Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 49 4 2018 02 20 Generalized Predictive Filter for Discrete-Time Linear Systems Generalized Predictive Filter for Discrete-Time Linear Systems 795 804 724 10.22060/mej.2016.724 FA M. Fathi Malek Ashtar University of Technology/Academic Institute of Aerospace Engineering N. Ghahramani Malek Ashtar University of Technology/Academic Institute of Electrical Engineering M.A. Shahi Ashtiani Malek Ashtar University of Technology/Academic Institute of Aerospace Engineering M. Fallah Malek Ashtar University of Technology/Academic Institute of Electrical Engineering A. Mohammadi Malek Ashtar University of Technology/Academic Institute of Electrical Engineering Journal Article 2015 11 07 In this paper, based on the duality between the predictive control and general estimation<br />problem, two new predictive filters, named generalized predictive filter and generalized predictive<br />Kalman filter, are developed. The major advantage of the new filters over the existing predictive filters<br />are that their structure are very simple and their application as a recursive filter is not complicated. Unlike<br />the Kalman filter, these proposed predictive filters assume that process noise and model error are not<br />equivalent and there are no limitations about the form of model error so that this model error can appear<br />in a nonlinear form or even a colored noise. By minimizing a quadratic cost function consisting of a<br />measurement residual term and a model error term respect to the process model error, the optimal model<br />error is determined. Compensation of this model error in the time update state model provides accurate<br />estimates even in the presence of dynamic uncertainty. Combination of Kalman filter and generalized<br />predictive filter improves the performance and robustness of Karman filter. The validity of the suggested<br />filters is illustrated by a numerical example and their performance and robustness are compared with<br />those of KF and the fading Kalman filter. In this paper, based on the duality between the predictive control and general estimation<br />problem, two new predictive filters, named generalized predictive filter and generalized predictive<br />Kalman filter, are developed. The major advantage of the new filters over the existing predictive filters<br />are that their structure are very simple and their application as a recursive filter is not complicated. Unlike<br />the Kalman filter, these proposed predictive filters assume that process noise and model error are not<br />equivalent and there are no limitations about the form of model error so that this model error can appear<br />in a nonlinear form or even a colored noise. By minimizing a quadratic cost function consisting of a<br />measurement residual term and a model error term respect to the process model error, the optimal model<br />error is determined. Compensation of this model error in the time update state model provides accurate<br />estimates even in the presence of dynamic uncertainty. Combination of Kalman filter and generalized<br />predictive filter improves the performance and robustness of Karman filter. The validity of the suggested<br />filters is illustrated by a numerical example and their performance and robustness are compared with<br />those of KF and the fading Kalman filter. https://mej.aut.ac.ir/article_724_74d1db4d0c0a65176030489ca6bdd2d5.pdf