Modeling of Venice Lagoon Time series with Improved Kalman Filter based neural networks

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IJCA Special Issue on Advanced Computing and Communication Technologies for HPC Applications
© 2012 by IJCA Journal
ACCTHPCA - Number 5
Year of Publication: 2012
Authors:
Archana R
A Unnikrishnan
R. Gopikakumari

Archana R, A Unnikrishnan and R Gopikakumari. Article: Modeling of Venice Lagoon Time series with Improved Kalman Filter based neural networks. IJCA Special Issue on Advanced Computing and Communication Technologies for HPC Applications ACCTHPCA(5):10-15, July 2012. Full text available. BibTeX

@article{key:article,
	author = {Archana R and A Unnikrishnan and R. Gopikakumari},
	title = {Article: Modeling of Venice Lagoon Time series with Improved Kalman Filter based neural networks},
	journal = {IJCA Special Issue on Advanced Computing and Communication Technologies for HPC Applications},
	year = {2012},
	volume = {ACCTHPCA},
	number = {5},
	pages = {10-15},
	month = {July},
	note = {Full text available}
}

Abstract

The identification of nonlinear and chaotic systems is an important and challenging problem. Neural network models, particularly Recurrent Neural Networks (RNN) trained with suitable algorithms, have received particular attention in the area of nonlinear identification due to their potentialities to approximate any nonlinear behavior. A method of nonlinear identification based on the RNN model trained with improved nonlinear Kalman filter is proposed in this paper. The neural network weights are estimated using the Extended Kalman Filter(EKF) algorithm, augmented by the Expectation Maximization(EM) algorithm is used to derive the initial states and covariance of the Kalman filter. It was shown that not only could this chaotic approach provide an accurate identification, but it was also more effective in the sense that the approach had a smaller mean squares error (MSE). An experimental case study using the famous Venice lagoon time series is analyzed by the proposed algorithm. The minimum embedding dimension of the time series is calculated using the method of false nearest neighbors. The Lyapunov exponents of the model are calculated, from the state space evolution, The numerical results presented here indicate that the traditional Extended Kalman Filter algorithm combined with EM techniques are effective in building a good NN model for nonlinear identification.

References

  • N. K Sinha and B Kuszta, Modeling and Identification of Dynamic systems,Van Nostrand Reinhold Company, New York,1983.
  • Simon Haykin, Neural Networks a comprehensive Foundation, Prentice Hall International Editions, 1999.
  • Fa-Long Luo and Rolf Unbehauen, Applied Neural Networks for Signal Processing, Cambridge University Press, 1997.
  • Yaakov Bar-Shalaom and Xiao-Rong Li, Estimation and Tracking: Principles, Techniques and Software. Artech House, Boston, London, 1993.
  • Greg Welch and Garry Bishop"An introduction to KalmanFilter"cc. cs. unc. edu/~tracker/s2001/kalman
  • A. S. Poznyak,Wen Yu and E. N Sanchez, "Identification and control of unknown chaotic systems via dynamic neural networks", IEEE Trans. on Circuits and Systems I: FundamentalTheoy and Applications, Vol. 46, No. 12 pp. 1491 -1495,1999.
  • G. V. Puskorius and L. A Feldkamp, " Neuro Control of nonlinear dynamical systems with Kalman Filter trained recurrent networks" IEEE Transactions on neural networks, Vol 5, No. 2, pp 279-297, 1994.
  • K. S. Narendra and K Parthasarathy, "Identification and control of Dynamical systems using neural networks", IEEE Transactions on Neural Networks, Vol 1, No. 2, pp 4-27, March 1990
  • Geist K U Parlitz and W Lauterborn"Comparison of different methods for computing Lyapunov exoonents"Progress of theoretical Physics 83-5 pp 875-893 1990.
  • Zhiven Zhu and Henry Leung "Identification of Linear Systems Driven by Chaotic Signals" IEEE transactions on circuits and systems—i: fundamental theory and applications, vol. 49, no. 2, February 2002
  • Ramon A. Felix, Edgar N. Sanchez, Senior Member, IEEE, and Guanrong Chen, Fellow, IEEE "Reproducing Chaos by Variable Structure Recurrent Neural Networks" IEEE transactions on neural networks, vol. 15, no. 6, November 200