Multi-target doa estimation method based on sparse array interpolation and singular value thresholding

Abstract

The present application relates to a kind of multi-target DOA estimation method based on sparse array interpolation and singular value threshold method, it belongs to array signal processing field, it is suitable for the multi-target direction finding of the number of array elements is few, its steps include: transmitting end antenna adopts uniform sparse structure arrangement, ensure that the virtual array of equivalent out with receiving end antenna is not redundant;Receiving end antenna is arranged according to non-uniform sparse structure, receives target echo signal;According to the rough direction range of target, interpolation filling of specific array element is carried out to original sparse array, the conversion matrix of sparse array is calculated;The array manifold matrix of sparse array interpolation optimization is calculated, and matrix filling is carried out using singular value threshold algorithm;High-precision DOA estimation of target signal source is realized using conventional beam forming algorithm.The present application can solve the angle ambiguity problem caused by sparse array, and the direction finding result of signal source is obtained using less array element aperture.

Description

Technical Field

[0001] This invention relates to the field of array signal processing, and in particular to a multi-target DOA estimation method based on sparse array interpolation and singular value thresholding, applicable to multi-target orientation estimation with a small number of array elements. Background Technology

[0002] Array signal processing, as a crucial component of signal processing, is widely applied in various fields, including civilian and defense applications. Its fundamental principle is to maximize the extraction of useful signals and characteristic information from the array while suppressing or eliminating interference and noise. The main objectives of array signal processing are to improve the accuracy of signal detection, enhance signal transmission efficiency within the array system, and reduce signal loss during propagation. Array signal processing technology holds significant value in various application scenarios, including radar, sonar, communication systems, biomedical imaging, and satellite navigation.

[0003] Array signal processing mainly includes two aspects: beamforming and DOA estimation. The primary goal of beamforming is to generate an array output signal with specific directionality based on the input signal and array structure. Beamforming can improve signal reception quality, reduce interference and noise, and increase signal transmission efficiency in the array system. The primary goal of DOA estimation is to estimate the direction of the incident signal from the received signal. Beamforming is used to control the directivity of the array signal to improve signal reception quality and transmission efficiency. DOA estimation is used to estimate the direction of the incident signal, thereby better understanding the spatial propagation characteristics of the signal.

[0004] The development of array signal processing technology is influenced by many factors, including array size, antenna structure, signal processing algorithms, and hardware technology. A larger antenna array aperture results in higher angular resolution for DOA estimation. Therefore, the traditional method to improve array angular resolution is to increase the antenna aperture. However, to avoid ambiguity in angles, this leads to excessive system complexity and significantly increased costs. Compared to traditional arrays, sparse arrays can increase virtual degrees of freedom, suppress mutual coupling, and reduce noise coherence by increasing element spacing. Furthermore, their low redundancy reduces resource waste and thus improves computational speed.

[0005] Patent application CN202210453142 discloses a generalized tag-based multi-Bernoulli DOA tracking method in a coprime array environment. This method introduces a generalized tag-based multi-Bernoulli filter to accurately estimate the number of signals and the DOA of the tracked signal. However, this method is limited by the coprime array arrangement and requires signal matching based on superimposed observation information. Patent application CN202211218992 discloses a novel symmetric sparse array design method based on hybrid near and far fields. This method utilizes an extended sparse array with symmetric characteristics to solve the DOA and distance estimation problems related to the number of degrees of freedom. This method designs a manifold symmetric sparse linear array, which contains redundant terms. The fourth-order cumulant matrix needs to be vectorized and straightened to remove these redundant terms. Summary of the Invention

[0006] To address the problem of DOA estimation for the number of targets with super-degrees of freedom in the prior art and to achieve high-precision DOA estimation with low computational complexity, this invention provides a multi-target DOA estimation method based on sparse array interpolation and singular value thresholding, which utilizes fewer array elements for multi-target DOA estimation.

[0007] This invention provides a multi-objective DOA estimation method based on sparse array interpolation and singular value thresholding, the specific steps of which include:

[0008] Step 1: The transmitting antenna adopts a uniform sparse structure to ensure that the virtual array equivalent to the receiving antenna is non-redundant.

[0009] Step 2: The receiving antenna is arranged according to a non-uniform sparse structure to obtain the received signal model:

[0010] The receiving antenna is arranged according to a non-uniform sparse structure to obtain the received signal model;

[0011] Step 3: Perform specific element interpolation and filling on the original sparse array according to the approximate direction range of the target, and calculate the sparse array transformation matrix: Perform specific element interpolation and filling on the original sparse array, and calculate the sparse array transformation matrix.

