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.