Robust Steady-State Kalman Predictor with Uncertain Parameters and Noise Variances

Abstract

For the linear time-invariant system with uncertain model parameters and noise variances, a minimax robust steady-state Kalman predictor is presented by a new approach of compensating the uncertain model parameters by a fictitious noise. By the Lyapunov equation approach, it is proved that when the conservative upper bounds of the fictitious noise and system noise variances are given, there exists a sufficiently small region of uncertain parameters disturbances, such that its actual prediction error variances are guaranteed to have a less-conservative upper bound. This region is called as the robust region of the parameters uncertainty. Furthermore, a simulation example is presented to demonstrate how to search the robust region and show the good performance of the proposed robust Kalman predictor.