Robust steady-state Kalman filter for uncertain discrete-time system

In this paper, the problem of designing robust steady-state Kalman filter is considered for linear discrete-time system with uncertain model parameters and noise variances. By the new approach of compensating the parameter uncertainties by a fictitious noise, the system model is converted into that with uncertain noise variances only. Using the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of the noise variances, a robust steady-state Kalman filter is presented. Based on the Lyapunov equation approach, we prove its robustness. The concept of the robust region is presented. A simulation example is presented to demonstrate how to search the robust region and show its good performance.