A target bearing estimation method based on fast-converging sparse Bayesian learning
Through parabolic modeling and fast-convergence sparse Bayesian learning algorithm, the performance degradation problem caused by the distortion of the towed array is solved, high-resolution and robust target direction estimation is achieved, and the computational complexity is reduced.
Patent Information
- Application Number
- CN202310366512.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-04-07
- Publication Date
- 2025-09-05
- Estimated Expiration
- 2043-04-07
AI Technical Summary
The distortion of the towed array leads to a decline in the performance of traditional beamforming algorithms, and the sparse Bayesian learning method has high computational complexity, making it difficult to achieve high-resolution and robust target direction estimation in practical applications.
The array element positions are corrected by parabola modeling, a spatial sparse model is constructed, and the signal and noise parameters are iteratively updated using a fast-converging sparse Bayesian learning algorithm to estimate the target direction.
It achieves fast and accurate target position estimation in formation distortion scenarios, reduces computational complexity and improves robustness, and performs particularly well under conditions of small number of snapshots and low signal-to-noise ratio.
Smart Images
Figure CN116559777B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of signal sound source localization, and in particular to a target orientation estimation method based on fast-convergence sparse Bayesian learning. Background Art
[0002] Towed arrays are typically oil-filled flexible arrays, and their shape changes with factors such as the towboat's maneuvers, its own gravity, ocean currents, and buoyancy, no longer maintaining a straight line. The array's shape continuously changes over time and space, resulting in formation distortion. If the array is still assumed to be a uniform linear array, the towed array's direction-finding performance will degrade. In the field of underwater acoustics, the performance of traditional beamforming algorithms deteriorates dramatically due to a small number of snapshots, array element position errors, and environmental interference. Research on robust, high-resolution direction-of-arrival (DOA) estimation techniques has far-reaching implications for ocean exploration. Most sparse Bayesian learning (SBL)-based methods require complex matrix operations to solve signal parameters, resulting in high computational complexity and a large amount of computation, which limits their practical applications. Summary of the Invention
[0003] In view of the problems existing in the prior art, the problem to be solved by the present invention is to provide a target direction estimation method based on fast convergence sparse Bayesian learning to achieve accurate estimation of the target direction.
[0004] The technical solution adopted by the present invention is: a target direction estimation method based on fast convergence sparse Bayesian learning, the method comprising the following steps:
[0005] Step 1: Create a parabola model for the distorted towed array. Define the x-axis as the direction from the head to the tail of the array, and use the bow height to represent the degree of formation curvature.
[0006] Step 2: Construct a spatial sparse model of the array signal: evenly divide the angle interval into multiple grid points to obtain an overcomplete angle set. Expand and map the towed array manifold matrix of the original signal onto the overcomplete angle set to obtain a spatial sparse signal.
[0007] Step 3: Iterate the posterior mean and posterior covariance matrix, signal power distribution, and noise variance of the spatial sparse signal: Based on the array received signal and the towed array manifold matrix, use a fast-converging sparse Bayesian learning algorithm to update the parameters to be estimated;
[0008] Step 4: Output the estimated value of the target signal arrival angle and perform a maximum search on the estimated value of the signal power distribution.
[0009] Furthermore, in step 1, parabola modeling is performed on the towed array with distorted formation, and the specific steps are as follows:
[0010] The towed array consists of M hydrophones, with a spacing of d between adjacent elements and a total length of L. s =(M-1)d; the parabola model is used to characterize the distorted towed array; a is the bow height of the parabola, and the x-axis direction is defined as the direction from the head to the tail of the array; the spatial position of the mth array element (x m ,y m ) is approximately a function of bow height and towed array length; L a represents the projection of the array along the x-axis; the position of the mth element in the parabolic array is approximately:
[0011]
[0012] Furthermore, the step 2 constructs a spatial sparse model of the array signal, and the specific steps are as follows:
[0013] Taking the projection of the array center on the x-axis as the reference point, the entire space is evenly divided into N grids according to the angle, and the overcomplete angle set θ is obtained. The array manifold matrix is expanded to the array manifold matrix of the overcomplete direction as follows:
[0014] A=[a(θ1) a(θ2)…a(θ N )]
[0015] in τ m (θ m )=(x m cosθ n +y m sinθ n ) / c,a(θ n ) is the array response vector at each angle, c is the speed of sound, f is the signal frequency, (x m ,y m ) is the spatial position of the mth array element.
