Bayesian Compressive Sensing Approaches for Direction of Arrival Estimation With Mutual Coupling Effects

Abstract

The problem of estimating the dynamic direction of arrival of far field signals impinging on a uniform linear array, with mutual coupling effects, is addressed. This work proposes two novel approaches able to provide accurate solutions, including at the endfire regions of the array. Firstly, a Bayesian compressive sensing Kalman filter is developed, which accounts for the predicted estimated signals rather than using the traditional sparse prior. The posterior probability density function of the received source signals and the expression for the related marginal likelihood function are derived theoretically. Next, a Gibbs sampling based approach with indicator variables in the sparsity prior is developed. This allows sparsity to be explicitly enforced in different ways, including when an angle is too far from the previous estimate. The proposed approaches are validated and evaluated over different test scenarios and compared to the traditional relevance vector machine based method. An improved accuracy in terms of average root mean square error values is achieved (up to 73.39% for the modified relevance vector machine based approach and 86.36% for the Gibbs sampling based approach). The proposed approaches prove to be particularly useful for direction of arrival estimation when the angle of arrival moves into the endfire region of the array.

2-D DOA tracking using variational sparse Bayesian learning embedded with Kalman filter

“…In [24], the time difference of arrival (TDOA) information was calculated by a pair of microphones and a distributed unscented KF method was used to track speakers in a nonlinear measurement model. The method combining KF with compression sensing was also used for dynamic DOA estimation [25,26]. The state transition function was built under the assumption that the bearing change rate had been known [25].…”

“…This assumption is hard to be satisfied in real applications. A Bayesian compressive sensing Kalman filter (BCSKF) method [26] was proposed to track dynamic moving sources. This method used the constant DOA changes in the KF prediction, which meant that the source moved to the designated direction with a fixed step.…”

“…First, a transition probabilities (TP) model is built to describe the state transition process of a signal. In this model, the source moves to an uncertain situation with an equal probability rather than a determining expected DOA change in [26]. In addition, TP model is convenient to build with a tracking framework and adopts sparse methods to estimate signal position.…”

“…There are three differences between the proposed approach and the method appeared in paper [26]. On the one hand, the proposed method constructs a realvalued steering matrix in signal model rather than splitting the complex value into several real-valued ones, which can reduce a half of the computational quantity approximately.…”

“…On the other hand, the KF estimation values is used instead of the Bayesian estimation values. The main contribution of paper [26] is putting the estimation parameters of KF to optimize the low bound of relate vector machine. However, the KF estimation will be embedded in VSBL to improve the precision further in this paper.…”