Robust estimation and filtering in the presence of bounded noise

In this paper problems of robust estimation and filtering are studied. No statistical assumption is used and the noise is considered a deterministic variable belonging to a set described by a Hilbert norm. We show that an optimal algorithm (in a worst case sense) is the well-known minimum variance estimator. For stable systems, an approximate state estimation is obtained by neglecting higher order powers. An upper bound of the approximation error is derived.