Sparse Arrays

Abstract

Direction-of-arrival (DOA) estimation of acoustic sources is of great interest in a number of applications. Acoustic vector sensors (AVSs) provide an edge over traditional scalar sensors since they measure the acoustic velocity field in addition to the acoustic pressure. It is known that a uniform linear array (ULA) of M conventional scalar sensors can identify up to M-1 DOAs. However, using second-order statistics, the class of sparse scalar sensor arrays have been shown to identify more source DOAs than the number of sensors. In this thesis, we extend these results using sparse AVS arrays. We first assume that the sources are quasi-stationary and use the Khatri-Rao subspace approach to estimate the source DOAs. In addition, a spatial-velocity smoothing technique is proposed to estimate the DOAs of stationary sources. For both scenarios, we show that the number of source DOAs that can be identified is significantly greater than the number of physical vector sensors. The second problem considered in this thesis is sensor selection for non-linear models. It is often necessary to guarantee a certain estimation accuracy by choosing the best subset of the available set of sensors. A non-linear measurement model in additive Gaussian noise is considered. To solve the sensor selection problem, which is inherently combinatorial, a greedy algorithm based on submodular cost functions is developed. The proposed low-complexity greedy algorithm is computationally attractive as compared to existing sensor selection solvers for non-linear models. The submodular cost ensures optimality of the greedy algorithm.