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.
Keywords. imprecise probabilities, statistical inference, dynamic systems, convex sets of probability measures, set-valued estimation
Authors addresses:
Darryl Morrell
Department of Electrical Engineering
Arizona State University
Tempe AZ 85287-5706
Wynn Stirling
Electrical and Computer Engineering
459 CB Brigham Young University
Provo, UT 84602
USA
E-mail addresses:
| Darryl Morrell | morrell@asu.edu |
| Wynn Stirling | wynn@ee.byu.edu |