Polynomial Filtering for Linear Discrete Time Non-Gaussian Systems

In this work we propose a new filtering approach for linear discrete time non-Gaussian systems that generalizes a previous result concerning quadratic filtering [A. De Santis, A. Germani, and M. Raimondi, IEEE Trans. Automat. Control, 40 (1995) pp. 1274-1278]. A recursive th-order polynomial estimate of finite memory 1 is achieved by defining a suitable extended state which allows one to solve the filtering problem via the classical Kalman linear scheme. The resulting estimate will be the mean square optimal one among those estimators that take into account -polynomials of the last 1 observations. Numerical simulations show the effectiveness of the proposed method.