Cramér-Rao Bounds for direction finding by an acoustic vector-sensor under unknown gain / phase uncertainties

An acoustic vector-sensor (a.k.a. vector-hydrophone in underwater applications) is composed of two or three spatially collocated but orthogonally oriented acoustic velocity-sensors, plus possibly a collocated acoustic pressure-sensor. An acoustic vector-sensor is versatile for direction-finding, due to its azimuth- elevation spatial response's independence from the incident source's frequency, bandwidth, or radial location (i.e., in the near field as opposed to the far field). Unavailable in the current open literature is how the direction-of-arrival (DOA) estimates may be adversely affected by any unknown non-ideality in the acoustic vector-sensor. The non-ideality may include any unknown deviation from the nominal gain response and/or phase response. This paper pioneers a characterization of these various unknown non-idealities' relative degradation on direction-finding accuracy through Cramer-Rao Bound (CRB) analysis of how the estimation accuracy is degraded relatively by each such unknown non-ideality.