Robust Kalman filter of discrete-time Markovian jump system with parameter and noise uncertainty

Robust Kalman filtering problems for discrete-time Markovian jump systems with parameter and noise uncertainty were investigated. Because of the existence of stochastic Markovian switching, the covariance matrices of system state noise and observation noise are time-varying or unmeasurable instead of stationary, meanwhile the system suffers from structure parameter uncertainty as well. By view of robust estimation, maximum admissible upper bound of the disturbance to noise covariance matrix was given based on the estimation performance, and an optimal state estimator was therefore adopted under the worst situation. Not only can this method minimize the worst performance function of uncertainty, but also the estimation error performance can be guaranteed to be within the given precision. A numerical example shows the validity of the method. Key–Words: Markovian jump systems;robust Kalman filter; uncertainty;