Robust estimation and filtering in the presence of bounded noise

Optimal algorithms for robust estimation and filtering are constructed. The noise is considered a deterministic variable belonging to a set described by a norm. Previous results, obtained for complete (one-to-one) and approximate information by M. Milanese and R. Tempo (ibid., vol.30, p.730-8, 1985), are extended to partial and approximate information. This information is considered useful in dealing with dynamic systems not completely identifiable and/or with two different sources of noise, such as process and measurement noise. For different norms characterizing the noise, optimal algorithms (in a min-max sense) are shown. In particular, for Hilbert norms a linear optimal algorithm is the well-known minimum variance estimator. For l_∞ norm an optimal algorithm, computable by linear programming, is presented. State estimation is formalized in the context of the general theory. For stable systems, an approximate state estimation is obtained by neglecting higher order powers. An upper bound determining the approximation introduced is derived. A numerical example illustrates the application of the theory