Broadband signal DOA estimation method based on fast sparse Bayesian learning
By optimizing DOA estimation through fixed-point update using fast sparse Bayesian learning and binary search, the problems of slow iterative convergence, insufficient frequency band adaptability, and low angle estimation accuracy in broadband signal DOA estimation are solved, thus achieving efficient underwater target detection.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-14
- Publication Date
- 2026-03-31
AI Technical Summary
Existing broadband signal DOA estimation methods based on sparse Bayesian learning suffer from limited iterative convergence speed, insufficient frequency band adaptability, and limited angle estimation accuracy, making it difficult to meet the needs of underwater real-time monitoring and high-precision detection.
We employ a fast sparse Bayesian learning method, accelerate parameter iteration through a fixed-point update formula, characterize spatial structure differences using the Hadamard product of subband signal variances, and combine it with a binary search method for angle refinement to optimize DOA estimation.
It significantly improves the iteration convergence rate, enhances frequency band adaptability and DOA estimation accuracy, and meets the rapid processing requirements of underwater real-time monitoring.
Smart Images
Figure CN121763201A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of underwater target detection technology, and particularly relates to a broadband signal DOA estimation method based on fast sparse Bayesian learning. Background Technology
[0002] my country possesses vast sea areas, and with the increasing intensity of marine resource development and the growing complexity of the maritime security situation, the demand for underwater target detection technology continues to grow. Direction-of-arrival (DOA) estimation, as one of the core technologies for underwater target detection, provides crucial spatial orientation information for subsequent precise target positioning and stable tracking, and is an important component of underwater monitoring systems.
[0003] In real-world marine environments, noise radiated by targets such as surface vessels and underwater vehicles typically exhibits broadband signal characteristics. Compared to narrowband signals, broadband signals not only contain richer spectral information but also possess stronger anti-interference capabilities. Therefore, broadband signal DOA estimation technology is of great significance for improving underwater target detection performance. Existing broadband signal DOA estimation methods based on sparse Bayesian learning (SBL) can utilize the spatial sparsity of signals to transform the DOA estimation problem into a sparse signal reconstruction problem, offering advantages such as high resolution and stable performance at low signal-to-noise ratios. However, these methods still have the following three key problems: Limited convergence speed and insufficient real-time performance: Most existing methods do not have an efficient strategy for hyperparameter updates, resulting in slow convergence speed and long running time during the iterative process, which is difficult to meet the needs of rapid signal processing in underwater real-time monitoring scenarios. Insufficient frequency band adaptability and limited accuracy: It is generally assumed that the frequency bands of broadband sound sources completely overlap, but in actual applications, the frequency bands of target signals often exhibit non-overlapping or partially overlapping characteristics. In this case, the method cannot make full use of the spatial structure differences of each sub-band, resulting in a significant decrease in the accuracy of DOA estimation. Limited accuracy of angle estimation: Directly determining DOA solely based on the peak value of the signal spatial energy distribution without refining the preliminary estimation results cannot eliminate the errors caused by discrete angle division, making it difficult to meet the requirements of high-precision detection; Therefore, a broadband signal DOA estimation method based on fast sparse Bayesian learning is needed to solve the above problems. Summary of the Invention
[0004] The purpose of this invention is to provide a broadband signal DOA estimation method based on fast sparse Bayesian learning to solve the problems mentioned in the background art.
[0005] To achieve the above objectives, the present invention provides the following technical solution: A broadband signal DOA estimation method based on fast sparse Bayesian learning includes the following steps: S1. Obtain the frequency domain array received signal data and establish a sparse signal model; S2. Based on the sparse signal model established in step S1, construct a Bayesian probability model; the probability model includes the likelihood distribution of the received signal, the prior distribution of the sound source signal, the posterior distribution of the sound source signal, and the marginal likelihood distribution of the received signal. S3. Based on the expectation-maximization algorithm (EM algorithm), derive the fixed-point update formula for the unknown hyperparameters in the probability model constructed in step S2. The hyperparameters include the subband signal power vector, noise accuracy, and spatial sparsity control parameter vector. S4. Use the fixed-point update formula obtained in step S3 to perform parameter iterative calculation, set the iteration stop condition, terminate the iteration when the stop condition is met, and output the estimated value of the spatial energy distribution vector of the sound source signal. S5. Extract the peak value of the spatial energy distribution vector of the sound source signal obtained in step S4. After arranging the peak values in descending order of amplitude, extract the spatial observation angle corresponding to the peak value as the coarse estimate of the DOA of the sound source. S6. For each coarse DOA estimate obtained in step S5, perform angle refinement processing using a binary search method within its corresponding angle interval to obtain a fine DOA estimate of the sound source location.
