performed. When the reference element position is q1=1, the element-by-element difference is 0, 1, 2, 3; when the reference element position is q2, the element-by-element difference is -1, 0, 1, 2; when the reference element position is q3, the element-by-element difference is -2, -1, 0, 1; when the reference element position is q4, the element-by-element difference is -3, -2, -1,. In this way, the difference coordination vector D is a 1×16 vector (0, 1, 2, -3, 1, 0, -1, 2, -2, 1-, 0, -1, 3)-,; the number of elements in the difference coordination vector D is counted as v, v=M 2 ; D has a total of v elements, of which c are non-repeating elements;

[0038] 2-3) Then sort the elements in the difference coordination vector D from small to large and remove the duplicate elements to get the integrated vector D c ; The integration vector D of the above example c is (-3,-2,-1,0,1,2,3);

[0039] 2-4) Using the difference synergy vector D and the integration vector D c Constructing a redundancy removal matrix Represents the real number field, the number of rows of the redundancy matrix F and the integration vector D c The number of elements in the redundancy removal matrix F is the same, and the t-th row reflects the integration vector D c The position and number of occurrences of the tth element in the difference coordination vector D are as follows: c The position set of the t-th element in the difference coordination vector D is {D q}, then for the redundancy matrix F, row D q The elements of the column are assigned the integrated vector D c The reciprocal of the number of times w that the tth element appears in the difference coordination vector D The elements in other positions of row t are assigned 0. t=1,2,…c,D q ∈{1,2,…v}.

[0040] For example, the integration vector D c The first element "-3" is at position 13 in D, and the number of times "-3" appears in D is 1. Then the elements in the first row of the redundancy removal matrix F are all 0 except the element in the 13th column which is 1; the integration vector D c The position of the second element "-2" in D is {9, 14}, and the number of times "-3" appears in D is 2. Then, in the first row of the redundancy removal matrix F, all elements except the 9th and 14th columns are 0.5.

[0041] 2-5) Multiply the redundancy removal matrix F by the covariance vector z to obtain the received vector z of the virtual signal D :

[0042] z D =Fz

[0043] 2-6) The virtual array steering vector is equivalent to the interval (-(M-1):(M-1)), so the dictionary matrix A of the virtual signal steering vector is xz Expressed as: n t Indicates the number of grid points. The number of grids can be divided arbitrarily according to needs. Each guide vector in the dictionary Expressed as:

[0044]

[0045] , T represents transpose, e is a natural constant, d is the array element spacing, λ is the wavelength of the received signal, Indicates the first t grid angle, l t =1,...,n t .

[0046] Step 3) Orthogonal Matching Pursuit (OMP) algorithm:

[0047] 3-1) Initialization steps:

[0048] Set the initialization current residual r k For z D , initialize the current dictionary matrix to A xz , k represents the number of iterations, initialize k = 0; let the set of steering vectors that can represent the signal angle be the atomic set Initialized to a full 0 matrix, L is the number of signal sources, Represents a set of integers; initialize OMP to estimate the angle θ omp is an empty set;

[0049] 3-2) Iteration steps:

[0050] Start the kth iteration:

[0051] Calculate the current dictionary matrix The q column and the current residual r k Matching degree II k (q):

[0052]

[0053] 1 represents the l1 norm; find the maximum value index will p s dictionary p s Grid corner corresponding to the column Deposit into θ omp in; and The pth s The columns are added to the atomic set A in order from the smallest to the largest number of iterations k. 0 middle;

[0054] Using A 0 and z D The explicit solution of the normal equation of the least squares solution of derives the optimal parameters of the least squares method.

[0055]

[0056] in, -1 represents the inverse of the matrix, H represents the conjugate transpose of a matrix;

[0057] Using A 0 、 and z D Update residual r k :

[0058]

[0059] Update the current dictionary matrix

[0060]

[0061] Among them, I 2M-1 Indicates the dimension The identity matrix, represents a complex domain;

[0062] Determine whether k = L. If so, it means that the OMP estimated angle θ of all sources is obtained. omp If not, it means k<L, update k=k+1, and return to iterative step 3-2).

