Joint state and parameter estimation for uncertain stochastic nonlinear polynomial systems

This article presents the joint state filtering and parameter identification problem for uncertain stochastic nonlinear polynomial systems with unknown parameters in the state equation over nonlinear polynomial observations, where the unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The obtained mean-square filter for the extended state vector also serves as the mean-square identifier for the unknown parameters. Performance of the designed mean-square state filter and parameter identifier is verified for both, positive and negative, parameter values.