Maximum likelihood identification of time varying and random system parameters†

Abstract

Abstract In many investigations of system identification, severe restrictions on the system are necessary in order to obtain the estimation/identification alogrithms; i.e., the system and observation model parameters (Φ, H, T) and the plant and observation noise moments are constrained to be time-invariant. In many cases of interest, however, the system parameters and/or plant and measurement noise moments are not constant, but time varying and perhaps even random parameters. The method of suboptimal maximum likelihood identification is extended such that the adaptive gains can be computed based on estimates of the random parameters or possibly by implementation of an augmented extended Kalman filter. This method leads to a nonlinear two-point boundary value problem which is resolved by the method of invariant embedding such as to lead to sequential identification algorithms. Examples demonstrate the efficiency of the proposed algorithms