Set-Valued Filtering and Smoothing

Darryl Morrell, Wynn C. Stirling

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


A theory of discrete-time optimal filtering and smoothing based on convex sets of probability distributions is presented. Rather than propagating a single conditional distribution as does conventional Bayesian estimation, a convex set of conditional distributions is evolved. For linear Gaussian systems, the convex set may be generated by a set of Gaussian distributions with equal covariance with means in a convex region of state space. The conventional point-valued Kalman filter is generalized to a set-valued Kalman filter, consisting of equations of evolution of a convex set of conditional means and a conditional covariance. The resulting estimator is an exact solution to the problem of running an infinity of Kalman filters and fixed-interval smoothers, each with different initial conditions. An application is presented to illustrate and interpret the estimator results.

Original languageEnglish (US)
Pages (from-to)184-193
Number of pages10
JournalIEEE Transactions on Systems, Man and Cybernetics
Issue number1
StatePublished - 1991

ASJC Scopus subject areas

  • General Engineering


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