[0006] In a further technical solution, S1 includes the following steps: S11. Divide the frequency range of the signal of interest into... Sub-bands; dividing the time-domain received signal data output by the array into sub-bands. Section, among which, The number of snapshots; perform Discrete Fourier Transform (DFT) on each segment of time-domain data to obtain a frequency-domain array received signal data vector in each sub-band, which is a snapshot vector; combine the data from the same sub-band... The frequency domain data matrix of this sub-band is composed of several snapshot vectors, and the frequency domain data matrices of all sub-bands together constitute the frequency domain array received signal dataset (hereinafter referred to as the received signal). S12. Define a set of discrete angles, where the discrete angles correspond to spatial observation angles; construct a steering matrix for each sub-band based on the discrete set, where the column vectors are steering vectors, and the steering vectors are determined by the array geometry, signal frequency, and discrete angles; establish a sparse signal model using the steering matrix, that is, represent the sub-band received signal as a linear combination of the corresponding sub-band steering matrix and the sub-band sound source signal.
[0007] In a further technical solution, step S2 includes the following steps: S21. Set the likelihood distribution of each column in the received signal matrix of each sub-band to follow a complex Gaussian distribution, and introduce noise precision (i.e., the reciprocal of the noise variance) to construct the covariance matrix of the likelihood distribution of the received signal. S22. Set the prior distribution of each column in the signal matrix of each sub-band sound source to follow a zero-mean complex Gaussian distribution, and introduce the sub-band signal power vector and the spatial sparsity control parameter vector. Define the Hadamard product of the two as the sub-band signal variance vector to construct the covariance matrix of the prior distribution of the sound source signal. S23. Based on Bayes' theorem, it can be deduced that: the posterior distribution of the sound source signal vector of each sub-band follows a complex Gaussian distribution; the marginal likelihood distribution of the received signal vector of each sub-band follows a zero-mean complex Gaussian distribution, and its covariance matrix is jointly determined by the noise accuracy, steering matrix and the covariance matrix of the prior distribution of the sound source signal of that sub-band.
[0008] In a further technical solution, in S3, the subband signal power vector, noise accuracy, and spatial sparsity control parameter vector are collectively referred to as "hyperparameters" to control the prior and likelihood distribution characteristics of the probability model.
[0009] In a further technical solution, step S4 includes the following steps: S41. Set the iteration count Initialize hyperparameters: Set the initial value of noise accuracy to 1; initialize the sub-band signal power vector based on the beamforming result of the received signal; initialize the spatial sparsity control parameter vector based on the initial value of each sub-band signal power vector; and set the initial value of the spatial energy distribution vector of the sound source signal to be equal to the initial value of the spatial sparsity control parameter vector. S42. Using the hyperparameters of the current iteration, calculate the posterior mean and posterior covariance of the sound source signal vectors of each sub-band. S43. Use the fixed-point update formula to update the sub-band signal power vector, noise accuracy, and spatial sparsity control parameter vector. S44. Using the posterior mean and covariance of the updated sub-band sound source signal vector, calculate the updated value of the spatial energy distribution vector of the sound source signal, and calculate the stopping decision parameter. This parameter is defined as the ratio of the L2 norm of the change in the energy distribution vector in two consecutive iterations to the L2 norm of the energy distribution vector in the current iteration, which is used to measure the degree of convergence of the iteration. S45. Determine if the iteration stop condition is met: If the stop decision parameter is less than the preset convergence threshold, or the iteration count reaches the preset maximum number of iterations, then terminate the iteration and output the estimated value of the final sound source signal spatial energy distribution vector; otherwise, increment the iteration count by 1 and return to S42 to continue the iteration.