[0063] Step 4) Gradient descent iterative DPL algorithm:

[0064] 4-1) Initialization steps:

[0065] Initialize the number of iterations i = 0 and use θ omp Initialize DPL accurate angle estimate is the precise angle of the lth source at the i-th iteration, l = 1, 2, ... L; set the tolerance value ε = 0.0001, the step size d l =0.01 / 100, the step size is iterated with a scaling of 0.01 / 100, the angle accuracy value is benchmarked, and the total number of DPL iterations G=10000;

[0066] 4-2) Iteration steps:

[0067] 4-2-1 Start the outer layer i-th iteration:

[0068] use Get the real array element receiving signal steering vector matrix A i :

[0069]

[0070] Among them, A i Each steering vector

[0071]

[0072] Then use the redundancy matrix F to A i Perform the transformation to obtain the transformed steering vector matrix is the kron inner product;

[0073] use and z D Calculate the virtual original signal S i :

[0074]

[0075] Calculate residuals

[0076]

[0077] According to S i 、 and tolerance value ε to construct the function of the angle

[0078]

[0079] Among them, ‖·‖2 is the l2 norm,

[0080] 4-2-2 Angle Updated inner iteration:

[0081] 4-2-2-1 Initialize the signal source number l=1;

[0082] 4-2-2-2 For the lth source angle: for the transformed steering vector matrix About Angle Derivative: d represents the derivative;

[0083] Among them, the intermediate Intermediate amount

[0084] To S i About Angle Find the partial derivative:

[0085]

[0086] in, Indicates partial derivative;

[0087] Then to S i The l1 norm of the angle Find the partial derivative:

[0088]

[0089] Among them, the intermediate Re means taking the real part, tr means the trace of the matrix, and diag means generating a diagonal matrix;

[0090] Residual About Angle Find the partial derivative:

[0091]

[0092] Among them, I M Indicates the dimension The identity matrix of

[0093] Residual The l2 norm of the angle Find the partial derivative:

[0094]

[0095] Using S i The l1 norm of the angle The partial derivative and residual of The l2 norm of the angle The partial derivative of the tolerance value ε is a function of the angle of arrival Derivative:

[0096]

[0097] Reuse step size d l and the function of the angle of approach The derivative of the angle To update:

[0098]

[0099] Determine whether l=L is satisfied. If so, the DPL accurate angle estimation value of this iteration is completed. And go to step 4-2-3, otherwise, l<L, update l=l+1, return to step 4-2-2-2 of this iteration, and start the above processing for the new l-th signal source angle;

[0100] 4-2-3 Determine whether i=G. If so, output the latest iteration of the DPL accurate angle estimate. As the final angle estimate, otherwise, i<G, update i=i+1, return to step 4-2-1, update A i 、 S i and

[0101] The DPL algorithm does not require a grid, but the computational complexity of using DPL directly is too high. The present invention first uses OMP to make a preliminary angle estimate and then uses DPL, which can well balance accuracy and computational cost.

[0102] In order to make the purpose, technical solution and technical effect of the present invention clearer, the present invention is further described in detail through simulation experiments.

[0103] This experiment conducted a simulation experiment on the invented off-grid DOA estimation algorithm based on covariance vector processing and compressed sensing.

[0104] Simulation Experiment 1: This experiment uses a linear array with four elements and a linear array structure. The angle estimates are [-10.58°, -5.82°, 16.34°], the fixed spacing between array elements is half a wavelength, the signal-to-noise ratio is set to 25dB, and the number of snapshots is single. This method estimates the incoming angle of the signal and compares it with the forward and backward spatial smoothing method, the L1-SVD method, and the atomic norm subspace method. All methods were verified in 50 Monte Carlo experiments, and the experimental results are shown in Table 1:

[0105] Table 1 Single snapshot 4-element performance comparison

[0106] [-10.58,-5.82,16.34] Signal coherence error Method of the present invention (-10.6447°,-5.7288°,17.0726°) 0.8885 Forward and backward smoothing The number of sub-array elements is less than the number of signal sources and cannot be estimated. L1-svd (-32.1°,-8.4°,17.0°) 24.76 Atomic norm subspace method (-23.8390°,-8.1087°,16.5633°) 15.7710

[0107] As can be seen from Table 1, the algorithm of the present invention shows significant advantages in the case of single snapshot, few array elements, and multiple signal sources. The algorithm can not only accurately estimate the arrival angle of the signal, but also has a high estimation accuracy. In order to further verify the advantages of this method under single snapshot conditions, the root mean square error (RMSE) performance curve of this algorithm and the atomic norm subspace method under different numbers of array elements was compared. While keeping other conditions unchanged, the experiment used arrays with 4, 8, 16 and 32 array elements for testing. The experimental results are shown in Figure 1. Figure 2 The array element performance curve comparison chart is shown as follows:

