The Nonlinear Filtering Problem for A Multistage System with Statistical Uncertainty

Abstract

This paper deals with the problem of state and parameter estimation [1,2] on the basis of available observations for a discrete-time nonlinear system when the distributions of the disturbances or the transitional distributions of the corresponding Markov processes are not specified precisely [3-8]. An approach proposed here is based on the investigation of the set of all conditional means or the set of all conditional distributions consistent with the available information for the process. The knowledge of the above sets allows to obtain minmax estimates for the unknown actual state of the system. The approach was first suggested in [8] for the linear-gaussian case. In the given work we attempt to present a rather general scheme for the investigation of the evolution of the "informational sets" mentioned above and perhaps for the specification of the best minmax estimate for the state of the system.