Sparse representation-like direction-of-arrival estimation method based on distributed algorithm

Abstract

The present invention belongs to the field of signal processing, and in particular relates to direction of arrival estimation of electromagnetic signals and sonar signals. Specifically, it is a sparse representation-based direction of arrival estimation method based on a distributed algorithm, which can be used for passive positioning and target detection. The method comprises the following steps: S1, establishing a distributed sparse representation model at the receiving end, S2, establishing a distributed DOA estimation model, and S3, solving the distributed model to obtain the DOA value. The method proposed in the present invention realizes the distributed solution of the algorithm, thereby essentially avoiding the shortcomings of the centralized algorithm. At the same time, it can maintain good estimation performance, which is similar to the estimation performance of the centralized algorithm. In addition, the adaptability under low snapshot numbers is better than that of the subspace-based method.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing, and in particular relates to direction-of-arrival (DOA) estimation of electromagnetic signals and sonar signals. The present invention specifically provides a sparse representation-based DOA estimation method based on a distributed algorithm, which can be used for passive positioning and target detection. Background Art

[0002] DOA (Direction of Arrival) estimation technology is an important research direction in array signal processing. It refers to using sensor arrays at different geographical locations to receive signals, obtain discrete observation data, and then process it through a series of mathematical algorithms to obtain useful information from the source signal while suppressing interference information. It has a wide range of applications in military and civilian fields such as autonomous driving, wireless communications, and radar.

[0003] Traditional DOA estimation technology is a centralized algorithm, requiring all elements in the array to transmit the received signal information to a central processor for processing by the relevant algorithm. However, this algorithm concept is limited in many scenarios. For example, in a large array composed of geographically dispersed sub-arrays, a large amount of observation data needs to be transmitted between sub-arrays to a central processor, but the capacity of the communication link limits the data transmission between sub-arrays. In addition, in many scenarios, centralized processing will completely fail. For example, in a sonar environment, because the signal is received by sub-arrays that are far apart, it loses coherence and cannot be centrally coherently processed.

[0004] Furthermore, while subspace-based methods perform well, they lack adaptability to challenging scenarios, such as low signal-to-noise ratios and small snapshot counts. Sparse representation-based methods, which incorporate compressed sensing techniques, are robust to these challenging scenarios. Therefore, to improve algorithm adaptability, it is necessary to design decentralized sparse representation-based DOA estimation algorithms. Summary of the Invention

[0005] The purpose of the present invention is to address the shortcomings of the above-mentioned existing technologies and propose a sparse representation-based DOA estimation method based on a distributed algorithm. This method decentralizes the solution process of sparse representation-based methods, thereby avoiding the impact of traditional centralized algorithms and achieving estimation performance similar to that of centralized algorithms, and can adapt to harsh scenarios such as single snapshots.

[0006] The specific technical solutions adopted in the present invention are as follows:

[0007] A sparse representation-based direction of arrival estimation method based on a distributed algorithm, the method comprising the following steps:

[0008] S1. Establish a distributed sparse representation model at the receiving end;

[0009] S2, establish a distributed DOA estimation model;

[0010] S3, solving the distributed model to obtain the DOA value;

[0011] In a further improvement of the present invention, in step S1, establishing a distributed sparse representation model includes the following process:

[0012] S11. First, divide the spatial domain [-90°, 90°] into grid points, that is, the supercomplete basis set is:

[0013]

[0014] Among them, the number of grids is generally set Much larger than the number of array elements M,

[0015] Assume that all signal sources fall within the set grid and obtain the corresponding flow matrix Right now:

[0016]

[0017] a(θ k )=[1,e iπcosθ ,…,e iπ(M-1)cosθ ] T ;

[0018] S12, use M array elements to form a uniform linear array with a spacing dimension of half the wavelength of the incident narrowband signal, recorded as array x; assume that there are K far-field narrowband signals with θ k , k = 1, ..., K, after receiving L = 1 snapshots, the signal received by array x is expressed as:

[0019]

[0020] Among them, y is the array element receiving data matrix, s is the sparse vector and noise n is the noise data matrix, the noise and signal are independent of each other; in addition, the sparse vector s is defined as the incident signal source x k (kth incident signal), that is,

[0021]

[0022] Among them, s n Represents the nth row element of the signal matrix S. Therefore, the DOA estimation problem is transformed into a sparse representation problem, that is, recovering the sparse vector s.

