A Framework for State-Space Estimation with Uncertain Models

This talk describes a framework for state-space estimation when the parameters of the underlying linear model are subject to bounded uncertainties. Compared with existing robust filters, the new filters are shown to perform regularization rather than deregularization and they require no existence conditions. The filters apply to both time-variant as well as time-invariant models, and they can handle finite- and infinite-horizon scenarios. In particular, they are shown to lead to stable steady-state operation and to guarantee bounded error variances. The resulting filter structures also turn out to be similar to various (time- and measurement-update, prediction, and information) forms of the Kalman filter, albeit ones that operate on corrected parameters rather than on the given nominal parameters. Extensive Monte-Carlo simulations and comparisons with H_oo, guaranteed-cost, set-valued state estimation, and robust minimum-variance filters are provided with promising performance.