Keywords

estimation theory, filtering and prediction theory, matrix algebra, probability, set theory, state estimation

Abstract

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 can 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 generated 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 Publication Citation

Morrell, D. R., and W. C. Stirling. "Set-Values Filtering and Smoothing." Systems, Man and Cybernetics, IEEE Transactions on 21.1 (1991): 184-93