Robust Kalman filter of continuous-time Markov jump linear systems based on state estimation performance
Xiaobo Xiao, Hongsheng Xi, Jin Zhu, Haibo Ji · International Journal of Systems Science · 2007
Robust Kalman filtering problem for a class of continuous-time Markov jump linear systems with uncertain second-order statistical properties is investigated. Uncertainty is modeled by allowing process and observation noises spectral density matrices to vary arbitrarily within given classes. The upper bounds of the perturbation to the noise covariance matrices are given based on the estimation error performance, and a steady-state estimator is therefore adopted under the worst situation. Not only can this method minimize the worst performance function of the uncertainty, but the error performance can be guaranteed to be within a given bound. Finally the developed theory is illustrated by a numerical example.