[0023] S13. Divide the M arrays into P sub-arrays (nodes), i.e., the number of sub-array elements is C = M / P. Each sub-array has a sub-processor that can only store and process data that can be obtained by the sub-array. In addition, the neighboring nodes of each node are specified, and the neighboring nodes of the i-th node are expressed as

[0024] Therefore, the original signal is also divided into components belonging to each sub-array. The following additions are made to the definition of the original model: (■) j represents the vector (or matrix) component belonging to the jth sub-matrix, j = 1, ..., P. For example, the incident signal X can be expressed as X = [x1, x2, ..., x P ], where x1 is the incident signal received by the first sub-array.

[0025] A further improvement of the present invention is that in step S2, a distributed DOA estimation model is established to jointly optimize the problems of these P sub-nodes.

[0026]

[0027] sts i -z=0

[0028] Among them, s i is the parameter solution of the ith subsystem, A i is the flow matrix of the i-th sub-matrix, y i is the received signal vector belonging to each submatrix, the auxiliary variable z serves as the global consistent variable of the problem, and λ is the regularization parameter and is greater than zero.

[0029] In a further improvement of the present invention, in step S3, the specific process of solving the above DOA estimation model is as follows:

[0030] S31. The solution step is an iterative form, specifically

[0031]

[0032] in, is the parameter solution of the i-th submatrix in the k+1th iteration, z k+1 is the global consistent solution of the k+1th iteration, is the Lagrange multiplier of the i-th submatrix in the k+1th iteration, and ρ is the Lagrange variable. When the number of iterations is greater than the maximum number of iterations or the residual pr of the original problem k and the residual dr of the dual problem k are all less than the threshold ∈ ADMM The iteration stops when

[0033]

[0034] in, The mean of the P sub-matrix parameter solutions at the kth iteration. Here, the average consensus protocol is used to obtain the mean.

[0035] The average consensus protocol is an algorithm based on the Laplace matrix of the distributed network. The Laplace matrix is ​​defined as when node i can communicate with node j, l ij = -1; otherwise, it is 0; the degree of freedom of the node itself (how many nodes it can communicate with) is l ii (l jj ), that is,

[0036]

[0037] Assume that the Laplace matrix L has R different eigenvalues ​​λ1,…,λ R , and λ R =0, then the initial weight is:

[0038]

[0039] The weights are then:

[0040] W(t)=L-λ t+1 I

[0041] If the mean value of x(t) is required, AC(x j (t)), then the iterative formula of the protocol is:

[0042] x(t+1)=W(t)x(t)

[0043] S32, in the iterative process, first calculate

[0044]

[0045] Then, find z k+1 :

[0046]

[0047] in, The solution for the P subsystem parameters for the k+1th iteration is The average value of The solution for the P subsystem parameters for the kth iteration is At the same time, SRK β (v) is the soft threshold operator, which is defined as

[0048]

[0049] Finally, update

[0050]

[0051] After the iteration stops and the final solution z is obtained, the DOA estimation result can be obtained through the spectrum of z.

[0052] Beneficial effects of the present invention: The method proposed in the present invention realizes the distributed solution of the algorithm, thereby essentially avoiding the shortcomings of the centralized algorithm; at the same time, it can maintain good estimation performance, which is similar to the estimation performance of the centralized algorithm; in addition, its adaptability at low snapshot numbers is better than that of the subspace method. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is the overall flow chart of the present invention.

[0054] Figure 2 This is a performance diagram of an example of the present invention under a small signal-to-noise ratio.

[0055] Figure 3 It is a performance graph of the example of the present invention and the centralized method.

[0056] Figure 4 It is a performance graph of the example of the present invention and the distributed method. Specific implementation plan

[0057] In order to deepen the understanding of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The embodiments are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0058] like Figure 1 As shown, a sparse representation-like direction of arrival estimation method based on a distributed algorithm includes the following steps:

[0059] S1. Establish a distributed sparse representation model at the receiving end;

[0060] S11. First, divide the spatial domain [-90°, 90°] into grid points, that is, the supercomplete basis set is

[0061]

[0062] Among them, the number of grids is generally set It is much larger than the number of array elements M. Assuming that all signal sources fall within the set grid, the corresponding flow matrix is ​​obtained Right now

[0063]

[0064] a(θ k )=[1,e iπcosθ,…,e iπ(M-1)cosθ ] T

[0065] S12, use M array elements to form a uniform linear array with a spacing dimension of half the wavelength of the incident narrowband signal, denoted as array x; suppose there are K far-field narrowband signals with a spacing dimension of θ k , k=1,…,K, after receiving L=1 snapshots, the signal received by array x is expressed as:

[0066]

[0067] Among them, y is the array element receiving data matrix, s is the sparse vector and noise n is the noise data matrix, and the noise and signal are independent of each other.

