Table of Contents
ISRN Computational Mathematics
Volume 2013 (2013), Article ID 249594, 7 pages
http://dx.doi.org/10.1155/2013/249594
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.

Linked References

  1. B. D. O. Anderson and J. B. Moore, Optimal Filtering, Dover Publications, New York, NY, USA, 2005.
  2. N. Assimakis, “Discrete time Riccati equation recursive multiple steps solutions,” Contemporary Engineering Sciences, vol. 2, no. 7, pp. 333–354, 2009. View at Google Scholar
  3. N. Assimakis and M. Adam, “Iterative and algebraic algorithms for the computation of the steady state Kalman filter gain,” submitted in Central European Journal of Computer Science. In press.
  4. N. D. Assimakis, D. G. Lainiotis, S. K. Katsikas, and F. L. Sanida, “A survey of recursive algorithms for the solution of the discrete time riccati equation,” Nonlinear Analysis, Theory, Methods and Applications, vol. 30, no. 4, pp. 2409–2420, 1997. View at Google Scholar · View at Scopus
  5. N. Assimakis, S. Roulis, and D. Lainiotis, “Optimal distributed algorithms for the solution of the discrete time Riccati equation,” Nonlinear Studies, vol. 12, no. 4, pp. 381–390, 2005. View at Google Scholar
  6. N. Assimakis, S. Roulis, and D. Lainiotis, “Recursive solutions of the discrete time Riccati equation,” Neural, Parallel and Scientific Computations, vol. 11, pp. 343–350, 2003. View at Google Scholar
  7. P. Benner and H. Faßbender, “On the numerical solution of large-scale sparse discrete-time Riccati equations,” Advances in Computational Mathematics, vol. 35, no. 2, pp. 119–147, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. D. G. Lainiotis, N. D. Assimakis, and S. K. Katsikas, “A new computationally effective algorithm for solving the discrete Riccati equation,” Journal of Mathematical Analysis and Applications, vol. 186, no. 3, pp. 868–895, 1994. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Lainiotis, N. Assimakis, and S. Katsikas, “Fast and numerically robust recursive algorithms for solving the discrete time Riccati equation: the case of nonsingular plant noise covariance matrix,” Neural, Parallel and Scientific Computations, vol. 3, no. 4, pp. 565–584, 1995. View at Google Scholar
  10. A. J. Laub, “A Schur method for solving algebraic Riccati equations,” IEEE Transactions on Automatic Control, vol. 24, no. 6, pp. 913–921, 1979. View at Google Scholar · View at Scopus
  11. A. C. M. Ran and L. Rodman, “Stable Hermitian solutions of discrete algebraic Riccati equations,” Mathematics of Control, Signals, and Systems, vol. 5, no. 2, pp. 165–193, 1992. View at Publisher · View at Google Scholar · View at Scopus
  12. D. R. Vaughan, “A nonrecursive algebraic solution for the discrete time Riccati equation,” IEEE Transactions on Automatic Control, vol. 15, no. 5, pp. 597–599, 1970. View at Google Scholar · View at Scopus