A framework for state-space estimation with uncertain models

This paper develops a framework for state-space estimation when the parameters of the underlying linear model are subject to uncertainties. Compared with existing robust filters, the proposed filters perform regularization rather than de-regularization. It is shown that, under certain stabilizability and detectability conditions, the steady-state filters are stable and that, for quadratically-stable models, the filters guarantee a bounded error variance. Moreover, the resulting filter structures are similar to various (timeand measurement-update, prediction, and information) forms of the Kalman filter, albeit ones that operate on corrected parameters rather than on the given nominal parameters. Simulation results and comparisons with H1, guaranteed-cost, and set-valued state estimation filters are provided. Keywords— Estimation, parametric uncertainty, set-valued estimation, Kalman filtering, H1-filtering, guaranteed-cost design, steady-state filter, quadratic stability, regularized least-squares.