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

Ping Kwan Tam, Kainam Thomas Wong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

68 Citations (Scopus)


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 Cramér-Rao bound analysis.
Original languageEnglish
Pages (from-to)969-982
Number of pages14
JournalIEEE Sensors Journal
Issue number8
Publication statusPublished - 1 Jan 2009


  • Acoustic interferometry
  • acoustic signal processing
  • acoustic velocity measurement
  • array signal processing
  • direction of arrival estimation
  • phased arrays
  • sonar arrays
  • sonar signal processing
  • underwater acoustic arrays

ASJC Scopus subject areas

  • Instrumentation
  • Electrical and Electronic Engineering

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