Sensor networks for diffusion fields: Detection of sources in space and time

Ivan Dokmanić, Juri Ranieri, Amina Chebira, Martin Vetterli

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

Abstract

We consider the problem of reconstructing a diffusion field, such as temperature, from samples collected by a sensor network. Motivated by the fast decay of the eigenvalues of the diffusion equation, we approximate the field by a truncated series. We show that the approximation error decays rapidly with time. On the other hand, the information content in the field also decays with time, suggesting the need for a proper choice of the sampling strategy. We propose two algorithms for sampling and reconstruction of the field. The first one reconstructs the distribution of point sources appearing at known times using the finite rate of innovation (FRI) framework. The second algorithm addresses a more difficult problem of estimating the unknown times at which the point sources appear, in addition to their locations and magnitudes. It relies on the assumption that the sources appear at distinct times. We verify that the algorithms are capable of reconstructing the field accurately through a set of numerical experiments. Specifically, we show that the second algorithm successfully recovers an arbitrary number of sources with unknown release times, satisfying the assumption. For simplicity, we develop the 1-D theory, noting the possibility of extending the framework to more general domains.

Original languageEnglish (US)
Title of host publication2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
Pages1552-1558
Number of pages7
DOIs
StatePublished - 2011
Externally publishedYes
Event2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 - Monticello, IL, United States
Duration: Sep 28 2011Sep 30 2011

Publication series

Name2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011

Other

Other2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
CountryUnited States
CityMonticello, IL
Period9/28/119/30/11

Keywords

  • Diffusion field
  • estimation
  • release time
  • sensor networks
  • source localization
  • sparse sampling

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Control and Systems Engineering

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