###
3rd International Symposium
on

Imprecise
Probabilities and Their Applications

ISIPTA '03

#####
University of Lugano

Lugano, Switzerland

14-17 July 2003

####
ELECTRONIC PROCEEDINGS

# An Extended Set-valued Kalman Filter

### Abstract

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

**Paper Download **

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** 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: **

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