[0012] Step 4: Calculate the array manifold matrix after sparse array interpolation optimization, and fill the matrix using the singular value thresholding algorithm;

[0013] Step 5: Use conventional beamforming algorithms to achieve high-precision DOA estimation of the target signal source. Preferably, the received signal in step 2 can be expressed as:

[0014] x(t) = As(t) + v(t)

[0015] x(t)∈C N*1 Denotes the received signal vector of the sparse array; A∈C N*KLet s(t) ∈ C represent the direction matrix. K*1 Let v(t) ∈ C represent the signal source vector. N*1 Represents the noise vector; where A and s(t) are respectively represented as:

[0016] A=[a(θ1) a(θ2) … a(θ K )]

[0017] s(t)=[s1(t) s2(t) … s K (t)] T

[0018] Define the sparse array position set as S = [0 r1 r2 … r N-1 ], a(θ) is:

[0019]

[0020] Preferably, in step 3, the angle range [θ] within the interval is determined based on the approximate direction of the target. i (1) θ i (2) Interpolation is performed, and the set of angles is defined as follows:

[0021] θ i =[θ i (1) θ i (1) +Δθ θ i (1) +2Δθ … θ i (2) ]

[0022] Δθ is the angle step value. Based on the set of angles, the array manifold is constructed. The array manifold of the original sparse array can be expressed as:

[0023] A i =[a(θ i (1) ) a(θ i (1) +Δθ) a(θ i (1) +2Δθ) … a(θ i (2) )]

[0024] The array manifold representation of the virtual array, derived from interpolation, is as follows:

[0025]

[0026] Then the sparse array transformation matrix B i :

[0027]

[0028] Preferably, the array manifold matrix after interpolation optimization in step 4 can be expressed as:

[0029]

[0030] Construct a Toeplitz matrix based on the arrayed manifold, and complete the constructed matrix using the singular value thresholding algorithm. Inputs include the observation matrix X, the sampling set Ω, the threshold parameter τ, the step factor δ, the stopping iteration condition ε, the increment l, and the maximum number of iterations k. max .

[0031] Initialization is as follows: Z 0 =k0δP Ω (X), r0=0, k0 satisfies Iterative process:

[0032] (1) Let s k =r k-1 +l, calculate Make

[0033] (2) Let calculate

[0034] (3) If ||P Ω (Y k -X)|| F / ||P Ω If (X)||≤ε, the loop ends;

[0035] (4) Let

[0036] Output Y k .

[0037] The beneficial effects of this invention are:

[0038] Compared with existing design methods, this invention can obtain more accurate multi-target DOA estimation results with fewer array elements; moreover, this invention is applicable to any array type and has no requirements on array arrangement.

[0039] Compared with patent CN202210453142, the method of the present invention uses an interpolation method to flexibly obtain a new array manifold matrix based on the array layout, with low algorithm complexity and no limitation by the array layout; compared with patent CN202211218992, the array manifold obtained by the method of the present invention does not have element redundancy, and the DOA estimation performance is stable. Attached Figure Description

[0040] Figure 1This is a schematic diagram of the process of the present invention;

[0041] Figure 2a This is a diagram illustrating the location of the MIMO virtual array in this invention;

[0042] Figure 2b This is a diagram illustrating the position of the interpolation array of the present invention;

[0043] Figure 3 This is a diagram showing the DOA estimation results of the method of the present invention compared with a uniform aperture array;

[0044] Figure 4 This is a comparison chart showing the optimized DOA estimation performance of the method of the present invention under the minimum redundancy array.

[0045] Figure 5 This is a comparison chart of the DOA estimation performance of the method of the present invention with that of uniform arrays and coprime arrays. Detailed Implementation

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments, so that those skilled in the art can easily implement the present invention.

[0047] Example: Figure 1 As shown, the present invention includes the following steps:

[0048] Step 1: This invention uses a MIMO radar structure. A MIMO array can be described using the mathematical concept of convolution; its virtual antenna array can be considered as being constructed by the convolution of transmitting and receiving antennas. Using MIMO technology can greatly improve angular resolution. The angular resolution of M transmitting antennas and N receiving antennas can be equal to the angular resolution of M*N antennas. When the positions of the N elements of the receiving antenna array are [d1 d2 … d…],… N When d n This represents the position of the nth element in the receiving array, where n = 1, 2, ..., N, and N represents the total number of elements in the receiving array. The spacing between the transmitting antenna elements is designed as d. N This ensures that the virtual array elements equivalent to MIMO mode are not redundant.

