Sliding Mode Kalman filter for Dynamic Systems with Parametric Uncertainties

Abstract This paper presents a robust variant of Kalman filter, named as Sliding Mode Kalman Filter (SMKF), for the dynamic systems which are perturbed with parametric uncertainty. Proposed filter which is a successor of Sliding Mode Observers (SMO) is designed to update the state estimates and the corrected error covariance with Kalman gain followed by a discontinuous gain for systems with linear signal models in presence of parametric uncertainties, modelling inaccuracies and unknown noise covariance matrices. Inspired from the concepts of the reaching law used in Sliding Mode Control (SMC) the discontinuous gain along with the Kalman gain is incorporated to upgrade the correction steps of the conventional Kalman filter for better convergence and estimation accuracy. Stability analysis of the proposed filter recommends it for the parameter varying dynamic systems with a restriction in the upper bound of unmodelled dynamics. Simulation studies reveal that the proposed SMKF outshines the standard Kalman filter and snsures relatively better estimation performance compared to its close contender, Sliding Innovation Filter (SIF). The efficacy and the robustness of the proposed SMKF is also demonstrated with experimental data obtained from a phase shift oscillator circuit.