[0016] Furthermore, the step 3 specifically includes the following sub-steps:
[0017] Step 31, initialize the signal power distribution γ and noise variance σ 2 , set the convergence conditions;
[0018] Step 32: Update the posterior mean μ and posterior covariance Σ of the transmitted signal X according to the array received signal and the array manifold matrix extended to the overcomplete angle set. x , the calculation formula is as follows:
[0019] Σ y =σ 2I+AΓA H
[0020]
[0021] Where Γ is the diagonal matrix of the signal power distribution γ, A is the array manifold matrix of the overcomplete direction, and Y is the signal received by the array; ∑ y is the covariance of the array received signal, I is the unit diagonal matrix;
[0022] Step 33, based on the μ and ∑ estimated in step 32 x , update the parameters γ and σ 2 , get the signal power distribution estimated in this iteration and noise variance The calculation formula is as follows:
[0023]
[0024] Where L is the number of snapshots, M is the number of array elements, and N is the number of space grids. is the Frobenius norm, (Σ x ) nn is the element in row n and column n of the posterior covariance matrix of X.
[0025] Step 34: If the convergence condition is met, the iteration is exited; otherwise, the above steps 32 and 33 are repeated to continue the iteration until the convergence condition is met.
[0026] Furthermore, the step 4 is specifically as follows:
[0027] Search for the signal power distribution estimate in step 3 The maximum value of , the corresponding spatial angle is the DOA estimation value.
[0028] Beneficial effects of the present invention:
[0029] The present invention corrects the position of the array elements of the distorted towed array through parabolic modeling, and expands the array manifold matrix to map to an overcomplete angle set under a spatial sparse model. Using the array received signal and the array manifold matrix, a fast-converging sparse Bayesian learning algorithm is used to iterate the parameters to be estimated for the signal and noise, and the estimated value of the signal power distribution is searched for the maximum value. The spatial angle corresponding to the maximum value is the estimated value of the target azimuth. Compared with traditional beamforming algorithms and sparse Bayesian methods, this method can quickly estimate the azimuth of the target signal in scenarios where the towed array's maneuvering and steering formation is distorted, and achieve high-resolution and high-robustness positioning performance when the number of snapshots is limited and the signal-to-noise ratio is low. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Figure 1This is a flow chart of a target orientation estimation algorithm based on fast-converging sparse Bayesian learning in a specific embodiment of the present invention;
[0031] Figure 2 2 is a diagram of DOA estimation results in a specific embodiment of the present invention. DETAILED DESCRIPTION
[0032] The specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings.
[0033] The target orientation estimation method based on fast-converging sparse Bayesian learning proposed by the present invention is described in detail below with reference to the embodiments and drawings.
[0034] Figure 1 The overall flow chart of the present invention is presented. During the array signal modeling phase, a parabolic model is first constructed for the distorted towed array. The bow height is used to characterize the degree of array curvature. The angle interval is evenly divided into multiple grid points to obtain an overcomplete angle set. The manifold matrix of the curved array is then expanded and mapped onto the overcomplete angle set. During the algorithm iteration phase, the FCSBL algorithm is used to iteratively update the posterior mean and covariance matrix of the sparse signal, the signal power distribution, and the noise variance based on the array received signal and the array manifold matrix. Finally, a maximum search is performed on the estimated value of the signal power distribution, and an estimated value of the target signal's DOA is output.
[0035] The specific implementation methods of the technical method of the present invention are as follows:
[0036] Step 1: Create a parabolic model for the distorted towed array, and use the bow height to represent the degree of formation curvature.
