The Smooth Variable Structure Filter

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, a new method for state estimation, referred to as the smooth variable structure filter (SVSF), is presented. The SVSF method is model based and applies to smooth nonlinear dynamic systems. It allows for the explicit definition of the source of uncertainty and can guarantee stability given an upper bound for uncertainties and noise levels. The performance of the SVSF improves with more refined definition of upper bounds on parameter variations or uncertainties. Furthermore, most filtering methods provide as their measure of performance the filter innovation vector or (output) estimation error. However in addition to the innovation vector, the SVSF has a secondary set of performance indicators that correlate to the modeling errors specific to each state or parameter that is being estimated. The combined robustness and multiple indicators of performance allow for dynamic refinement of internal models in the SVSF. Dynamic refinement and robustness are features that are particularly advantageous in fault diagnosis and prediction. In this paper, the applications of the SVSF to linear and nonlinear systems, including one pertaining to fault detection, are provided. The characteristics of this filter in terms of its accuracy and rate of convergence are discussed. </para>