[0049] Step 2: The receiving antenna is arranged in a non-uniform sparse structure to obtain the received signal model. Since this invention is not limited by array arrangement, the receiving antenna is arranged in a non-uniform, extremely sparse structure, eliminating the need to consider the element placement. The received signal model obtained through the receiving array elements can be expressed as:

[0050] x(t) = As(t) + v(t)

[0051] x(t)∈c N*1Denotes the received signal vector of the sparse array; A∈C N*K Let s(t) ∈ C represent the direction matrix. K*1 Let v(t) ∈ C represent the signal source vector. N*1 Let A represent the noise vector. Here, A and s(t) are respectively represented as:

[0052] A=[a(θ1) a(θ2) … a(θ K )]

[0053] s(t)=[s1(t) s2(t) … s K (t)] T

[0054] Define the sparse array position set as S = [0 r1 r2 … r N-1 ], a(θ) is:

[0055]

[0056] Step 3: Perform specific element interpolation and filling on the original sparse array according to the approximate direction range of the target, and calculate the sparse array transformation matrix: Due to the sparsity of the array elements, the spacing between adjacent elements is greater than half a wavelength, resulting in angular ambiguity. This invention eliminates angular ambiguity by performing specific element interpolation and filling on the original sparse array. The core part of the interpolation algorithm is calculating the sparse array transformation matrix:

[0057] The approximate angular range of the target is known [θ]. i (1) θ i (2) ], refine the interpolation for this region, and define the angle set as: θ i =[θ i (1) θ i (1) +Δθ θ i (1) +2Δθ … θ i (2) ], where Δθ is the angle step value.

[0058] The array manifold is constructed based on the set of angles. The array manifold of the original sparse array can be represented as:

[0059] A i =[a(θ) i (1) ) a(θ i (1) +Δθ) a(θ i (1) +2Δθ) … a(θ i (2) )]

[0060] A specific virtual array is constructed according to the requirements, and the array manifold is represented as follows:

[0061]

[0062] Suppose that the virtual array is obtained by linear interpolation of the array manifold of the real array; in other words, suppose there exists a matrix B. i Make

[0063] Then B is called i Given the transformation matrix from a real sparse array to a virtual array, we obtain B. i Least squares solution:

[0064]

[0065] Meanwhile, interpolation is not perfectly accurate; the interpolation error is defined as:

[0066] In the formula ||·|| F Denotes the F-norm. When err(B i When B is sufficiently small, it can be considered that... i This is acceptable; otherwise, the angle interval needs to be divided into smaller intervals and the transformation matrix recalculated.

[0067] Step 4: Calculate the array manifold matrix after sparse array interpolation optimization, and fill the matrix using the singular value thresholding algorithm.

[0068] The array manifold matrix after interpolation optimization can be represented as: Based on the transformation matrix, a Toeplitz matrix is ​​constructed from the interpolated and optimized array echo information. The Singular Value Thresholding (SVT) algorithm is then used to complete the matrix. The completed matrix provides a high-precision, high-resolution estimate of the Data of Ability (DOA) for multiple targets. Matrix completion theory is an important data processing method. It assumes that the matrix satisfies low-rank property, but missing elements lead to incomplete information. Matrix completion theory uses known information and adheres to the low-rank constraint of the matrix to complete the missing information. The Singular Value Thresholding algorithm process is as follows:

[0069] Input observation matrix X, sampling set Ω, threshold parameter τ, step factor δ, stopping iteration condition ε, increment l, maximum number of iterations k max .

[0070] Initialization is as follows: Z 0 =k0δP Ω (X), r0=0, k0 satisfies

[0071] Iterative process:

[0072] (1) Let s k =r k-1 +l, calculate Make

[0073] (2) Let calculate

[0074] (3) If ||P Ω (Y k -X)|| F / ||P Ω If (X)||≤ε, the loop ends;

[0075] (4) Let

[0076] Output Y k .

[0077] Step 5: Achieve high-precision DOA estimation of the target signal source using a conventional beamforming algorithm. Construct steering vectors for each angle within the field of view. Utilize the phase difference between the signals received by multiple array elements, perform phase compensation and summation at the receiver, and find the maximum value to determine the target direction. This algorithm is simple and intuitive, and has the lowest computational complexity.

[0078] The effects of the present invention can be further illustrated by the following examples.

[0079] Simulation Experiment 1: An array structure with 2 transmitting elements and 3 receiving elements was used. The physical arrangement of the transmitting elements was {0 10}, and the physical arrangement of the receiving elements was {0 6 9}. The angles of the four incident signal sources were [5 12 18 25], and the signal-to-noise ratio was 10dB. Figure 2a This is a diagram showing the location of the MIMO virtual array. Figure 2b This is a diagram illustrating the interpolated array positions. Angle estimation was performed using the method of this invention, and the simulation results were compared with those of a uniform array of 20 elements with a real aperture {0 1 2 … 18 19}. Figure 3 As shown.