[0037] The towed array consists of M hydrophones, with a spacing of d between adjacent elements and a total length of L. s =(M-1)d. When the ship turns slowly, the horizontal array will bend and the towed array will be distorted. Its formation can be represented by a parabola model. a is the bow height of the parabola. The x-axis direction is defined as the direction from the head of the array to the tail. The spatial position of the mth array element (x m ,y m ) can be approximately expressed as a function of bow height and towed array length. a represents the projection of the array along the x-axis, that is, the straight-line distance between the head and tail of the curved array. Therefore, the position of the mth element in the parabolic array can be approximately expressed as:
[0038]
[0039] Step 2: Construct a spatial sparse model of the array signal. That is, evenly divide the angle interval into multiple grid points to obtain an overcomplete angle set. Expand and map the manifold matrix of the curved array in step 1 onto the overcomplete angle set:
[0040] Taking the projection of the array center on the x-axis as the reference point, the entire space is evenly divided into N grids according to the angle, and the overcomplete angle set θ is obtained. The array manifold matrix is expanded to the array manifold matrix of the overcomplete direction as follows:
[0041] A=[a(θ1) a(θ2)…a(θ N )]
[0042] in τ m (θ n )=(x m cosθ n +y m sinθ n ) / c,a(θ n ) is the array response vector at each angle, c is the speed of sound, and f is the signal frequency. (x m ,y m ) is the spatial position of the mth array element.
[0043] Step 3: Iterate the posterior mean and posterior covariance matrix of the sparse signal, the signal power distribution, and the noise variance. That is, based on the array received signal and the array manifold matrix, use the fast converging sparse Bayesian learning algorithm (FCSBL) to update the parameters to be estimated. This includes the following sub-steps:
[0044] Step 31, initialize the signal power distribution γ and noise variance σ 2 , set the convergence condition, that is, the maximum number of iterations or the iteration stopping threshold.
[0045] Step 32: Update the posterior mean μ and posterior covariance Σ of the incident signal X according to the array received signal and the array manifold matrix extended to the overcomplete angle set. x , the calculation formula is as follows:
[0046] Σ y =σ 2 I+AΓA H
[0047]
[0048] Where Γ is the diagonal matrix of the signal power distribution γ, A is the array manifold matrix of the overcomplete direction, and Y is the signal received by the array; ∑ y is the covariance of the array received signal, I is the unit diagonal matrix;
[0049] Step 33, based on the μ and ∑ estimated in step 32 x , update the parameters γ and σ2 , the calculation formula is as follows:
[0050]
[0051] Where L is the number of snapshots, M is the number of array elements, and N is the number of space grids. is the Frobenius norm. (∑ x ) nn is the element in row n and column n of the posterior covariance matrix of X.
[0052] Step 34: If the maximum number of iterations is reached or the convergence rate is less than the iteration stop threshold, the iteration is exited. Otherwise, the above steps 32 and 33 are repeated to continue the iteration. The convergence rate is defined as the ratio of the relative change in signal power to the signal power obtained after the previous iteration is completed:
[0053] ε=||γ (new) -γ (old) || / ||γ (old) ||
[0054] Step 4: Output the estimated value of the direction-of-arrival (DOA) of the target signal and perform a maximum search on the estimated value of the signal power distribution:
[0055] Estimated value of signal power distribution in step 3 The search is performed, and the spatial angle corresponding to the maximum value is the DOA estimation value.
[0056] Example:
[0057] This example applies the above-mentioned fast DOA estimation algorithm to an 80-element uniform towed array with an element spacing of 2m, which meets the half-wavelength array. After the array is bent, the tangent direction of the first element is 10° relative to the original array direction, corresponding to a bow height of 6.96m. Four uncorrelated signals with a signal-to-noise ratio of 15dB are incident from 29.5°, 60°, 166°, and 170° respectively, and a weak signal with a signal-to-noise ratio of -3dB is incident from 100.5°. The center frequency of the five sound sources is 375Hz, and the number of snapshots is 10. Set the resolution of the spatial grid to 0.5° and the threshold for stopping the iteration to 5×10 -5 .like Figure 2 The figure shows the DOA estimation results of weak signal sources under four interference sources using SBL and FCSBL algorithms respectively.
