New novel time-varying and robust smoothing boundary layer width for the smooth variable structure filter

In this paper, a new novel form of the Smooth Variable Structure Filter (SVSF) is proposed. The SVSF is a recently proposed predictor-corrector filter for state and parameter estimation, and it is based on the sliding mode control concepts. It defines a hyperplane and then applies a discontinuous corrective action that forces the estimate to go back and forth across that plane. Thereby, the SVSF is robust and stable technique. The proposed SVSF uses a saturated function with an associated fixed-width smoothing boundary layer to eliminate chattering. However, it has been noticed that the filter performance could be improved by using a time-varying smoothing boundary layer that is directly linked to the output´s a priori estimation error. In this paper, a solution for a time-varying, stable and robust smoothing boundary layer width is obtained based on using two filters; the first is to maintain stability, and the second is to obtain the modified estimate vector that minimizes the diagonal elements of the error covariance matrix. The proposed method is tested on an electro-hydrostatic actuator proposed in [1] and its performance is compared with the Kalman Filter performance.