Near-field/far-field array manifold of an acoustic vector-sensor near a reflecting boundary

Abstract

The acoustic vector-sensor (a.k.a. the vector hydrophone) is a practical and versatile sound-measurement device, with applications in-room, open-air, or underwater. It consists of three identical uni-axial velocity-sensors in orthogonal orientations, plus a pressure-sensor—all in spatial collocation. Its far-field array manifold [Nehorai and Paldi (1994). IEEE Trans. Signal Process. 42, 2481–2491; Hawkes and Nehorai (2000). IEEE Trans. Signal Process. 48, 2981–2993] has been introduced into the technical field of signal processing about 2 decades ago, and many direction-finding algorithms have since been developed for this acoustic vector-sensor. The above array manifold is subsequently generalized for outside the far field in Wu, Wong, and Lau [(2010). IEEE Trans. Signal Process. 58, 3946–3951], but only if no reflection-boundary is to lie near the acoustic vector-sensor. As for the near-boundary array manifold for the general case of an emitter in the geometric near field, the far field, or anywhere in between—this paper derives and presents that array manifold in terms of signal-processing mathematics. Also derived here is the corresponding Cramér-Rao bound for azimuth-elevation-distance localization of an incident emitter, with the reflected wave shown to play a critical role on account of its constructive or destructive summation with the line-of-sight wave. The implications on source localization are explored, especially with respect to measurement model mismatch in maximum-likelihood direction finding and with regard to the spatial resolution between coexisting emitters.