Recursive filtering for nonlinear systems subject to measurement outliers

Abstract

In this paper, an innovative recursive filtering algorithm (RFA) is proposed for a class of nonlinear systems (NSs) subject to multiplicative noises (MNs) and measurement outliers (MOs). Initially, the MNs are employed to formulate the random influence on the NSs with the stochastic noises. Next, the outlier phenomenon could occur unpredictably during measurement transmission. Then, a self-adaptive saturation function is introduced to the constructed filter to mitigate the influence of MOs on the filter performance. In this paper, we design a resistant-outlier filter for NSs with MNs and MOs, and the filter gain ensures that the trace of the filtering error covariance matrix is minimized by solving the constructed Riccati-like difference equations. Moreover, the exponential boundedness of the filtering error in the sense of mean square is analyzed. Finally, the feasibility of the proposed RFA is illustrated by a simulation example when the MOs occur.