Polynomial filtering and identification of discrete-time nonlinear uncertain stochastic systems

This paper deals with the problem of system identification and state estimation for nonlinear uncertain stochastic systems, in the discrete-time framework. By suitably extending the state space with the inclusion of the unknown vector of parameters, the filtering and identification problems are simultaneously solved. The algorithm here proposed applies the optimal polynomial filter of a chosen degree μ to the Carleman approximation of the same degree of the extended nonlinear system. Simulations support theoretical results.