Generalized Predictive Filter for Discrete-Time Linear Systems

In this paper, based on the duality between the predictive control and general estimation problem, two new predictive filters, named generalized predictive filter and generalized predictive Kalman filter, are developed. The major advantage of the new filters over the existing predictive filters are that their structure are very simple and their application as a recursive filter is not complicated. Unlike the Kalman filter, these proposed predictive filters assume that process noise and model error are not equivalent and there are no limitations about the form of model error so that this model error can appear in a nonlinear form or even a colored noise. By minimizing a quadratic cost function consisting of a measurement residual term and a model error term respect to the process model error, the optimal model error is determined. Compensation of this model error in the time update state model provides accurate estimates even in the presence of dynamic uncertainty. Combination of Kalman filter and generalized predictive filter improves the performance and robustness of Karman filter. The validity of the suggested filters is illustrated by a numerical example and their performance and robustness are compared with those of KF and the fading Kalman filter.