Sequential sparse Bayesian learning for time-varying direction of arrival

Abstract

This paper presents methods for the estimation of the time-varying directions of arrival (DOAs) of signals emitted by moving sources. Following the sparse Bayesian learning (SBL) framework, prior information of unknown source amplitudes is modeled as a multi-variate Gaussian distribution with zero-mean and time-varying variance parameters. For sequential estimation of the unknown variance, we present two sequential SBL-based methods that propagate statistical information across time to improve DOA estimation performance. The first method heuristically calculates the parameters of an inverse-gamma hyperprior based on the source signal estimate from the previous time step. In addition, a second sequential SBL method is proposed, which performs a prediction step to calculate the prior distribution of the current variance parameter from the variance parameter estimated at the previous time step. The SBL-based sequential processing provides high-resolution DOA tracking capabilities. Performance improvements are demonstrated by using simulated data as well as real data from the SWellEx-96 experiment.

Frequency Analysis of Acoustic Data Using Multiple-Measurement Sparse Bayesian Learning

“…The SBL solves the linear system of Equation (4) while exploiting common frequency components across multiple measurements. As demonstrated in studies using the sparse representation [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 ], the sparse estimations from the SBL using the multiple measurements have advantages for frequency detection in terms of enhancing resolution and reducing noise, which is supported by the comparison results of Section 4 and Section 5 . It is noteworthy that the feasibility of SBL in detecting low-frequency components in passive sonar signals is examined using the in-situ data by the current study.…”

“…Recently, the SBL has been used in finding the direction of arrivals (DOAs) [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ], localizing acoustic sources [ 35 , 36 , 37 , 38 ], and mode extraction [ 39 ]. Similar to CS, the SBL suffers from the basis mismatch arising from the discrete representation in the linear system, and the off-grid SBL models using approximations are proposed in order to relieve the problem [ 25 , 26 , 27 , 28 , 29 , 30 ].…”

“…Similar to CS, the SBL suffers from the basis mismatch arising from the discrete representation in the linear system, and the off-grid SBL models using approximations are proposed in order to relieve the problem [ 25 , 26 , 27 , 28 , 29 , 30 ]. On the other hand, noise in the measurements degrades the SBL based beamforming performance and the SBL is expanded to enhance the performance by using multiple measurements [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 ]. In the SBL using multiple measurements, the commonality of the source signals over the multiple measurements is exploited, and it increases the robustness of the SBL to the noise.…”

“…Here, based on the properties demonstrated in the previous works [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 ], the SBL using multiple measurements is used for detecting frequency components corresponding to the tonal signals in the passive sonar system after the linear system for the frequency analysis is established. The sparse tonal signals and the multiple measurements along the sensors in the sonar system should allow the SBL to have obvious frequency detections.…”

Parametric Models for Doa Trajectory Localization

“…This is commonly done by processing overlapping blocks and applying tracking filters such as Kalman filter [12] or particle filter [13] over block DOA estimates to obtain source motion trajectories. Recently some works have addressed the problem of DOA trajectory estimation using Bayesian analysis [14] and neural networks [15,16].…”