THE SMOOTH VARIABLE STRUCTURE-KALMAN FILTER: A ROBUST AND OPTIMAL ESTIMATION STRATEGY

Abstract

State estimation strategies are vital for obtaining knowledge of a dynamic system'sstate where one is faced with challenges such as limited measurement capability, sensor noise, and uncertain system dynamics. The Kalman filter (KF), is one of the most popular tools in state estimation and provides the optimal solution for linear state estimation problems. The Smooth Variable Structure Filter (SVSF) is a relatively new estimation strategy based on variable structure theory and sliding mode concepts. Although the SVSF is not an optimal filter it is highly robust to modeling uncertainty and system change. The Smooth Variable Structure Filter ? Kalman Filter (SVSF-KF) is an adaptive estimation algorithm that attempts to provide an optimal KF estimate during normal system operation and the robust SVSF estimate during a fault. The existing SVSF-KF method uses a time varying smoothing boundary layer (VBL) to detect system change and an adaptive gain. This method while effective in some cases, has been shown to suffer several drawbacks. We propose three new approaches for implementing the aim of the SVSF-KF. One, an adaptive gain formulation based on the normalize innovation square, termed the NIS SVSF-KF, and two using multiple model frameworks, termed the MMAE SVSF-KF and IMM SVSF-KF respectively. The new methods are demonstrated via computer experiment on a simple harmonic oscillator scenario and an electro-hydrostatic actuator benchmark case. All three methods show significant improvement over the original SVSF-KF.