Quadratic filtering for simultaneous state and parameter estimation of uncertain systems

The aim of this paper is to investigate the problem of the joint estimation of both the state and parameters for a class of discrete-time linear systems driven by additive noise, not necessarily Gaussian. A recursive quadratic filter with respect to the observations is here proposed and implemented, by opportunely extending the state space also with the inclusion of the parameters vector. The algorithm is achieved with the systematic use of the Kronecker algebra, which constitutes a powerful tool for polynomial manipulations of vectors and matrices. Numerical simulations are also reported, showing the high performances of the proposed methods with respect to the usually adopted Extended Kalman Filter.