Discrete-time filtering for nonlinear polynomial systems over linear observations

This paper designs a discrete-time filter for nonlinear polynomial systems driven by additive white Gaussian noises over linear observations. The solution is obtained by computing the time-update and measurement-update equations for the state estimate and the error covariance matrix. A closed form of this filter is obtained by expressing the conditional expectations of polynomial terms as functions of the estimate and the error covariance. As a particular case, a third degree polynomial is considered to obtain the finite-dimensional filtering equations. Numerical simulations are performed for a third degree polynomial system and an induction motor model. Performance of the designed filter is compared with the extended Kalman one to verify its effectiveness.