[0010] In a further technical solution, step S5 includes the following steps: S51. Extract the peak value of the spatial energy distribution vector of the sound source signal output in step S4; S52. After sorting the peak values in descending order by amplitude, record the previous... The index of the position of each peak in the energy distribution vector ( (Number of sound sources), forming a set of locations; S53. Based on the location set, extract the corresponding discrete angles (i.e., spatial observation angles) from the discrete angle set, and use them as the DOA coarse estimate values of the sound source location to form a DOA coarse estimate set.
[0011] In a further technical solution, step S6 includes the following steps: S61, Regarding the first obtained in step S5 One rough estimate of DOA ( The corresponding angle refinement interval is determined; the angle refinement interval is defined as the range between adjacent angles in the discrete angle set for the coarse estimate of DOA. By using this interval selection method, we can ensure that the refined interval mainly includes the sound source corresponding to the coarse estimate of DOA, while avoiding an excessively wide interval that would increase the computational load of the binary search. S62. Based on the marginal likelihood maximization criterion, construct an objective function for angle refinement processing. This function is the sum of the ratios of specific parameters of each sub-band. The specific parameters are calculated by the steering vector corresponding to the candidate angle within the refinement interval, the marginal likelihood covariance matrix of the received signal after excluding the current coarse estimate of DOA, and the sampling covariance matrix of the received signal. The covariance matrix after excluding the current coarse estimate of DOA is formed by removing the rows and columns corresponding to the coarse estimate of DOA and its adjacent discrete angles from the marginal likelihood covariance matrix of the received signal. This covariance matrix can suppress the interference of high spatial energy components at adjacent spatial observation angles of the current coarse DOA estimate, thereby improving the accuracy of fine processing; S63. The objective function is maximized within the angle refinement interval using a binary search method, and the candidate angle that maximizes the objective function within the refinement interval is taken as the optimal angle. S64. The optimal angle is used as the fine estimate of the corresponding coarse DOA estimate, forming a fine DOA estimate set. The elements in this set are the high-precision DOA estimates of each sound source.
[0012] Compared with the prior art, the beneficial effects of the present invention are: 1) This invention significantly accelerates the convergence rate of parameter iteration in sparse Bayesian learning by using a fixed-point update formula, effectively improving the real-time processing capability of the technical solution. 2) This invention, by using parameterized signal variance (i.e., the Hadamard product of subband signal variance and spatial sparsity control parameter vector) in the prior distribution modeling of subband signals, fully explores the spatial structural differences of subband signals, effectively characterizes the spatial sparsity of different subband signals, and improves frequency band adaptability. 3) This invention designs an angle refinement process based on the marginal likelihood maximization criterion to optimize the coarse DOA estimation, obtain a more accurate DOA estimation, and effectively improve the accuracy of DOA estimation.
[0013] To more clearly illustrate the structural features and effects of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description
[0014] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a performance comparison chart of the SBL-based broadband signal DOA estimation method under different signal-to-noise ratio conditions when the broadband target signal frequency bands of the present invention do not overlap. Figure 3 This is a performance comparison chart of the SBL-based broadband signal DOA estimation method under different signal-to-noise ratio conditions when the broadband target signal frequency bands partially overlap. Detailed Implementation
[0015] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0016] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.
[0017] Example 1 like Figure 1-3 As shown, this embodiment of the invention provides a broadband signal DOA estimation method based on fast sparse Bayesian learning, including the following steps: S1. Obtain the frequency domain array received signal data and establish a sparse signal model; S11. Divide the frequency range of the signal of interest into... Each sub-band, sub-band number is The time-domain received signal data output by the array is divided into... Section, among which This is the number of snapshots, and the snapshot sequence number is... Perform a Discrete Fourier Transform (DFT) on each segment of time-domain data to obtain a frequency-domain array received signal data vector for each sub-band; this vector is a snapshot vector. Then, combine the data from the same sub-band... The frequency domain matrix of the sub-band is composed of snap vectors, and the frequency domain data of all sub-bands together constitute the frequency domain array received signal dataset (hereinafter referred to as the received signal). S12, Set the discrete angle set: ; in, The number of discrete angles. For the first The discrete angle, corresponding to the first discrete angle A spatial observation angle; Based on discrete angle set Construct the guidance matrix for each sub-band: , ; Among them, the List Indicates the first Each sub-band corresponds to a discrete angle. The guiding vector ( The steering vector is determined by the array geometry, signal frequency, and discrete angle. Establishing a sparse signal model using the steering matrix: , ; in, Indicates the first The received signal matrix of each sub-band, with dimension [missing information]. , For the number of array sensors, the matrix's first... List For the first The first The received signal vector of a snapshot; Indicates the first The sound source signal matrix of each sub-band has a dimension of , of which List For the first The first A snapshot of the sound source signal vector; Indicates the first The noise matrix of each sub-band has dimensions of , of which List For the first Size A noise vector for each snapshot; Assume that the noise in each subband is zero-mean complex Gaussian white noise, and that the noise in different subbands is independent of each other.
