An Extended Set-valued Kalman Filter.
Darryl R. Morrell, Wynn C. Stirling · 2003
Set-valued estimation offers a way to account for imprecise knowledge of the prior distribution of a Bayesian statistical inference problem. The set-valued Kalman filter, which propagates a set of conditional means corresponding to a convex set of conditional probability distributions of the state of a linear dynamic system, is a general solution for linear Gaussian dynamic systems. In this paper, the set-valued Kalman filter is extended to the non-linear case by approximating the non-linear model with a linear model that is chosen to minimize the error between the non-linear dynamics and observation models and the linear approximation. An application is presented to illustrate and interpret the estimator results.