[0080] The simulation results demonstrate the effectiveness of the proposed method. It achieves the same DOA estimation results as a uniform array using fewer array elements, while further reducing sidelobes, showcasing the advantages of this invention.

[0081] Simulation Experiment 2: Using a 6-element minimum redundancy array, the array elements were arranged according to the minimum redundancy array structure. The target signal was the same as in the previous experiments. Angle estimation was performed using the method of this invention. The simulation results were compared with those of the original minimum redundancy array. Figure 4 As shown.

[0082] Simulation results show that the proposed method is equally effective in minimum redundancy arrays, and improves the angular resolution of the original array, resulting in more accurate signal estimation and precise estimation of the target signal's position.

[0083] Simulation Experiment 3: A 6-element coprime array was used, with the element positions arranged according to the coprime array structure. Two incident signals were used, with incident angles of 5° and 10°, and a signal-to-noise ratio of 10dB. Angle estimation was performed using a coprime array, a uniform array with the same number of elements, and the method of this invention, respectively. The simulation results are compared. Figure 5 As shown.

[0084] from Figure 5 It can be seen that when the targets are 5° apart, uniform arrays and coprime arrays with the same number of array elements are no longer able to correctly resolve the targets and estimate the angles. However, the spectral peaks obtained by the method of this invention are sharper and have better resolution, demonstrating the superiority of the method of this invention.

[0085] In summary, the simulation experiments verified the correctness, effectiveness, and superiority of the present invention.

[0086] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the scope of the claims of the present invention should be within the protection scope of the present invention.

Claims

1. A multi-objective DOA estimation method based on sparse array interpolation and singular value thresholding, characterized in that, Includes the following steps: Step 1: The transmitting antenna adopts a uniform sparse structure to ensure that the virtual array equivalent to the receiving antenna is not redundant; Step 2: The receiving antenna is arranged in a non-uniform sparse structure to receive the target echo signal; Step 3: Based on the approximate directional range of the target, perform specific element interpolation and filling on the original sparse array, and calculate the sparse array transformation matrix; Step 4: Calculate the array manifold matrix after sparse array interpolation optimization, and fill the matrix using the singular value thresholding algorithm; Step 5: Use conventional beamforming algorithms to achieve high-precision DOA estimation of the target.

2. The multi-objective DOA estimation method based on sparse array interpolation and singular value thresholding as described in claim 1, characterized in that, In step 1, the array spacing at the transmitting end is the array aperture of the receiving end antenna. The sparse array MIMO mode achieves a larger array aperture with the same number of array elements, thus obtaining higher accuracy in resolution and angle estimation. The number of transmitting antennas is M, and the number of receiving antennas is N, which is equivalent to one array element transmitting. The receiving mode is achieved by N equivalent receiving array elements; the positions of the N elements of the receiving antenna array are... , This indicates the position of the nth element in the receiving array. , This indicates the total number of elements in the receiving array. To ensure that the virtual array equivalent to MIMO mode does not generate redundant elements, the spacing between the transmitting antenna elements is designed as follows: .

3. The multi-objective DOA estimation method based on sparse array interpolation and singular value thresholding as described in claim 1, characterized in that, In step 2, the receiving antenna is arranged in a non-uniform sparse structure to receive the target echo signal; the received signal can be expressed as: (1) This represents the received signal vector of the sparse array; Represents the direction matrix. Represents the signal source vector. Represents the noise vector; where and They are represented as follows: (2) (3) Define the sparse array location set as , for: (4) 。 4. The multi-objective DOA estimation method based on sparse array interpolation and singular value thresholding as described in claim 1, characterized in that, In step 3, specific element interpolation and filling are performed on the original sparse array according to the approximate direction range of the target, and the sparse array transformation matrix is ​​calculated; the angle range of the approximate direction of the target is considered. To perform interpolation, define the angle set as follows: (5) Given the angle step values, construct the array manifold based on the angle set. The array manifold of the original sparse array can be represented as: (6) The array manifold representation of the virtual array, derived from interpolation, is as follows: (7) The sparse array transformation matrix is ​​then... : (8) 。 5. The multi-objective DOA estimation method based on sparse array interpolation and singular value thresholding as described in claim 1, characterized in that, In step 4, the sparse array interpolation-optimized array manifold matrix is ​​calculated, and matrix filling is performed using the singular value thresholding algorithm. The interpolation-optimized array manifold matrix can be represented as: (9) Construct a Toeplitz matrix based on the array manifold, and complete the constructed matrix using the singular value thresholding algorithm; input the observation matrix. sampling set Threshold parameter Step factor Stop iteration condition Increment Maximum number of iterations ; Initialization is as follows: , , satisfy ; Iterative process: (1) Let ,calculate , making ; (2) Let ,calculate ; (3) If End the loop; (4) Order ; Output .

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