[0018] S2. Based on the sparse signal model established in step S1, construct a Bayesian probability model, which includes the likelihood distribution of the received signal, the prior distribution of the sound source signal, the posterior distribution of the sound source signal, and the marginal likelihood distribution of the received signal. S21. Set the receiving signal for each sub-band Each column The likelihood distribution of follows a complex Gaussian distribution, and its probability density function satisfies: ; in, The mean vector is The covariance matrix is The complex Gaussian distribution; is the mean of the likelihood distribution; Let be the covariance matrix of the likelihood distribution. Indicates the first The noise accuracy of each subband (i.e., the reciprocal of the noise variance). express 3D identity matrix This represents the matrix inversion operation; S22, Set the sound source signals for each sub-band Each column The prior distribution of is a zero-mean complex Gaussian distribution, and its probability density function satisfies: ; Where 0 represents a zero-mean vector; Let be the covariance matrix of the prior distribution, and ( This represents the operation of constructing a diagonal matrix from vectors, that is, using vector elements as diagonal elements of the diagonal matrix. Let V be the variance vector of the subband signal, with dimension . And satisfy , This represents the Hadamard product, which is the element-wise multiplication of two vectors of the same dimension. The vector represents the spatial sparsity control parameters, with dimension . ;in, This represents the transpose operation, the first... element Used to control the The signal sparsity intensity corresponding to each spatial observation angle, the smaller the value, the lower the probability of a sound source existing at that angle; Indicates the first The signal power vector of each sub-band has a dimension of Among them, the first element Used to characterize the The first The power intensity of the sound source signal corresponds to each spatial observation angle; S23. According to Bayes' theorem The derivation yields The posterior distribution is a complex Gaussian distribution: ; in, Indicates the first The first The posterior mean (dimension) of the sound source signal vector captured in a snapshot. ), Indicates the first The posterior covariance matrix (dimensions) of the sound source signals in each sub-band ); The derivation yields The marginal likelihood distribution is a zero-mean complex Gaussian distribution: ; in, The covariance matrix (dimensions) of the marginal likelihood distribution ),and , This represents the conjugate transpose operation; Construct the spatial energy distribution vector of the sound source signal based on the posterior mean and covariance of the signal. (dimension) ), Among them, the element , express The One element, express The One diagonal element, Used to characterize the The total energy of all sub-band sound source signals from a spatial observation angle.
[0019] S3. Based on the expectation-maximization algorithm (EM algorithm), derive the fixed-point update formula for the unknown hyperparameters in the probability model constructed in step S2. The hyperparameters include the subband signal power vector, noise accuracy, and spatial sparsity control parameter vector. The subband signal power vector defined by S2 ( ), noise accuracy ( and spatial sparsity control parameter vector These are collectively referred to as "hyperparameters" and are used to control the prior and likelihood distribution characteristics of a probability model. Let the iteration count be ( Based on the Expectation-Maximization (EM) algorithm, the fixed-point update formula for hyperparameters is derived, specifically including: (1) Define intermediate calculation parameters: , ; (2) Subband signal power vector The Middle The formula for updating the fixed point of each element is as follows: ; (3) Noise accuracy Fixed-point update formula: ; (4) Spatial sparsity control parameter vector The Middle The formula for updating the fixed point of an element is: ; in, This represents the updated parameter value in the current iteration. This indicates the parameter value before the update. L2 norm operation of vectors Represents a constant with a small value, such as This is used to avoid the hyperparameter estimates being zero and to ensure numerical stability.
