CramÉr-Rao Bounds for Direction Finding by an Acoustic Vector Sensor Under Nonideal Gain-Phase Responses, Noncollocation, or Nonorthogonal Orientation

An acoustic vector-sensor (also known as 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. Such an acoustic vector sensor is versatile for direction-finding, due to its azimuth-elevation spatial response's independence from the incident source's frequency, and bandwidth. However, previously unavailable in the open literature is how the acoustic vector sensor's far-field direction-of-arrival estimates may be adversely affected by any unknown nonideality in the acoustic vector sensor's gain response, phase response, collocation, or orthogonal orientation among its constituent velocity sensors. This paper pioneers a characterization of how these various unknown nonidealities degrade direction-finding accuracy, via Cramer-Rao bound analysis.