[0068] S13. Divide the M arrays into P sub-arrays (nodes), i.e., the number of sub-array elements is C = M / P. Each sub-array has a sub-processor that can only store and process data that can be obtained by the sub-array. In addition, the neighboring nodes of each node are specified, and the neighboring nodes of the i-th node are expressed as Therefore, the original signal is also divided into components belonging to each sub-array. The following additions are made to the definition of the original model: (■) j represents the vector (or matrix) component of the jth submatrix with a row dimension of C, where j = 1,…,P. For example, the incident signal X can be represented as X = [x1, x2,…, x P ], where x1 is the C×1-dimensional incident signal received by the first sub-array.

[0069] S2. Establish a distributed DOA estimation model to jointly optimize the problems of these P sub-nodes.

[0070]

[0071] sts i -z=0

[0072] Among them, s i is the parameter solution of the ith subsystem, A i is the flow matrix of the i-th sub-matrix, y i is the received signal vector belonging to each submatrix, the auxiliary variable z serves as the global consistent variable of the problem, and λ is the regularization parameter and is greater than zero.

[0073] S3. Calculate the weight w(θ) by the distributed conjugate gradient method. The specific form is:

[0074] S31. The solution step is an iterative form, specifically

[0075]

[0076] in, is the parameter solution of the i-th submatrix in the k+1th iteration, z k+1 is the global consistent solution of the k+1th iteration, is the Lagrange multiplier of the i-th submatrix in the k+1th iteration, and ρ is the Lagrange variable. When the number of iterations is greater than the maximum number of iterations or the residual pr of the original problem k and the residual dr of the dual problem k are all less than the threshold ∈ ADMM The iteration stops when

[0077]

[0078] in, The mean of the P sub-matrix parameter solutions at the kth iteration. Here, the average consensus protocol is used to obtain the mean.

[0079] The average consensus protocol is an algorithm based on the Laplace matrix of the distributed network. The Laplace matrix is ​​defined as when node i can communicate with node j, l ij = -1; otherwise, it is 0; the degree of freedom of the node itself (how many nodes it can communicate with) is l ii (l jj ), that is,

[0080]

[0081] Assume that the Laplace matrix L has R different eigenvalues ​​λ1,…,λ R , and λ R =0, then the initial weight is:

[0082]

[0083] The weights are then:

[0084] W(t)=L-λ t+1 I

[0085] If the mean value of x(t) is required, AC(x j (t)), then the iterative formula of the protocol is:

[0086] x(t+1)=W(t)x(t)

[0087] S32, in the iterative process, first calculate

[0088]

[0089] Then, find z k+1 :

[0090]

[0091] in, The solution for the P subsystem parameters for the k+1th iteration is The average value of The solution for the P subsystem parameters for the kth iteration is At the same time, SRK β (v) is the soft threshold operator, which is defined as:

[0092]

[0093] Finally, update

[0094]

[0095] After the iteration stops and the final solution z is obtained, the DOA estimation result can be obtained through the spectrum of z.

[0096] The effects of the present invention are further described with reference to simulation examples. MUSIC (Multiple Signal Classification) is an angle estimation method.

[0097] The following simulation examples are all based on a 12-ULA array with an element spacing of λ / 2, which is divided into P = 6 sub-arrays and the neighboring nodes of the sub-arrays are specified. In the sub-array division, the neighboring nodes of each sub-array are specified as follows:

[0098]

[0099] In the algorithm solution process, because it is based on a single-block shooting scenario, the snapshot is always L = 1; the regularization parameter λ = 0.625 is selected, and the spatial domain is divided into angles with an interval of 2°. Then, the iterative grid optimization method is used for processing. The maximum number of iterations of the ADMM algorithm is set to 2000, and the iteration stop threshold is 10 -4 .

[0100] Simulation Example 1: Consider a low signal-to-noise ratio scenario. Assume that two far-field uncorrelated signal sources are incident on the distributed array from the directions of [-10°, 10°], and the signal-to-noise ratio (SNR) is 0 dB. Figure 2 The spatial spectrum of the distributed on-grid method for low signal-to-noise ratio (SNR) conditions is shown. The pink dashed line represents the correct direction of arrival (DOA) of the signal source. The spectrum peaks are located at -10° and 10°, indicating that the direction of arrival can be accurately predicted. Although spurious peaks may occur, they do not affect the estimation results.

