Generalized Predictive Filter for Discrete-Time Linear Systems

Document Type : Research Article

Authors

1 Malek Ashtar University of Technology/Academic Institute of Aerospace Engineering

2 Malek Ashtar University of Technology/Academic Institute of Electrical Engineering

Abstract

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.

Keywords

Main Subjects

References

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Amirkabir Journal of Mechanical Engineering
Volume 49, Issue 4
March 2018
Pages 795-804

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