DOA estimation method for wide-area random sparse array targets based on sparse energy field reconstruction

Abstract

The present invention discloses a method for DOA estimation of wide-area random sparse array targets based on sparse energy field reconstruction, which relates to the technical field of target direction of arrival estimation. It mainly solves the problem of target direction of arrival estimation of wide-area random sparse array targets. Its implementation process is: 1. Determine the basic parameters of the system; 2. Set the number of weight vector groups and generate weight vectors, calculate the measurement energy field; 3. Calculate the theoretical signal of each grid point; 4. Construct an over-complete dictionary; 5. Sparsely reconstruct the energy field and solve the matrix to be reconstructed; 6. Obtain the DOA estimation result. The existing DOA method has the problems of low resolution and a sudden increase in computational complexity when applied to wide-area random sparse array systems. The present invention performs sparse reconstruction DOA estimation based on the energy field, converts the sparse reconstruction algorithm from the signal domain to the energy field domain, introduces the weight vector decoupling node number and computational complexity, and achieves super-resolution target DOA estimation while avoiding the substantial increase in computational complexity caused by the increase in array scale.

Description

Technical Field

[0001] The present invention relates to the technical field of target direction of arrival (DOA) estimation, and in particular to a wide-area random sparse array target DOA estimation method. Background Art

[0002] Wide-area random sparse arrays are increasingly being used in radar, underwater acoustics, and other detection and early warning applications. Their unique characteristics enhance system countermeasures, detection accuracy, and power, enabling super-resolution DOA estimation. Among existing DOA estimation methods, traditional DOA methods, such as beam scanning, struggle to achieve high-precision positioning results. Subspace algorithms require processing multiple snapshots of data and can only achieve super-resolution DOA estimation at high signal-to-noise ratios. These algorithms are not applicable to super-resolution DOA estimation of targets in wide-area random sparse arrays. Signal sparse reconstruction methods based on compressed sensing theory exploit the sparsity of target distribution in space to obtain high-precision DOA estimation results. The paper titled "Research on Several Issues in DOA Estimation Based on Distributed Arrays and Sparse Reconstruction" leverages the sparsity of the array and the signal to propose an l1-norm optimization algorithm based on the real-valued array covariance matrix vector to recover the sparse energy vector and obtain the corresponding target DOA. Patent publication number CN111679248A proposes a joint sparse reconstruction positioning method for target azimuth and range based on a horizontal L-shaped submarine array. This method reconstructs sparse signals using a sparse array matrix and a normalized sparse source matrix to obtain the target's azimuth. However, the computational complexity of existing signal sparse reconstruction methods is related to the number of nodes, and wide-area sparse arrays are typically large. Therefore, when applying signal sparse reconstruction algorithms to this system, the computational complexity increases dramatically by the 3.5th power of the number of arrays due to the significant increase in array size, making them impractical. Summary of the Invention

[0003] The present invention is used to solve the problem of DOA estimation for wide-area random sparse array targets based on sparse energy field reconstruction. Existing DOA methods, when applied to wide-area random sparse array systems, suffer from low resolution and a sudden increase in computational complexity. This invention uses sparse reconstruction DOA estimation based on the energy field, converting the sparse reconstruction algorithm from the signal domain to the energy field domain. It introduces a weight vector to decouple the number of nodes and computational complexity. This achieves super-resolution DOA estimation while avoiding the significant increase in computational complexity caused by increasing array size.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] A method for estimating DOA of wide-area random sparse array targets based on sparse energy field reconstruction includes the following steps:

[0006] Step 1: Determine the basic system parameters, including the wide-area random sparse array distribution range, the number of nodes N, the target search space, the number of targets K, the carrier frequency, the grid size, and the number of grids L;

[0007] Step 2: Set the number of weight vector groups Q to generate a set of N×Q phase compensation values ​​randomly distributed in the range [0, 2π), and then obtain an N×Q-dimensional weight matrix W; the weight matrix W is weighted with the received N×1-dimensional single snapshot data y to obtain the measurement energy field information matrix E. m =W H y;

[0008] Step 3: Assume that the center point of each grid point in the search area radiates a signal with an amplitude of 1, and then obtain the theoretical signal y of a single grid point in N×1 dimension. grid (l), where l represents the lth grid point;

[0009] Step 4: The theoretical signal y of the lth grid point grid (l) The Q×1-dimensional theoretical energy field information matrix E corresponding to the grid point is obtained by weighted calculation with the weight matrix W grid (l) = W H y grid (l); The theoretical energy field information matrix corresponding to all grid points constitutes a Q×L dimensional overcomplete dictionary;

[0010] Step 5: Use the overcomplete dictionary and the measured energy field information matrix to sparsely represent the received single snapshot data, and use the convex optimization toolbox to solve the complex matrix to be reconstructed;

[0011] Step 6: Obtain the target DOA estimation result based on the complex matrix to be reconstructed, that is, the target power spectrum and the number of targets.

