POLYNOMIAL FILTERING FOR LINEAR DISCRETE-TIME NON-GAUSSIAN SYSTEMS

In this work we propose a new filtering approach for linear discrete t ime 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 nu th-o rder polynomial estimate of finite memory Delta is achieved by definin g a suitable extended state which allows one to solve the filtering pr oblem via the classical Kalman linear scheme. The resulting estimate w ill be the mean square optimal one among those estimators that take in to account nu-polynomials of the last Delta observations. Numerical si mulations show the effectiveness of the proposed method.