DOA Estimation Exploiting a Single Moving Acoustic Vector Sensor: A Cramér-Rao Bound-Based Study

Abstract

Motivated by the emerging interest in direction-of-arrival (DOA) estimation exploiting array motions, this paper investigates a practical application scenario involving a single moving acoustic vector sensor (AVS). By reasonably arranging observations at different times, we construct a flexible measurement model for the resulting dual-AVS synthetic array. Since multiple components of an AVS are physically co-located, incorporating a synthetic aperture via the translation motion can contribute to remarkable performance improvement. Aiming at an explicit analysis, we delve into the corresponding Cramér-Rao bound (CRB) in the single-source case and formulate a CRB optimization problem to determine the optimal measurement model. Thanks to significant simplifications, we derive a closed-form CRB expression, which provides insight into the system performance and favors the analytical solution of the optimization problem. Regarding DOA estimation, especially for the spatially nonuniform noise specific to AVSs, we propose a weighted maximum likelihood estimator (WMLE) to fully leverage the promised theoretical gain in terms of the CRB. Further noting the intrinsic relationship between the WMLE performance and array data arrangement, we design a two-phase iterative procedure that updates the DOA estimate and the measurement matrix structure alternately to approximate the global optimal solution. Numerical experiments corroborate our analytical derivations and validate the statistical efficiency of the proposed methods. Their mean-square errors are tightly lower bounded by the derived CRBs at high signal-to-noise ratios.