Probability-guaranteed set-membership filtering for systems with incomplete measurements

In this note, the probability-guaranteed set-membership filtering problem is investigated for a class of time-varying systems with incomplete measurements. The uniform distribution over known finite ranges is assumed for mutually independent stochastic variables existing in the functions of system matrices. The process noise and measurement noise are unknown, bounded and confined to a specified ellipsoidal set respectively, which is handled by transformation to the inequality constraints. The purpose is to design a set-membership filter, for all the admissible unknown but bounded noises, known deterministic input and incomplete measurements, such that the ellipsoidal set including all possible states can be determined by a convex optimization approach with probability constraint. A recursive linear matrix inequality (RLMI) approach is proposed to address the probability-guaranteed set-membership filtering problem. Finally, a simulation example demonstrates the effectiveness of the proposed filtering scheme.