Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 417623, 10 pages
Research Article

Iterative and Algebraic Algorithms for the Computation of the Steady State Kalman Filter Gain

1Department of Electronic Engineering, Technological Educational Institute of Central Greece, 3rd km Old National Road Lamia-Athens, 35100 Lamia, Greece
2Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou Street, 35100 Lamia, Greece

Received 24 February 2014; Accepted 31 March 2014; Published 4 May 2014

Academic Editors: F. Ding, L. Guo, and H. C. So

Copyright © 2014 Nicholas Assimakis and Maria Adam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Kalman filter gain arises in linear estimation and is associated with linear systems. The gain is a matrix through which the estimation and the prediction of the state as well as the corresponding estimation and prediction error covariance matrices are computed. For time invariant and asymptotically stable systems, there exists a steady state value of the Kalman filter gain. The steady state Kalman filter gain is usually derived via the steady state prediction error covariance by first solving the corresponding Riccati equation. In this paper, we present iterative per-step and doubling algorithms as well as an algebraic algorithm for the steady state Kalman filter gain computation. These algorithms hold under conditions concerning the system parameters. The advantage of these algorithms is the autonomous computation of the steady state Kalman filter gain.