An hybrid Cramér-Rao bound in closed form for direction-of-arrival estimation by an 'acoustic vector sensor' with gain-phase uncertainties

Ping Kwan Tam, Kainam Thomas Wong, Yang Song

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)


An 'acoustic vector sensor' (also known as a 'vector hydrophone' in underwater or sea-surface applications) is composed of three orthogonally oriented uni-axial particle-velocity sensors, plus a 'pressure-sensor' (i.e., a microphone or a hydrophone) - all collocated in a point-like spatial geometry. (This collocated setup is versatile for direction finding, because its azimuth-elevation spatial response is independent of frequency.) This paper investigates how the acoustic vector sensor's direction finding accuracy would be degraded by random deviations from its nominal gain response and/or phase response. Each type of deviation is statistically modeled herein as a random variable with a small variance, reasonably so for a well-built acoustic vector sensor. The resulting hybrid Cramér-Rao bound (HCRB) is derived exactly in open form for azimuth-elevation arrival-angle estimation, but also approximated to produce a closed form that is simple enough to yield qualitative observations. This closed-form hybrid Cramér-Rao lower bound's tightness is illustrated by a new estimator developed in this paper.
Original languageEnglish
Article number6763044
Pages (from-to)2504-2516
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number10
Publication statusPublished - 15 May 2014


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

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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