[0012] Furthermore, step five is specifically as follows:

[0013] Using an overcomplete dictionary The received single snapshot data is sparsely represented to obtain in is the complex matrix to be reconstructed with K-sparseness, Each row of corresponds to the target location one by one. Only the grid point where the target is located is not zero, which represents the amplitude coefficient and initial phase information corresponding to the target direction.

[0014] Using the convex optimization toolbox to solve the complex matrix to be reconstructed The objective function of the convex optimization toolbox is set as λ is the wavelength.

[0015] Compared with the background technology, the present invention has the following beneficial effects:

[0016] The present invention addresses the problem that the number of receiving nodes in a wide-area random sparse array system increases dramatically, leading to a sharp increase in the computational complexity of the traditional signal sparse reconstruction method. This method performs a linear transformation on the received signal and converts the signal reconstruction into an energy field reconstruction. Compared with the classical sparse signal reconstruction method, after converting to energy field reconstruction, the computational complexity of this method is O(Q 3.5 ×L 3 ), the relationship between the amount of computation and the number of receiving nodes is transformed into the relationship between the number of weight vector groups. When the number of detection scene grids is constant, the ratio of the computational complexity of this method to the sparse signal reconstruction method is (Q / N) 3.5 It can effectively reduce the amount of calculation while ensuring high resolution, and can achieve ultra-high precision target resolution with low computational complexity in a wide-area random sparse array system. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a flow chart of an embodiment of the present invention;

[0018] Figure 2 is the target power spectrum of the embodiment of the present invention. DETAILED DESCRIPTION

[0019] The present invention will be further described below with reference to specific embodiments. The embodiments described below with reference to the accompanying drawings are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0020] Figure 1 The present invention provides a flowchart of a method for estimating the DOA of a wide-area random sparse array target based on sparse energy field reconstruction.

[0021] like Figure 1 As shown, a wide-area random sparse array target DOA estimation method based on sparse energy field reconstruction specifically includes the following steps:

[0022] Step 1: Determine the basic parameters of the system;

[0023] This example considers a wide-area random sparse distribution scenario, in which the 2 Randomly distribute N=200 nodes within the range, and ensure that there is a node at each of the four corner positions, ensuring that the array aperture is 100×100m 2, the distance between any two nodes in the array is greater than half a wavelength. The system carrier frequency is set to 1.3GHz. According to the empirical formula 51λ / d, the 3dB beam width is 0.1°, so the grid size is set to one-fifth of the 3dB beam width, that is, 0.02°. Set K=3 targets, all distributed on a sphere with a radius of R=3000m and the center of the array as the sphere center, within the range of ±2° in azimuth and pitch. At this time, the grid search number is L=40000, and the spherical coordinates of the three targets are expressed as (-0.5, 0.03, 3000), (1.2, 0.03, 3000), (1.3, 0.03, 3000), and the target distance R<d 2 / λ satisfies the near-field detection requirements of a wide-area random sparse array. The grid search number of 40,000 is much larger than the number of receiving nodes (200) and the number of targets (3), thus meeting the sparsity requirement. The single-node signal-to-noise ratio is set to D = 15 dB.

[0024] Step 2: Set the number of weight vector groups and generate weight vectors, and calculate the measurement energy field;

[0025] Set the number of weight vector groups to Q = 100, generate 200 × 100 phase compensation values ​​randomly distributed in the range [0, 2π), and obtain a weight matrix W = [a1, a2, ..., a 100 ], The 100×1-dimensional measurement energy field information E is obtained by weighting it with the received single snapshot data y. m =W H y;

[0026] Step 3: Calculate the theoretical signal of each grid point;

[0027] Assuming that each grid point radiates a signal outward, regardless of the initial phase, and the amplitude is 1, the theoretical signal of the lth grid point can be obtained Its latitude is 200×1.

[0028] Step 4: Construct an overcomplete dictionary;

[0029] The theoretical signal y at this grid point grid (l) The 100×1 dimensional theoretical energy field information E corresponding to the grid point is obtained by weighted calculation with the weight matrix W. grid (l) = W H y grid (l). The theoretical energy field information corresponding to all grid points constitutes a set with a latitude of 100×40000 That is the overcomplete dictionary matrix, which will serve as the overcomplete dictionary for sparse reconstruction of the measured energy field information.

