Continuously discrete estimation of stochastic processes for observations with memory under anomalous noise: Synthesis

An mean square optimal unbiased filter-interpolator-extrapolator for continuous-time processes is synthesized on the basis of the set of realizations of continuous and discrete time processes. It is supposed that these processes depend not only on the current values of an unobserved process, but on an arbitrary number of its preceding values as well; the extrapolation is performed at an arbitrary number of future instants, and anomalous noise occurs in discrete observations.