SMOOTH VARIABLE STRUCTURE FILTERING: THEORY AND APPLICATIONS

Abstract

<p>Filtering strategies play an important role in estimation theory, and are used to extract knowledge of the true states typically from noisy measurements or observations made of the system. The name ‘filter’ is appropriate since it removes unwanted noise from the signal. In 2007, the smooth variable structure filter (SVSF) was introduced. This filter is based on the sliding mode control and estimation techniques, and is formulated in a predictor-corrector fashion. The SVSF makes use of an existence subspace and of a smoothing boundary layer to keep the estimates bounded within a region of the true state trajectory. This creates a robust and stable estimation strategy. The research presented in this thesis focuses on advancing the development and implementation of the SVSF.</p> <p>In its original form, the SVSF does not utilize a state error covariance matrix, which is a measure of the accuracy of the state estimates. Therefore, the first major contribution of this research is the formulation of an SVSF strategy with a covariance derivation. This creates a number of research opportunities that can only be pursued and rely on the availability of the error covariance matrix. In an effort to further improve the estimation accuracy, a time-varying smoothing boundary layer is created by minimizing the covariance. This contribution significantly improves the SVSF, and provides a mechanism for combining the SVSF with other popular estimation strategies. A linear system example with the presence of uncertainties is studied which demonstrates that the proposed SVSF improves the estimation accuracy by approximately 20%. Furthermore, a new model-based fault detection strategy is created based on the interacting multiple model (IMM) method. This new method (IMM-SVSF) is applied on an experimental apparatus for the purposes of fault detection. It is able to improve upon the fault detection probability by 10-30% (depending on the fault), when compared with the most commonly used strategy. The IMM-SVSF method is also found to work extremely well for target tracking problems, demonstrating an improvement of roughly 40%. This research results in a number of novel contributions, and significantly advances the development of the SVSF.</p>