[0020] S4. Use the fixed-point update formula obtained in step S3 to perform parameter iterative calculation, set the iteration stop condition, terminate the iteration when the stop condition is met, and output the estimated value of the spatial energy distribution vector of the sound source signal. S41, Let the iteration count... Initialize hyperparameters: Initial value of noise accuracy , That is, the initial assumption is that the noise variance of each sub-band is 1; Subband signal power vector initial value , Initialization based on beamforming results of received signals. express The conjugate transpose of ; Initial values of spatial sparsity control parameter vector Initialize the signal power vectors of each sub-band based on their initial values; Initial value of the spatial energy distribution vector of the sound source signal: ; S42. Using the hyperparameter values of the current iteration, calculate the posterior mean of the sound source signal vectors for each sub-band. With posterior covariance : ; ; in, , , , , ; S43. Update the hyperparameters using the fixed-point update formula. , and ; S44. Using the updated posterior mean and covariance, calculate the updated value of the spatial energy distribution vector of the sound source signal. And calculate the stop decision parameters: ; in, The L2 norm represents the change in the energy distribution vector between two consecutive iterations. This represents the L2 norm of the current iteration's energy distribution vector. Used to measure the convergence of the iteration; S45. Determine if the iteration stopping condition is met: If... ( (for the preset convergence threshold), or ( If the maximum number of iterations is preset, the iteration terminates, and the final estimated value of the spatial energy distribution vector of the sound source signal is output. Otherwise, let Return to S42 to continue the iteration.
[0021] S5. Extract the peak value of the spatial energy distribution vector of the sound source signal obtained in step S4. After arranging the peak values in descending order of amplitude, extract the spatial observation angle corresponding to the peak value as the coarse estimate of the DOA of the sound source. S51. Extract the spatial energy distribution vector of the sound source signal output in step S4. The peak value; S52. After sorting the obtained peak values in descending order by amplitude, record the first... Each peak is in the energy distribution vector Position index in ( , (where the number of sound sources is), that is, The location index corresponds to the sequence number of the spatial observation angle; the location set is defined as: ; S53, Based on Location Set From a discrete perspective, sets Extract the corresponding space observation angle These angles are used as coarse estimates of the DOA (Directional Aspect) of the sound source; the coarse DOA estimate set is defined as follows: ; in, Indicates the first A rough estimate of the DOA of each sound source. ; S6. For each coarse DOA estimate obtained in step S5, the angle is refined by using a binary search method within its corresponding angle range to obtain a fine DOA estimate of the sound source location. S61, Regarding the first obtained in step S5 A rough estimate of DOA ( ), determine its corresponding angle refinement range ,in, , They are respectively In a discrete set of angles, adjacent angles can be selected using this interval selection method to ensure that the refined interval mainly includes... The corresponding sound source, while avoiding an excessively wide interval that would increase the computational load of the binary search method; S62. Based on the marginal likelihood maximization criterion, construct the objective function for angle refinement: ; in, This indicates that it is defined within the angle range. Candidate angle variables within (i.e., the fine angles to be optimized); , Indicates the first Each person carries a corresponding candidate angle. The steering vector is determined by the array geometry, sub-band frequency, and candidate angle. The calculated value is related to the discrete angle steering vector. The construction methods are consistent; Indicates the first The sampling covariance matrix of the sub-band received signal; This represents the covariance matrix of the marginal likelihood distribution of the received signal after excluding the current coarse estimate of DOA. It is a guiding matrix Remove and space observation angle , , The matrix obtained after the corresponding guiding vector (dimension) ), It is the covariance matrix Remove and space observation angle , , The matrix obtained after corresponding rows and columns (dimensions) ), used to suppress the interference of spatial energy components at adjacent spatial observation angles on the current angle optimization; This represents the matrix conjugate transpose operation. This represents the matrix inversion operation; S63. Use the binary search method in the angle interval. Internal iteration maximizes the objective function : Set the number of iterations This is used to control the error of the final fine angle, and the error does not exceed [a certain value]. ; Initialize the left endpoint of the search interval Right endpoint ; The current rough estimate of DOA As one of the candidate angles, and calculated respectively and the left endpoint of the search interval mean angle ,as well as and the right endpoint of the search interval mean angle These three factors together constitute a candidate angle set. The objective function is then selected from the candidate angle set. The largest angle is considered the optimal angle. ,like Then let , ,like Then let ,like Then let And the optimal angle is used as the current coarse estimate of DOA. The updated value, that is, let Repeat the above steps until completion. V The next iteration yields the final optimal angle; S64, Optimal Angle As the first A rough estimate of DOA The corresponding precise estimates are defined as follows: ; in, That is, the first High-precision DOA estimation for each sound source.
