Table of Contents
ISRN Computational Mathematics
Volume 2013 (2013), Article ID 249594, 7 pages
Research Article

Kalman Filter Riccati Equation for the Prediction, Estimation, and Smoothing Error Covariance Matrices

1Department of Electronic Engineering, Technological Educational Institute of Central Greece, 35100 Lamia, Greece
2Department of Computer Science and Biomedical Informatics, University of Thessaly, 35100 Lamia, Greece

Received 2 August 2013; Accepted 2 October 2013

Academic Editors: D. S. Corti, F. W. S. Lima, and H. J. Ruskin

Copyright © 2013 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 classical Riccati equation for the prediction error covariance arises in linear estimation and is derived by the discrete time Kalman filter equations. New Riccati equations for the estimation error covariance as well as for the smoothing error covariance are presented. These equations have the same structure as the classical Riccati equation. The three equations are computationally equivalent. It is pointed out that the new equations can be solved via the solution algorithms for the classical Riccati equation using other well-defined parameters instead of the original Kalman filter parameters.