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.