[0030] Step 5: Sparse reconstruction of the energy field and solving the matrix to be reconstructed;

[0031] The received single snapshot data is sparsely represented using the overcomplete dictionary and the measured energy field information matrix to obtain in is a 40000×1 dimensional complex matrix to be reconstructed with 3-sparsity, Each row of corresponds to the target location. Only the grid point where the target is located is not zero, which represents the amplitude coefficient and initial phase information corresponding to the target direction. Use the convex optimization toolbox to solve the complex matrix to be reconstructed The objective function of the CVX toolbox is set as λ is the wavelength.

[0032] Step 6: Obtain DOA estimation results;

[0033] The target DOA estimation result is obtained based on the complex matrix to be reconstructed, i.e., the target power spectrum and the number of targets. Figure 2 The average running time of 100 Monte Carlo experiments is 3.564s, and the root mean square error of DOA estimation is 0.0082°.

[0034] In a given scenario in a specific embodiment, compared with the classical sparse signal reconstruction method, the computational complexity of the energy field reconstruction method is (1 / 2) 3.5 , approximately 0.0884, effectively reducing computational complexity. This method also achieves spatial target resolution better than one-third of the beamwidth and a root mean square error (RMS) for DOA estimation below 0.01°. To verify the effectiveness of this method in reducing computational complexity, 100 Monte Carlo experiments were performed, yielding an average runtime of 5.249 seconds compared to a DOA estimation method based on signal reconstruction. This method achieved only 0.679 of the computational complexity of the signal reconstruction-based method, effectively reducing computational time and complexity.

[0035] Based on the objective function analysis, the computational complexity of the signal reconstruction method is O(N 3.5 ×L 3 ), where N represents the number of array elements and L represents the number of spatial search grids. The computational complexity of the energy field sparse reconstruction method proposed in this paper is O(Q 3.5 ×L 3 ), where Q represents the number of weight vector groups. When the number of spatial search grids is the same, the difference in computational complexity between the two methods is reflected in the number of receiving nodes and the number of weight vector groups. In the implementation example, the number of weight vector groups is 1 / 2 of the number of nodes. Compared with the signal reconstruction method, this method can reduce the number of weight vector groups by 2. 3.5 However, when comparing the computation time obtained in the simulation experiment, it is found that it does not meet the requirement of 2 3.5This relationship is because Matlab and the CVX toolbox have internal optimization processes during calculations, so the incremental relationship of computational complexity cannot be directly reflected in the calculation time.

[0036] The above content is a further detailed description of the present invention in conjunction with specific embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, they can make various other specific modifications and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and these modifications and combinations are still within the scope of protection of the present invention.

Claims

1. A method for DOA estimation of wide-area random sparse array targets based on sparse energy field reconstruction, characterized in that: The following steps are involved: Step 1: Determine the basic system parameters, including the wide-area random sparse array distribution range, the number of nodes N, the target search space, the number of targets K, the carrier frequency, the grid size, and the number of grids L; Step 2: Set the number of weight vector groups Q, generate a set of N×Q phase compensation values ​​randomly distributed in the range [0, 2π), and then obtain an N×Q-dimensional weight matrix W; The weight matrix W is weighted with the received N×1-dimensional single snapshot data y to obtain the measured energy field information matrix E m =W H y; Step 3: Assume that the center point of each grid point in the search area radiates a signal with an amplitude of 1, and then obtain the theoretical signal y of a single grid point in N×1 dimension. grid (l), where l represents the lth grid point; Step 4: The theoretical signal y of the lth grid point grid (l) The Q×1-dimensional theoretical energy field information matrix E corresponding to the grid point is obtained by weighted calculation with the weight matrix W grid (l) = W H y grid (l); The theoretical energy field information matrix corresponding to all grid points constitutes a Q×L dimensional overcomplete dictionary; Step 5: Use the overcomplete dictionary and the measured energy field information matrix to sparsely represent the received single snapshot data, and use the convex optimization toolbox to solve the complex matrix to be reconstructed; Step 6: Obtain the target DOA estimation result based on the complex matrix to be reconstructed, that is, the target power spectrum and the number of targets.

2. The method for DOA estimation of wide-area random sparse array targets based on sparse energy field reconstruction according to claim 1, characterized in that: Step 5 is as follows: Using an overcomplete dictionary Perform sparse representation on the received single snapshot data to obtain in is the complex matrix to be reconstructed with K-sparseness, Each row of corresponds to the target location one by one. Only the grid point where the target is located is not zero, which represents the amplitude coefficient and initial phase information corresponding to the target direction. Using the convex optimization toolbox to solve the complex matrix to be reconstructed The objective function of the convex optimization toolbox is set as λ is the wavelength.

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