A New Robust Filtering Strategy for Linear Systems

Abstract For linear and well-defined estimation problems with Gaussian white noise, the Kalman filter (KF) yields the best result in terms of estimation accuracy. However, the KF performance degrades and can fail in cases involving large uncertainties such as modeling errors in the estimation process. The smooth variable structure filter (SVSF) is a relatively new estimation strategy based on sliding mode theory and has been shown to be robust to modeling uncertainties. The SVSF makes use of an existence subspace and of a smoothing boundary layer to keep the estimates bounded within a region of the true state trajectory. Currently, the width of the smoothing boundary layer is chosen based on designer knowledge of the upper bound of modeling uncertainties, such as maximum noise levels and parametric errors. This is a conservative choice, as a more well-defined smoothing boundary layer will yield more accurate results. In this paper, the state error covariance matrix of the SVSF is used for the derivation of an optimal time-varying smoothing boundary layer. The robustness and accuracy of the new form of the SVSF was validated and compared with the KF and the standard SVSF by testing it on a linear electrohydrostatic actuator (EHA).