[0108] It can be seen from the experimental results that when the number of array elements is small and close to the number of signal sources, under single-snapshot conditions, the forward and backward smoothing decorrelation method cannot effectively decouple the signal because the number of array elements in the sub-array is less than the number of signal sources, resulting in the inability to complete effective DOA estimation. The L1-SVD compressed sensing method is more sensitive to the choice of regularization parameters and requires multiple parameter adjustments, which makes the experimental results less stable, the overall angle estimation performance is not ideal, and the accuracy is affected by the grid deviation problem. The estimation accuracy of the atomic norm subspace method also decreases significantly under these conditions. In contrast, the algorithm proposed in the present invention can still achieve high-precision arrival angle estimation under the above-mentioned unfavorable conditions, and its estimation performance continues to be better than the atomic norm subspace method as the number of array elements increases.

[0109] Simulation Experiment 2: This experiment uses a linear array with 8 elements, a fixed spacing of half a wavelength between array elements, a signal-to-noise ratio of 25 dB, and a snapshot count of 100. The angle estimates are [-10.58°, -5.82°, 16.34°]. The method of the present invention is used to estimate the incoming angle of the signal and is compared with the forward and backward spatial smoothing method, the L1-SVD method, and the atomic norm subspace method. All methods are verified in 50 Monte Carlo experiments. The experimental results are shown in Table 1:

[0110] Table 2 100 Snapshot 8-element performance comparison

[0111] [-10.58,-5.82,16.34] Signal coherence error Method of the present invention (-10.5829,-5.7655,-16.3697) 0.0758 Forward and backward smoothing (-10.5100,-5.7900,-16.3300) 0.4322 L1-svd (-12.1,-7.0,-17.4) 3.76 Atomic norm subspace method (-13.1115,-6.9341,-16.9514) 4.2570

[0112] From the results of Experiment 2, it can be seen that with the increase in the number of array elements, the estimation performance of the forward and backward spatial smoothing decorrelation method under coherent signal conditions is improved, and angle estimation can be achieved to a certain extent. However, its accuracy is still significantly lower than the method proposed in the present invention. For the L1-SVD compressed sensing method, since it is highly sensitive to the regularization parameter, it needs to be repeatedly adjusted to obtain a better solution, which leads to poor stability of the experimental results, and the accuracy is limited by the influence of the grid deviation problem. Therefore, the overall angle estimation performance has not yet reached the ideal level. Although increasing the number of array elements can improve its estimation effect to a certain extent, it is still necessary to further expand the array scale to achieve more accurate angle estimation. At the same time, the atomic norm subspace method still shows a large estimation error under the conditions of this experiment.

[0113] Simulation experiment three: In order to further verify the advantages of the method of the present invention in angle estimation accuracy, this experiment used 16 array elements, 100 snapshots, and set the signal-to-noise ratio to -5dB, 0dB, 10dB, 15dB and 25dB respectively. The forward and backward spatial smoothing method, L1-SVD method, and atomic norm subspace method were used in the experiment and compared with the method proposed in this invention. All methods were verified in 50 Monte Carlo experiments. The experimental results are shown in Figure 2. Figure 3 As shown, a comparison of the signal-to-noise performance curves is shown.

[0114] The results of Experiment 3 show that when the number of array elements and the number of snapshots remain at an optimal and fixed level, a low signal-to-noise ratio will cause the forward and backward spatial smoothing method and the L1-SVD method to produce large estimation errors. The estimation error of the L1-SVD method is not only affected by the grid deviation problem, but also by the interference of coherent signals. The atomic norm subspace method is insensitive to changes in the signal-to-noise ratio when processing coherent signals, but its angle estimation error is always large. In contrast, the method proposed in the present invention can still achieve relatively accurate angle estimation under low signal-to-noise ratio conditions, and as the signal-to-noise ratio increases, its estimation accuracy has significant advantages over other algorithms.

[0115] Simulation experiment 4: In order to further verify the advantages of the method of the present invention in the case of low snapshots and multiple sources in angle estimation, this experiment used 16 array elements, the signal-to-noise ratio was set to 10dB, and the number of snapshots was 5, 10, 20 and 50 respectively. The forward and backward spatial smoothing method, L1-SVD method, and atomic norm subspace method were used in the experiment and compared with the method of the present invention. All methods were verified in 50 Monte Carlo experiments. The experimental results are shown in Figure 4. Figure 4 As shown, a comparison of snapshot number performance curves is shown.

