Robustification of Kalman filter models

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

113 Scopus Citations
View graph of relations

Author(s)

  • Richard J. Meinhold
  • Nozer D. Singpurwalla

Detail(s)

Original languageEnglish
Pages (from-to)479-486
Journal / PublicationJournal of the American Statistical Association
Volume84
Issue number406
Publication statusPublished - Jun 1989
Externally publishedYes

Abstract

Kalman filter models based on the assumption of multivariate Gaussian distributions are known to be nonrobust. This means that when a large discrepancy arises between the prior distribution and the observed data, the posterior distribution becomes an unrealistic compromise between the two. In this article we discuss a rationale for how to robustify the Kalman filter. Specifically, we develop a model wherein the posterior distribution will revert to the prior when extreme outlying observations are encountered, and we point out that this can be achieved by assuming a multivariate distribution with Student-t marginals. To achieve fully robust results of the kind desired, it becomes necessary to forsake an exact distribution-theory approach and adopt an approximation method involving “poly-t” distributions. A recursive mechanism for implementing the multivariate-t—based Kalman filter is described, its properties are discussed, and the procedure is illustrated by an example. © 1989 Taylor & Francis Group, LLC.

Research Area(s)

  • Automatic control, Bayes law, Bounded influence functions, Kalman filtering, Multivariate Student-t distributions, Non-Gaussian filtering, Poly-t densities, Robustness, Signal processing

Citation Format(s)

Robustification of Kalman filter models. / Meinhold, Richard J.; Singpurwalla, Nozer D.
In: Journal of the American Statistical Association, Vol. 84, No. 406, 06.1989, p. 479-486.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review