Parameter Estimation Using a Combined Variable Structure and Kalman Filtering Approach

Abstract

A method that is often used for parameter estimation is the extended Kalman filter (EKF). EKF is a model-based strategy that implicitly considers the effect of modeling uncertainties. This implicit consideration often leads to the tuning of the filter by trial and error. When formulated for parameter estimation, the “tuned” EKF becomes sensitive to uncertainties in its internal model. The EKF’s robustness can be improved by combining it with the recently proposed variable structure filter (VSF) concept. In a combined form, the modeling uncertainties no longer affect stability, but impact the performance and the quality of the estimation process. Furthermore, the VSF concept provides a secondary set of indicators of performance that is in addition to the estimation error and that pertains to the range of parametric uncertainties. As such, the robustness of the combined method and its multiple indicators of performance allow the use of intelligent adaptation for improving the performance of the estimation process. For real-time applications, online neural network adaptation may be used to improve the performance by progressively reducing specific modeling uncertainties in the system. In this paper, a new parameter estimation method that uses concepts associated with the EKF, the VSF, and neural network adaptation is introduced. The performance of this method is considered and discussed for applications that involve parameter estimation such as fault detection.