[0022] Example 2 This embodiment is based on the method described in Embodiment 1, and a simulation experiment is conducted to verify the performance advantages of the broadband signal DOA estimation method based on fast sparse Bayesian learning proposed in this invention compared with existing methods.
[0023] In the simulation experiment, a uniform linear array was used, with 10 sensors, an element spacing of 0.125m, and a sampling frequency of 30kHz; the spatial observation angle range was [missing information]. ,according to A discrete angle set is obtained by uniformly dividing the array into discrete intervals; three uncorrelated far-field broadband target signals are incident on the array at incident angles of [missing information]. , and (in , , which is an independently and randomly selected angle offset, used to construct a real DOA that does not strictly fall on a preset discrete angle, simulating an actual detection scenario.
[0024] To verify the frequency band adaptability of the present invention, two scenarios were set up: (1) Non-overlapping frequency bands: the frequency bands of the three broadband target signals are 3kHz~3.9kHz, 4.1kHz~5kHz, and 5.1kHz~6kHz, respectively; (2) Partially overlapping frequency bands: the frequency bands of the three broadband target signals are 3kHz~4.5kHz, 3.5kHz~5kHz, and 4.5kHz~6kHz, respectively.
[0025] Signal and data parameter settings: The frequency range of the signal of interest is 3kHz to 6kHz, divided into 50Hz intervals. Each sub-band has a frequency domain array receiving signal data snapshot count of 10 ... The noise is zero-mean complex Gaussian white noise with a signal-to-noise ratio ranging from -10dB to 16dB, increasing in 2dB steps; the convergence threshold for the iteration stopping condition is... The maximum number of iterations is In this embodiment, the comparison method parameters (to ensure fairness in the comparison) are as follows: OW-SBLRVM: This method employs an angle refinement scheme that estimates discrete angle errors and compensates for them to the DOA estimation results, using methods consistent with the present invention. Discrete angle intervals and hyperparameter updates do not use fixed-point update formulas; W-HSBL: A process without angle refinement is employed to ensure the accuracy of the basic estimate. Discrete angle interval (smaller than that of the present invention) Hyperparameter updates did not use the fixed-point update formula; Experimental Results and Analysis: The experimental results, using the root mean square error of DOA estimation (measuring estimation accuracy) and average running time (measuring real-time performance) as indicators, compare the performance of the present invention with two comparative methods. The results are as follows: Figure 2 , Figure 3 As shown.
[0026] Figure 2 The results show a comparison of algorithm performance in scenarios where frequency bands do not overlap. Figure 2 (a) is a comparison chart of estimation accuracy. Figure 2 (b) is a real-time comparison chart. Figure 2 (a) It can be seen that, across the entire signal-to-noise ratio range, the root mean square error of the estimation method of this invention is significantly lower than that of the comparative method, proving that this invention has higher estimation accuracy. Figure 2 (b) It can be seen that the average running time of the present invention is significantly lower than that of the two comparative methods, proving that the present invention has higher running efficiency and better real-time performance (although W-HSBL does not have a fine-grained processing step, it uses a 1° discrete interval, which increases the amount of computation, and W-HSBL and OW-SBLRVM do not use the fixed point update formula in the parameter iteration step, so their convergence rate is slower than that of the present invention), proving that the present invention effectively solves the problem of slow iteration convergence of the existing methods and has better real-time performance; Figure 3 The results show a comparison of algorithm performance in scenarios with partial frequency band overlap. Figure 3 (a) is a comparison chart of estimation accuracy. Figure 3 (b) is a real-time comparison chart. Figure 3 (a) It can be seen that the present invention still maintains the lowest root mean square error, due to Figure 3 (b) It can be seen that the average running time of the present invention remains optimal, proving that even in scenarios with partial overlap of frequency bands, the present invention has higher estimation accuracy and faster running speed. The above simulation results demonstrate that the present invention, through Hadamard product modeling of sub-band signal variances, can effectively characterize the spatial structural differences of different sub-bands, solving the problem of insufficient frequency band adaptability of existing methods.
