Kalman Filtering with Model Uncertainties

In the classical Kalman filter theory, one of the key assumptions is that a priori knowledge of the system model, which represents the actual system, is known without uncertainty. Our focus in this research is to estimate the state of a system that is subjected to stochastic disturbances by using an erroneous model along with the available stored measurements. We examine two approaches that take the effects of uncertain parameters into the account since these uncertain parameters degrade the estimate of the state. In the first approach, the errors in the nominal model, which are approximated by fictitious noise and covariance of the fictitious noise, are computed by using stored data. It is premised that the norm of discrepancy between correlation functions of the measurements and their estimates from the nominal model is minimum. The second approach involves the identification of a Kalman filter model on the premise that the norm of discrepancy between the measurements and their estimates is minimum. This paper reviews the two approaches and illustrates their performances numerically.