A simple adaptive algorithm of stochastic approximation type for system parameter and state estimation

A simple adaptive filter optimal in the sense of minimum prediction error (MPE) is proposed to estimate the state of high dimensional systems in which the process and observation noise statistics are unknown. It is shown that the implementation of this adaptive filter requires a solution of only two n-dimensional linear difference equations and no solution for nonlinear matrix equations like the algebraic Riccatti equation (ARE) is needed. A connection of adaptive filters with steady-state Kalman filters (SSKF) is discussed. The numerical example is given to demonstrate the efficiency of proposed approach