A New Form of the Smooth Variable Structure Filter with a Covariance Derivation

State and parameter estimation is important for the control of systems, particularly when not all of the system information is available for the designer. Filters are used to extract state information from measurements, which are typically corrupted by noise. A common measure of the performance of an estimate by a filter is through the use of a covariance matrix. This essentially provides a measure of the error in the estimate. Furthermore, knowledge of this covariance can lead to a more accurate derivation and greater number of applications for the filter. Introduced in 2007, the smooth variable structure filter (SVSF) is a relatively new filter. It is a predictor-correct estimator based on sliding mode control and estimation. In its current form, the SVSF is not a classical filter in the sense that it does not have a covariance matrix. This paper introduces the SVSF in a new form without affecting its original proof of stability, and outlines the derivation of a covariance matrix that can be used for comparative purposes as well as other applications. A linear mechanical system referred to as an electrohydrostatic actuator (EHA) is used to numerically demonstrate the new SVSF. The results are compared with the classical Kalman filter (KF), which is the most common and efficient filtering strategy for linear systems.