Optimal sensor design for infinite-time Kalman filters

Shu Xia Tang, Kirsten A. Morris

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

1 Scopus citations

Abstract

This paper is concerned with state estimation for systems governed by partial differential equations. Kalman filters are optimal state estimators in that they minimize the estimation error variance for given measurements. The focus of this paper is the achievement of additional minimization of the error variance by also optimizing over the sensor design. The optimal sensor design problem is thus incorporated into the estimation problem. Not only the sensor location but also other factors such as sensor shape and the effect of the sensors on system dynamics are included in the optimization criteria. The problem is first stated formally, and then it is shown to be well-posed and to possess an optimal solution. Applications to a one-dimensional diffusion equation and also to a two-dimensional wave equation are given. A computational framework for calculation of optimal shape is described.

Original languageEnglish
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages64-69
Number of pages6
ISBN (Electronic)9781509028733
DOIs
StatePublished - Jan 18 2018
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: Dec 12 2017Dec 15 2017

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Conference

Conference56th IEEE Annual Conference on Decision and Control, CDC 2017
CountryAustralia
CityMelbourne
Period12/12/1712/15/17

Keywords

  • Kalman filter
  • distributed parameter systems
  • infinite-dimensional systems
  • optimal estimation
  • optimal sensor design

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  • Cite this

    Tang, S. X., & Morris, K. A. (2018). Optimal sensor design for infinite-time Kalman filters. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 64-69). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8263644