[0101] Simulation Example 2: Verify whether the distributed ES method can approach the estimation performance of the centralized ES method. RMSE (Root Mean Square Error) is used to measure it. Its calculation formula is:

[0102]

[0103] Here, mt = 1000. Assume that two far-field uncorrelated signals are incident on the distributed array from the directions [-10°, 5°], and the signal-to-noise ratio varies within the range SNR = [0.20] dB with a step size of 2. The centralized algorithm still treats the entire ULA array as a whole. Figure 3 A performance comparison chart of the distributed and centralized on-grid methods as the signal-to-noise ratio changes is presented. It can be seen that the distributed method gradually approaches the centralized result as the signal-to-noise ratio increases. Therefore, the distributed on-grid method has an estimation performance similar to that of the centralized method.

[0104] Simulation Example 3: Comparison with the distributed MUSIC algorithm. The experimental assumptions are consistent with those of Simulation Example 2. Figure 4 The estimation performance of the two methods is compared with changes in the signal-to-noise ratio. A comparison shows that in single-block scenarios, the on-grid method can correctly locate the source direction, while the mean square error of distributed MUSIC is very large, making it completely incapable of accurately estimating the source direction.

[0105] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A sparse representation-based direction of arrival estimation method based on a distributed algorithm, characterized in that: The following steps are involved: S1. Establish a distributed sparse representation model at the receiving end; S2, establish a distributed DOA estimation model; S3, solving the distributed model to obtain the DOA value; In step S1, establishing a distributed sparse representation model includes the following process: S11. First, divide the spatial domain [-90°, 90°] into grid points; S12. Use M array elements to form a uniform linear array with a spacing dimension of half the wavelength of the incident narrowband signal, denoted as array x; S13, divide the M array elements into P sub-arrays, that is, the number of sub-array elements is C = M / P. Each sub-array has a sub-processor, and can only store and process data that can be obtained by the sub-array. Define the neighboring nodes of each node, and express the neighboring nodes of the i-th node as In step S2, a distributed DOA estimation model is established to jointly optimize the problems of these P child nodes: s.t.s i -z=0 Among them, s i is the parameter solution of the ith subsystem, A i is the flow matrix of the i-th sub-matrix, y i is the received signal vector belonging to each sub-matrix, the auxiliary variable z serves as the global consistent variable of the problem, and λ is the regularization parameter and is greater than zero; In step S3, the specific process of solving the DOA estimation model is as follows: S31. The solution step is an iterative form, specifically in, is the parameter solution of the i-th submatrix in the k+1th iteration, z k+1 is the global consistent solution of the k+1th iteration, is the Lagrange multiplier of the i-th submatrix in the k+1th iteration, ρ is the Lagrange variable, when the number of iterations is greater than the maximum number of iterations or the residual pr of the original problem k and the residual dr of the dual problem k are all less than the threshold ∈ ADMM The iteration stops when in, The average value of the parameter solutions of the P sub-matrixes in the kth iteration is obtained using the average consensus protocol. The average consensus protocol is set according to the Laplace matrix of the distributed network. The Laplace matrix is ​​defined as when node i communicates with node j, I ij =-1; otherwise, it is 0; the degree of freedom of the node itself is I ii The value of Assume that the Laplace matrix L has R different eigenvalues ​​λ1,…,λ R , and λ R =0, then the initial weight is: The weights are then: W(t)=L-λ t+1 I If the mean value of x(t) is required, AC(x j (t)), then the iterative formula of the protocol is: x(t+1)=W(t)x(t) S32, in the iterative process, first calculate Then, find z k+1 : in, The solution for the P subsystem parameters for the k+1th iteration is The average value of The solution for the P subsystem parameters for the kth iteration is The average value of SRK β (v) is the soft threshold operator, which is defined as Finally, update After the iteration stops and the final solution z is obtained, the DOA estimation result is obtained through the spectrum of z.

2. The sparse representation-based direction of arrival estimation method based on a distributed algorithm according to claim 1, characterized in that: The S11 divides the spatial domain [-90°, 90°] into grid points, that is, the supercomplete basis set is: Among them, the number of grids is generally set Much larger than the number of array elements M, Assume that all signal sources fall within the set grid and obtain the corresponding flow matrix Right now: a(θ k )=[1,e iπcosθ ,…,And iπ(M-1)cosθ ] T 。 3. The sparse representation-based direction of arrival estimation method based on a distributed algorithm according to claim 2, characterized in that: The S12 is set with K far-field narrowband signals θ k , k = 1, ..., K, after receiving L = 1 snapshots, the signal received by array x is expressed as: Among them, y is the data vector received by the array element, s is the sparse vector, and n is the noise data vector. The noise and signal are independent of each other. In addition, the sparse vector s is defined as the vector of the incident signal source x. k Composition, incident signal source x k ,Right now Among them, s n Represents the n-th row element of the signal matrix S.

Images