[0058] The proposed FCSBL method has lower sidelobes. The simulation was performed on an Intel(R) Core(TM) i7-8700 CPU with 8.00GB of RAM and MATLAB (version R2021a). The SBL algorithm ran in 3.451199 seconds, while the FCSBL algorithm ran in only 0.151236 seconds.
[0059] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.
Claims
1. A target direction estimation method based on fast-converging sparse Bayesian learning, characterized in that: The method comprises the following steps: Step 1: Create a parabola model for the distorted towed array. Define the x-axis as the direction from the head to the tail of the array, and use the bow height to represent the degree of formation curvature. Step 2: Construct a spatial sparse model of the array signal: evenly divide the angle interval into multiple grid points to obtain an overcomplete angle set. Expand and map the towed array manifold matrix of the original signal onto the overcomplete angle set to obtain a spatial sparse signal. Step 3: Iterate the posterior mean and posterior covariance matrix, signal power distribution, and noise variance of the spatially sparse signal: Based on the array received signal and the towed array manifold matrix, use a fast-converging sparse Bayesian learning algorithm to update the parameters to be estimated. This includes the following sub-steps: Step 31, initialize the signal power distribution γ and noise variance σ 2 , set the convergence conditions; Step 32: Update the posterior mean μ and posterior covariance ∑ of the transmitted signal X according to the array received signal and the array manifold matrix extended to the overcomplete angle set. x , the calculation formula is as follows: ∑ y =s 2 I+AGA H Where Γ is the diagonal matrix of the signal power distribution γ, A is the array manifold matrix of the overcomplete direction, and Y is the signal received by the array; ∑ y is the covariance of the array received signal, I is the unit diagonal matrix; Step 33, based on the μ and ∑ estimated in step 32 x , update the parameters γ and σ 2 , get the signal power distribution estimated in this iteration and noise variance The calculation formula is as follows: Where L is the number of snapshots, M is the number of array elements, and N is the number of space grids. is the Frobenius norm, (∑ x ) nn is the element in the nth row and nth column of the posterior covariance matrix of X; Step 34: If the convergence condition is met, then the iteration is exited; otherwise, the above steps 32 and 33 are repeated to continue the iteration until the convergence condition is met; Step 4: Output the estimated value of the target signal arrival angle and perform a maximum search on the estimated value of the signal power distribution.
2. The method for target orientation estimation based on fast-converging sparse Bayesian learning according to claim 1, characterized in that: Step 1 is to perform parabolic modeling on the towed array with distorted formation. The specific steps are as follows: The towed array consists of M hydrophones, with a spacing of d between adjacent elements and a total length of L. s =(M-1)d; the parabola model is used to characterize the distorted towed array; a is the bow height of the parabola, and the x-axis direction is defined as the direction from the head to the tail of the array; the spatial position of the mth array element (x m ,y m ) is approximately a function of bow height and towed array length; L a represents the projection of the array along the x-axis; the position of the mth element in the parabolic array is approximately:
3. The method for target orientation estimation based on fast-converging sparse Bayesian learning according to claim 1, characterized in that: The step 2 constructs a spatial sparse model of array signals, and the specific steps are as follows: Taking the projection of the array center on the x-axis as the reference point, the entire space is evenly divided into N grids according to the angle, and the overcomplete angle set θ is obtained. The array manifold matrix is expanded to the array manifold matrix of the overcomplete direction as A = [a(θ1)a(θ2)…a(θ N )] in τ m (θ n )=(x m cosθ n +y m sinθ n ) / c,a(θ n ) is the array response vector at each angle, c is the speed of sound, f is the signal frequency, (x m ,y m ) is the spatial position of the mth array element, and M is the number of array elements.
4. The method for target orientation estimation based on fast-converging sparse Bayesian learning according to claim 1, characterized in that: The step 4 is specifically as follows: Search for the signal power distribution estimate in step 3 The maximum value of , the corresponding spatial angle is the DOA estimation value.