Robust FIR State Estimation of Dynamic Processes Corrupted by Outliers

The outlier is a common issue in the design of state estimators for an industrial process. In this paper, a robust finite impulse response (FIR) filter is proposed for time-invariant state-space models with its noise following the Student's t distributions. A batch solution is first derived by maximizing the likelihood, and then, an equivalent iterative realization is given to provide a clearer insight into the FIR structure. It shows that the essence of the proposed approach is the convergence of the maximum likelihood estimates in horizon scale through iterations, and the state estimate at each sampling instant is independent of the degree-of-freedom (DOF) parameter of the Student's t distribution. Based on this, a modified algorithm that updates the DOF parameter in each iteration is further proposed. Applications to a moving target tracking example and a 3-DOF helicopter system demonstrate that the proposed methods can exhibit good immunity against outliers during the filtering.