Omnidirectional bats, point-to-plane distances, and the price of uniqueness

Miranda Krekovic, Ivan Dokmanic, Martin Vetterli

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study simultaneous localization and mapping with a device that uses reflections to measure its distance from walls. Such a device can be realized acoustically with a synchronized collocated source and receiver; it behaves like a bat with no capacity for directional hearing or vocalizing. In this paper we generalize our previous work in 2D, and show that the 3D case is not just a simple extension, but rather a fundamentally different inverse problem. While generically the 2D problem has a unique solution, in 3D uniqueness is always absent in rooms with fewer than nine walls. In addition to the complete characterization of ambiguities which arise due to this non-uniqueness, we propose a robust solution for inexact measurements similar to analogous results for Euclidean Distance Matrices. Our theoretical results have important consequences for the design of collocated range-only SLAM systems, and we support them with an array of computer experiments.

Original languageEnglish (US)
Title of host publication2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3261-3265
Number of pages5
ISBN (Electronic)9781509041176
DOIs
StatePublished - Jun 16 2017
Externally publishedYes
Event2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States
Duration: Mar 5 2017Mar 9 2017

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
CountryUnited States
CityNew Orleans
Period3/5/173/9/17

Keywords

  • Collocated source and receiver
  • SLAM
  • first-order echoes
  • indoor localization
  • point-to-plane distance matrix (PPDM)
  • room geometry reconstruction

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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