Localization of acoustic source via optimal beamfomer design

Z.G. Feng, Ka Fai Cedric Yiu, Chi Kin Randolph Leung, S. Nordholm

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

In localizing acoustic sources in an enclosed area, the effect of reverberation remains a difficult obstacle. With various reflections within the area, the acoustic energy map of the enclosure is becoming rather complex and spiky, so finding the correct location is often tricky and erroneous. In this paper, a new framework of an acoustic source localization system is proposed. First of all, based on a room model, the frequency response between a point in the room and a microphone can be calculated. The idea is to discretize the room and to form a map of beamformers for all discrete points. The beamformer design is formulated as a functional optimization problem, and the optimized frequency response function can be sought directly. We show that, under some mild conditions, any source location will be the global maximizer of a response function. Once the bearmforming map is constructed, the implementation in finding the source location can be done in real time. For illustration, we demonstrate how the proposed method localizes the source with three numerical examples.
Original languageEnglish
Pages (from-to)37-56
Number of pages20
JournalPacific Journal of Optimization
Volume11
Issue number1
Publication statusPublished - 2015

Keywords

  • Localization
  • Beamformer design
  • Reverberation
  • Semi-definite programming

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Control and Optimization
  • Mechanical Engineering
  • Acoustics and Ultrasonics

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