[0116] The results of Experiment 4 show that when the number of array elements is optimal and the signal-to-noise ratio is low, a low number of snapshots will cause the forward and backward spatial smoothing method to produce large errors in angle estimation. In contrast, the atomic norm subspace method and the L1-SVD method are not sensitive enough to changes in the number of snapshots under this condition. For the L1-SVD method, its estimation error is affected by the grid deviation problem and coherent signals; while the atomic norm subspace method always has a large angle estimation error when processing coherent signals. Unlike the above methods, the method proposed in the present invention can still perform angle estimation more accurately even under low snapshot conditions, and as the number of snapshots increases, its estimation accuracy has a significant advantage over other algorithms.

[0117] In summary, the off-grid DOA estimation algorithm based on covariance vector processing and compressed sensing can still make relatively accurate estimates of the direction of arrival angle under unfavorable conditions such as few array elements, multiple signal sources, low snapshots and low signal-to-noise ratio, demonstrating its superiority and robustness in complex environments.

[0118] The above description is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless otherwise specified, may be replaced by other features that are equivalent or have similar purposes; all disclosed features, methods, or steps in the process, except for mutually exclusive features and / or steps, may be combined in any manner. Any non-essential modifications or replacements made by those skilled in the art based on the features of the technical solution of the present invention fall within the scope of protection of the present invention.

Claims

1. A method for estimating off-grid DOA based on covariance vectorization and compressed sensing, characterized in that: The specific steps include: Step 1) Calculate the covariance matrix of the received data; Step 2) First, the covariance matrix is ​​vectorized into a covariance vector. Then, a difference coordination vector is obtained by performing element-by-element difference between the position of each array element in the array and the reference array element position. Then, each element in the difference coordination vector is sorted from small to large and duplicate elements are removed to obtain an integrated vector. A de-redundancy matrix is ​​constructed using the difference coordination vector and the integrated vector. Finally, the de-redundancy matrix is ​​multiplied by the covariance vector to obtain the received vector of the virtual signal, and a dictionary matrix of the virtual signal steering vector is constructed. The number of rows in the de-redundancy matrix is ​​the same as the number of elements in the integration vector, and the t-th row in the de-redundancy matrix reflects the position and number of occurrences of the t-th element of the integration vector in the difference synergy vector. Step 3) Orthogonal Matching Pursuit (OMP) algorithm: Initialize the OMP residual using the received vector of the virtual signal, and initialize the OMP dictionary matrix using the dictionary matrix of the virtual signal steering vector; During the iteration process, the grid angle corresponding to the steering vector with the highest matching degree with the OMP residual in the OMP dictionary matrix is ​​used as the OMP estimated angle of the signal source corresponding to the current iteration. The OMP residual and the OMP dictionary matrix are then updated until the OMP estimated angles of all signal sources are obtained. Step 4) Gradient descent iterative DPL algorithm: The OMP estimated angles of all sources are used to initialize the DPL accurate angle estimation value, and the DPL accurate angle estimation value of all sources is obtained through DPL iteration as the final output direction of arrival (DOA) estimation value.

2. The method according to claim 1, wherein: DPL iteration is a two-layer nested iteration; During the outer iteration, the precise DPL angle estimate is first used to obtain the steering vector matrix of the real element receiving signal. This is then transformed using a de-redundancy matrix and vectorization operations to obtain the steering vector matrix of the virtual element receiving signal. The virtual element receiving signal steering vector matrix and the receiving vector of the virtual signal are then used to obtain the virtual original signal and the DPL residual, thereby constructing a function of the steering angle and starting the inner iteration. During the inner iteration process, the function of the arrival angle of the DPL precise angle estimate of the signal source corresponding to the current inner iteration is first derived, and then the DPL precise angle estimate is updated according to the step size and the derivative of the function of the arrival angle until the DPL precise angle estimate of all signal sources is updated. After the inner iteration is completed, it is determined whether the outer iteration has reached the stopping condition. If not, the outer iteration process is returned to. If so, the latest DPL precise angle estimate of all signal sources is used as the final output DOA estimate.

