Ultimately Bounded Filtering Subject to Impulsive Measurement Outliers

Abstract

This article is concerned with the ultimately bounded filtering problem for a class of linear time-delay systems subject to norm-bounded disturbances and impulsive measurement outliers (IMOs). The considered IMOs are modeled by a sequence of impulsive signals with certain known minimum norm (i.e., the minimum of the norms of all impulsive signals). In order to characterize the occasional occurrence of IMOs, a sequence of independent and identically distributed random variables is introduced to depict the interval lengths (i.e., the durations between two adjacent IMOs) of the outliers. In order to achieve satisfactory filtering performance, a novel parameter-dependent filtering approach is proposed to protect the filtering performance from IMOs by using a special outlier detection scheme, which is developed based on a particular input–output model. First, the ultimate boundedness (in mean square) of the filtering error is investigated by using the stochastic analysis technique and the Lyapunov-functional-like method. Then, the desired filter gain matrix is derived through solving a constrained optimization problem. Furthermore, the designed filtering scheme is applied to the case where the statistical properties about the interval lengths of outliers are completely unknown. Finally, a simulation example is provided to demonstrate the effectiveness of our proposed filtering strategy.