The smooth variable structure filter: A comprehensive review

The smooth variable structure filter (SVSF) is a type of sliding mode filter formulated in a predictor-corrector format and has seen significant development over the last 15 years. In this paper, we provide a comprehensive review of the SVSF and its variants. The developments, applications and improvements of the SVSF in terms of robustness and optimality are investigated. In addition, the combination of the SVSF with different filtering strategies is considered in an effort to improve estimation accuracy while maintaining robustness to model uncertainty. State estimation techniques such as the unscented and cubature Kalman filters (UKF & CKF), SVSF, the combination of SVSF with UKF (UK-SVSF), and the combination of CKF with SVSF (CK-SVSF) are applied on a 4-DOF industrial robotic arm. The SVSF state estimation performance is examined under different operating conditions. The results of these filters have been compared based a number of statistics such as the root mean squared error (RMSE) and mean absolute error (MAE), among others. It is shown that the UK-SVSF and CK-SVSF strategies acquire the best performance in the presence of uncertainties.