Nonlinear Filters

7Smooth Variable‐Structure Filter

7.1 Introduction

The smooth variable‐structure filter (SVSF) algorithm has been derived based on a stability theorem [97]. Inspired by the variable‐structure control (VSC) theory, the SVSF uses an inherent switching action to guarantee convergence of the estimated states to within a neighborhood of their true values. Similar to the mentioned Bayesian filters in the previous chapters, the SVSF has been formulated in a predictor–corrector form [56, 58, 62, 98]. Robustness against bounded uncertainties is an inherent characteristic of the VSC, which has been inherited by the SVSF [99]. The distinguishing features of the SVSF from other filters can be summarized as follows [97]:

• The SVSF takes advantage of the inherent robustness of the VSC against bounded uncertainties. Hence, its convergence can be guaranteed for bounded uncertainty and noise. Moreover, a fairly precise estimate of the upper bound on the uncertainties will enhance the performance of the SVSF.
• Unlike other filtering strategies that implicitly consider uncertainty and rely on trial and error for tuning, the SVSF formulation allows for explicit identification of the source of uncertainty and assigning a bound to it. Taking account of this information in the design, alleviates tuning by trial and error to a large extent.
• In order to quantify the degree of uncertainty and modeling mismatch associated with each estimated state or parameter, the SVSF uses a secondary set of performance ...