3. The method according to claim 1, wherein: The t-th row in the redundancy removal matrix reflects the position and number of occurrences of the t-th element of the integration vector in the difference synergy vector: When the integration vector D c The position set of the t-th element in the difference coordination vector D is {D q }; There are v elements in the difference coordination vector D, of which c are non-repeated elements; for the redundancy removal matrix F, row D q The elements of the column are assigned the integration vector D c The reciprocal of the number of times w that the tth element appears in the difference coordination vector D The elements in other positions of row t are assigned 0. t=1,2,…c,D q ∈{1,2,…v}.

4. The method according to claim 1, wherein: The specific method of constructing the dictionary matrix of the virtual signal steering vector is: The virtual array steering vector is equivalent to the interval (-(M-1):(M-1)), where M is the total number of elements in the antenna array; the dictionary matrix A of the virtual signal steering vector is xz Expressed as: Among them, n t represents the number of grid points, A xz Each steering vector in Expressed as: Where T represents transpose, e is a natural constant, d is the array element spacing, and λ is the wavelength of the received signal. Indicates the first t grid angle, l t =1,...,n t .

5. The method according to claim 4, wherein: The orthogonal matching pursuit OMP algorithm is specifically: Initialization steps: Set the initialization of the current OMP residual r k is the receiving vector z of the virtual signal D , initialize the current OMP dictionary matrix to Dictionary matrix A of virtual signal steering vector xz , k represents the number of iterations, initialize k = 0; let the set of steering vectors that can represent the signal angle be the atomic set Initialized to a full 0 matrix, L is the number of signal sources, Represents a set of integers; initialize OMP to estimate the angle θ omp is an empty set; Iteration steps: Start the kth iteration: Calculate the current dictionary matrix The q column and r k Matching degree II k (q): 1 represents the l1 norm; find the maximum value index will p s dictionary p s Grid corner corresponding to the column Deposit into θ omp middle; and will The pth s The columns are added to the atomic set A in order from the smallest to the largest number of iterations k. 0 middle; Using A 0 and z D Get the optimal parameters of the least squares method in, -1 represents the inverse of the matrix, H represents the conjugate transpose of a matrix; Using A 0 、 and z D Update residual r k : Update the current OMP dictionary matrix Among them, I 2M-1 Indicates the dimension The identity matrix, represents a complex domain; Determine whether k = L. If so, it means that the OMP estimated angle θ of all sources is obtained. omp If not, update k=k+1 and return to the iterative step.

6. The method according to claim 2, wherein: The initialization steps in the gradient descent iterative DPL algorithm are: Initialize the number of iterations i = 0 and use θ omp Initialize DPL accurate angle estimate θ omp Estimate the OMP angle for all sources; is the exact angle of the lth source at the i-th iteration, l=1,2,…L; set the tolerance value ε and step size d l And DPL presets the total number of iterations G.

7. The method according to claim 6, wherein: The specific steps of the iterative process in the gradient descent iterative DPL algorithm are: 1) Start the outer layer i-th iteration: use Get the real array element receiving signal steering vector matrix A i : Among them, A i Each steering vector Then use the redundancy matrix F to A i The transformed virtual array element receives the signal by steering vector matrix is the kron inner product; use and z D Calculate the virtual original signal S i : Calculate DPL residuals According to S i 、 and tolerance value ε to construct the function of the angle Among them, ‖·‖2 is the l2 norm, 2) Update the DPL accurate angle estimate through inner layer iteration 3) Determine whether i=G. If so, output the latest DPL accurate angle estimate. As the final angle estimation value, otherwise, update i=i+1 and return to step 1).

8. The method according to claim 7, wherein: DPL accurate angle estimation through inner iteration The specific method is: 2-1) Initialize the signal source number l=1; 2-2) For the lth source angle: the transformed steering vector matrix About Angle Derivative: d represents the derivative; Among them, the intermediate Intermediate amount To S i About Angle Find the partial derivative: To S i The l1 norm of the angle Taking the partial derivative we get Among them, the intermediate Re means taking the real part, tr means the trace of the matrix, and diag means generating a diagonal matrix; Residual About Angle Find the partial derivative: Among them, I M Indicates the dimension The identity matrix of Residual The l2 norm of the angle Find the partial derivative: Function of the angle to the direction Taking the derivative we get: Reuse step size d l and the function of the angle of approach The derivative of the angle To update: Determine whether l=L is satisfied. If so, the DPL accurate angle estimation value of this iteration is completed. And go to step 3), otherwise, l<L, update l=l+1, and return to step 2-2) of this iteration.

Images