On stochastic observability of non-linear discrete-time dynamical systems

The purpose of this paper is to present sufficient conditions for the stochastic observability of non-linear discrete-time dynamical systems. The stochastic observability with probability one is defined and then an estimation algorithm of the initial system state is constructed for the given non-linear stochastic system. Theorems are developed giving sufficient conditions and then the stochastic convergence of the estimator sequence is examined. Secondly, the definition and sufficient conditions of the stochastic observability in a sense of normed square are given. Finally, comparative discussions on the sufficient conditions are developed, Verifications of sufficient conditions are shown by digital simulation studies.