[0027] Key advantages verified: Angle refinement processing effect: This invention adopts Discrete interval plus binary search refinement process, the final estimation accuracy is better than that of using Discrete-interval W-HSBL demonstrates that refined angle processing effectively eliminates errors caused by discrete angle division, and the final estimation result is superior to that using... Discrete intervals and OW-SBLRVM with refined angle processing demonstrate that the binary search refinement process proposed in this invention has better performance and solves the problem of insufficient angle estimation refinement in existing methods. Frequency band adaptability verification: The present invention maintains optimal performance in both frequency band scenarios, demonstrating its ability to characterize the differences in sub-band spatial structure and adapt to the complex characteristics of non-overlapping or partially overlapping target signal frequency bands in practical applications. Real-time verification: The fixed-point update formula improves the iteration convergence speed. Even with the addition of angle refinement processing steps, a shorter average running time is still achieved, meeting the rapid processing requirements of underwater real-time monitoring. In summary, this invention addresses the problems of slow iterative convergence, insufficient frequency band adaptability, and low angle estimation accuracy of existing SBL-type methods through three core designs: hyperparameter fixed-point update formula, subband signal variance Hadamard product modeling, and angle binary search refinement. It has significant technical advantages in underwater broadband signal DOA estimation.
[0028] The above description is merely 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 within the protection scope of the present invention.
Claims
1. A method for wideband signal DOA estimation based on fast sparse Bayesian learning, characterized in that, The method comprises the following steps: S1, obtaining frequency domain array receiving signal data and establishing a sparse signal model; S2, based on the sparse signal model established in step S1, constructing a Bayesian probability model; the probability model comprises a receiving signal likelihood distribution, a sound source signal prior distribution, a sound source signal posterior distribution, and a receiving signal marginal likelihood distribution; S3, based on an expectation maximization algorithm (EM algorithm), deriving a fixed point update formula for unknown hyperparameters in the probability model constructed in step S2, the hyperparameters comprising a subband signal power vector, a noise precision, and a spatial sparsity control parameter vector; S4, performing parameter iterative calculation using the fixed point update formula obtained in step S3, setting an iteration stop condition, terminating iteration when the stop condition is met, and outputting an estimated value of a sound source signal spatial energy distribution vector; S5, extracting a peak value of the sound source signal spatial energy distribution vector obtained in step S4, arranging the peak values in descending order of amplitude, and extracting a spatial observation angle corresponding to the peak value as a DOA coarse estimation value of the sound source direction; S6, for each DOA coarse estimation value obtained in step S5, performing angle refinement processing in the corresponding angle interval using a dichotomy search method to obtain a DOA fine estimation value of the sound source direction.
2. The wideband signal DOA estimation method based on fast sparse Bayesian learning according to claim 1, characterized in that, The S1 comprises the following steps: S11. Divide the frequency range of the signal of interest into... Sub-bands; dividing the time-domain received signal data output by the array into sub-bands. Section, among which, The number of snapshots; perform Discrete Fourier Transform (DFT) on each segment of time-domain data to obtain a frequency-domain array received signal data vector for each sub-band, which is a snapshot vector; combine the data from the same sub-band... The frequency domain data matrix of this sub-band is composed of several snapshot vectors, and the frequency domain data matrices of all sub-bands together constitute the frequency domain array received signal dataset (hereinafter referred to as the received signal). S12, setting a discrete angle set, wherein the discrete angles correspond to spatial observation angles; based on the discrete set, constructing a steering matrix of each subband, the column vectors of the steering matrix being steering vectors, the steering vectors being determined by array geometry, signal frequency, and discrete angles; and using the steering matrix to establish a sparse signal model, i.e., representing the subband receiving signal as a linear combination of the corresponding subband steering matrix and the subband sound source signal.
