On the Move: Localization with Kinetic Euclidean Distance Matrices

Puoya Tabaghi, Ivan Dokmanic, Martin Vetterli

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

Abstract

In this paper, we propose kinetic Euclidean distance matrices (KEDMs) - a new algebraic tool for localization of moving points from spatio-temporal distance measurements. KEDMs are inspired by the well-known Euclidean distance matrices (EDM) which model static points. When objects move, trajectory models may enable better localization from fewer samples by trading off samples in space for samples in time. We develop the theory for polynomial trajectory models used in tracking and simultaneous localization and mapping. Concretely, we derive a semidefinite relaxation for KEDMs inspired by similar algorithms for the usual EDMs, and propose a new spectral factorization algorithm adapted to trajectory reconstruction. Numerical experiments show that KEDMs and the new semidefinite relaxation accurately reconstruct trajectories from incomplete, noisy distance observations, scattered over multiple time instants. In particular, they show that temporal oversampling can considerably reduce the required number of measured distances at any given time.

Original languageEnglish (US)
Title of host publication2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4893-4897
Number of pages5
ISBN (Electronic)9781479981311
DOIs
StatePublished - May 2019
Event44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
Duration: May 12 2019May 17 2019

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2019-May
ISSN (Print)1520-6149

Conference

Conference44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
CountryUnited Kingdom
CityBrighton
Period5/12/195/17/19

Keywords

  • Euclidean distance matrix
  • polynomial spectral factorization
  • semidefinite programming
  • trajectory localization

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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