A theory of set-valued estimation
A theory of estimation based on convex sets of probability distributions is presented and used to develop set-valued estimation algorithms. Set-valued estimators provide a robust and intuitively pleasing method of approaching estimation problems in which a unique solution may not exist. All solutions which are consistent with the available data and contextual information are obtained. Thus, a set-valued estimator may be used in the estimation of the state of a weakly or partially observable system.
In this work, the discrete-time filtering, prediction, and smoothing problems are addressed. The set-valued filter and predictor are obtained using a very general Markov system model; these estimators are specialized to two particular system models to obtain explicit estimation algorithms. The first system model is linear and based on a continuous state space, and the set-valued filter, predictor, and smoother are derived using this model. These estimators are extended to non-linear systems through a linear approximation. The second (possibly non-linear) system model is based on a discrete state space, and the filter and predictor are derived using this model.