Robust state estimation for uncertain systems with missing measurements and random sensor delay

Abstract

This paper is concerned with the robust Kalman filter design for linear uncertain systems subject to randomly varying delay and missing measurements. Norm-bounded uncertainties and stochastic uncertainties simultaneously enter into the state matrix. Some Bernoulli random variables are introduced to account for the phenomena of random delay and missing measurements. Merging the stochastic uncertainties into the process noise and utilizing the state augmentation, the original system is transformed into the stochastic parameterized uncertain system. For the augmented system, a robust filter is proposed. Sufficient conditions that ensure an upper bound on the filtering error variance being minimized are derived for all allowed uncertainties. An illustrative example is given to demonstrate the effectiveness and applicability of the developed method.