On Convergence of the Unscented Kalman-Bucy Filter using Contraction Theory

J.P. Maree, Lars Imsland, Jerome Jouffroy

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilizing stochastic contraction theory to conclude on exponential convergence of the Unscented Kalman-Bucy Filter. The underlying process and measurement models of interest are Itô-type stochastic differential equations. In particular, statistical linearisation techniques are employed in a virtual-actual systems framework to establish deterministic contraction of the estimated expected mean of process values. Under mild conditions of bounded process noise, we extend the results on deterministic contraction to stochastic contraction of the estimated expected mean of process state. It follows that for regions of contraction, a result on convergence, and thereby incremental stability, is concluded for the Unscented Kalman-Bucy Filter. The theoretical concepts are illustrated in two case studies.
Original languageEnglish
JournalInternational Journal of Systems Science
Volume47
Issue number8
Pages (from-to)1816-1827
ISSN0020-7721
DOIs
Publication statusPublished - 2016

Keywords

  • Stochastic contraction
  • Unscented Kalman-Bucy Filter
  • Virtual-actual framework
  • Static linearization

Fingerprint

Dive into the research topics of 'On Convergence of the Unscented Kalman-Bucy Filter using Contraction Theory'. Together they form a unique fingerprint.

Cite this