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ISRN Signal Processing
Volume 2012 (2012), Article ID 625897, 5 pages
http://dx.doi.org/10.5402/2012/625897
Research Article

On the Convergence of the Modified Riccati Equation

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

Received 5 March 2012; Accepted 26 April 2012

Academic Editors: C.-W. Kok and C.-M. Kuo

Copyright © 2012 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.

Abstract

The modified Riccati equation arises in the implementation of Kalman filter in target tracking under measurement uncertainty and it cannot be transformed into an equation of the form of the Riccati equation. An iterative solution algorithm of the modified Riccati equation is proposed. A method is established to decide when the proposed algorithm is faster than the classical one. Both algorithms have the same behavior: if the system is stable, then there exists a steady-state solution, while if the system is unstable, then there exists a critical value of the measurement detection probability, below which both iterative algorithms diverge. It is established that this critical value increases in a logarithmic way as the system becomes more unstable.