3. The wideband signal DOA estimation method based on fast sparse Bayesian learning according to claim 1, characterized in that, The S2 comprises the following steps: S21, setting the likelihood distribution of each column in the receiving signal matrix of each subband to follow a complex Gaussian distribution, and introducing a noise precision (i.e., the reciprocal of noise variance) to construct a covariance matrix of the receiving signal likelihood distribution; S22, setting the prior distribution of each column in the sound source signal matrix of each subband to follow a zero-mean complex Gaussian distribution, and introducing a subband signal power vector and a spatial sparsity control parameter vector, and defining the Hadamard product of the two as a subband signal variance vector to construct a covariance matrix of the sound source signal prior distribution; S23, based on the Bayesian theorem, it can be derived that the posterior distribution of each subband sound source signal vector follows a complex Gaussian distribution; and the marginal likelihood distribution of each subband receiving signal vector follows a zero-mean complex Gaussian distribution, and the covariance matrix thereof is determined by the noise precision, the steering matrix, and the covariance matrix of the sound source signal prior distribution of the subband.
4. The wideband signal DOA estimation method based on fast sparse Bayesian learning according to claim 1, characterized in that, In the S3, the subband signal power vector, the noise precision, and the spatial sparsity control parameter vector are collectively referred to as "hyperparameters" for controlling the prior and likelihood distribution characteristics of the probability model.
5. The wideband signal DOA estimation method based on fast sparse Bayesian learning according to claim 1, characterized in that, The S4 comprises the following steps: S41, set iteration count ; initialize hyperparameters: set the initial value of noise precision to 1; initialize the subband signal power vector based on the beamforming result of the received signal; initialize the spatial sparsity control parameter vector based on the initial value of each subband signal power vector; and set the initial value of the sound source signal spatial energy distribution vector to be equal to the initial value of the spatial sparsity control parameter vector; S42, using the hyperparameters of the current iteration, calculating the posterior mean and the posterior covariance of each subband sound source signal vector; S43, using the fixed point update formula, updating the subband signal power vector, the noise precision, and the spatial sparsity control parameter vector; S44, calculate the updated value of the sound source signal spatial energy distribution vector using the updated posterior mean and covariance of the sub-band sound source signal vector, and calculate a stop decision parameter defined as the ratio of the L2 norm of the energy distribution vector change between two consecutive iterations to the L2 norm of the current iteration energy distribution vector, which is used to measure the convergence degree of the iteration; S45, judge whether the iteration stop condition is met: if the stop decision parameter is less than a preset convergence threshold, or the iteration count reaches a preset maximum iteration number, terminate the iteration and output the final estimate of the sound source signal spatial energy distribution vector; otherwise, increment the iteration count and return to S42 to continue the iteration.
6. The method of claim 1, wherein, The S5 comprises the following steps: S51, extract the peak value of the sound source signal spatial energy distribution vector output by the step S4; S52, record the position index of the first peak in the energy distribution vector after arranging the peaks in descending order according to the amplitude size form a position set S53, based on the position set, extract the corresponding discrete angle (i.e. spatial observation angle) from the discrete angle set as the DOA coarse estimate value of the sound source direction, and form a DOA coarse estimate set.
7. The method of claim 1, wherein, The S6 comprises the following steps: S61, Regarding the first obtained in step S5 One rough estimate of DOA ( The corresponding angle refinement interval is determined; the angle refinement interval is defined as the range between adjacent angles in the discrete angle set for the coarse estimate of DOA. S62, based on the marginal likelihood maximization criterion, construct a target function for angle refinement processing, which is the sum of the ratios of specific parameters for each sub-band; the specific parameters are calculated from the steering vector corresponding to the candidate angle in the refinement interval, the received signal marginal likelihood covariance matrix excluding the current DOA coarse estimate value, and the received signal sample covariance matrix; wherein the covariance matrix excluding the current DOA coarse estimate value is formed by removing the rows and columns corresponding to the DOA coarse estimate value and its adjacent discrete angles from the received signal marginal likelihood covariance matrix; S63, maximize the target function in the angle refinement interval using the dichotomy search method, and take the candidate angle that maximizes the target function in the refinement interval as the optimal angle; S64, take the optimal angle as the fine estimate value of the corresponding DOA coarse estimate value, and form a DOA fine estimate set, the elements in the set being the high-precision DOA estimate values of each sound source.