Abstract-March 1, 2016 The directions of arrival (DOA) of plane waves are estimated from multi-snapshot sensor array data using Sparse Bayesian Learning (SBL). The prior source amplitudes is assumed independent zero-mean complex Gaussian distributed with hyperparameters the unknown variances (i.e. the source powers). For a complex Gaussian likelihood with hyperparameter the unknown noise variance, the corresponding Gaussian posterior distribution is derived. For a given number of DOAs, the hyperparameters are automatically selected by maximizing the evidence and promote sparse DOA estimates. The SBL scheme for DOA estimation is discussed and evaluated competitively against LASSO ( 1-regularization), conventional beamforming, and MUSIC.
The single sensor probability hypothesis density (PHD) and cardinalized probability hypothesis density (CPHD) filters have been developed in the literature using the random finite set framework. The existing multisensor extensions of these filters have limitations such as sensor order dependence, numerical instability or high computational requirements. In this paper we derive update equations for the multisensor CPHD filter. The multisensor PHD filter is derived as a special case. Exact implementation of the multisensor CPHD involves sums over all partitions of the measurements from different sensors and is thus intractable. We propose a computationally tractable approximation which combines a greedy measurement partitioning algorithm with the Gaussian mixture representation of the PHD. Our greedy approximation method allows the user to control the tradeoff between computational overhead and approximation accuracy.Index Terms-Random finite sets, multisensor CPHD filter, multisensor PHD filter, multisensor multitarget tracking.
Sparse Bayesian learning (SBL) has emerged as a fast and competitive method to perform sparse processing. The SBL algorithm, which is developed using a Bayesian framework, approximately solves a non-convex optimization problem using fixed point updates. It provides comparable performance and is significantly faster than convex optimization techniques used in sparse processing. We propose a signal model which accounts for dictionary mismatch and the presence of errors in the weight vector at low signal-to-noise ratios. A fixed point update equation is derived which incorporates the statistics of mismatch and weight errors. We also process observations from multiple dictionaries. Noise variances are estimated using stochastic maximum likelihood. The derived update equations are studied quantitatively using beamforming simulations applied to direction-of-arrival (DoA). Performance of SBL using single-and multi-frequency observations, and in the presence of aliasing, is evaluated. SwellEx-96 experimental data demonstrates qualitatively the advantages of SBL.
The multi-snapshot, multi-frequency sparse Bayesian learning (SBL) processor is derived and its performance compared to the Bartlett, minimum variance distortionless response, and white noise constraint processors for the matched field processing application. The two-source model and data scenario of interest includes realistic mismatch implemented in the form of array tilt and data snapshots not exactly corresponding to the range-depth grid of the replica vectors. Results demonstrate that SBL behaves similar to an adaptive processor when localizing a weaker source in the presence of a stronger source, is robust to mismatch, and exhibits improved localization performance when compared to the other processors. Unlike the basis or matching pursuit methods, SBL automatically determines sparsity and its solution can be interpreted as an ambiguity surface. Because of its computational efficiency and performance, SBL is practical for applications requiring adaptive and robust processing.
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