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Particle Filter Applied to Noisy Synchronization in Polynomial Chaotic Maps

Authors: Moussa Yahia, Pascal Acco, Malek Benslama


Polynomial maps offer analytical properties used to obtain better performances in the scope of chaos synchronization under noisy channels. This paper presents a new method to simplify equations of the Exact Polynomial Kalman Filter (ExPKF) given in [1]. This faster algorithm is compared to other estimators showing that performances of all considered observers vanish rapidly with the channel noise making application of chaos synchronization intractable. Simulation of ExPKF shows that saturation drawn on the emitter to keep it stable impacts badly performances for low channel noise. Then we propose a particle filter that outperforms all other Kalman structured observers in the case of noisy channels.

Keywords: saturation, chaos synchronization, Fast ExPKF, Particlefilter, Polynomial maps

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[1] M. B. Luca, S. Azou, G. Burel, and A. Serbanescu, On Exact Kalman Filtering of Polynomial Systems, IEEE Trans. Circuits Syst. I, vol. 53, no. 6. pp. 1329-1340, 2006.
[2] H. Fujisaka and T. Yamada, Stability Theory of Synchronized Motion in Coupled-Oscillator Systems, Prog. Theor. Phys., vol.69, pp. 32-47, 1983.
[3] L. Pecora and T. Caroll, Synchronization in chaotic systems, Phys. Rev. Lett., vol. 64, no. 2, pp. 821-823, 1990.
[4] M. Hasler Synchronization of chaotic systems and transmission of information, Int. J. Bifurcation and Chaos, vol. 8, no. 4, pp. 647-659, 1998.
[5] K. M. Cuomo, A. V. Oppenheim and S. H. Strogratz, Synchronization of Lorenz-based chaotic circuits with application to communication, IEEE Trans. Circuits Syst. II, vol. 40, no. 10, pp. 626-633, 1993.
[6] G. Kolumb'an, M. P. Kennedy, and L. O. Chua, The role of synchronization in digital communication using chaos ÔÇö Part I: Fundamentals od digital communications, IEEE Trans. on Circuits Syst. I vol 44, pp927-936, Oct 1997
[7] ÔÇö- Part II: Chaotic modulation and chaotic synchronisation, IEEE Trans. on Circuits Syst. I vol 45, pp 1129-1140, Nov 1998
[8] ÔÇö- Part III: Performance bounds for correlation receivers, IEEE Trans. on Circuits Syst. I vol 47, pp1673-1683, Dec 2000
[9] A. Gelb, Applied Optimal Estimation, MIT Press, Cambridge, 1974.
[10] Y. Bar-Shalom and X.-R. Li, Estimation and Tracking: Principles, Techniques and Software. Artech House, Boston, 1993.
[11] S. Julier, J. Uhlmann and H. F. Durrant-Whyte, A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE Trans. Automat. Contr., vol. 45, no. 3, pp. 477-482, 2000.
[12] E. A. Wan and R. van der Merwe, Kalman Filtering and Neural Networks, chap. 7 : The Unscented Kalman Filter, published by Wiley Publishing (editors S. Haykin), 2001.
[13] M. Norgaard, N. K. Poulsen and O. Ravn, New developments in state estimation for nonlinear systems, Automatica, vol. 36, pp. 1627-1638, 2000.
[14] N. J. Gordon, D. J. Salmond and A. F. M. Smith, Novel approach to nonlinear/NonGuassian Bayesian State Estimation, IEE Proc. vol. 140 no. 2, pp107-113, 1993
[15] M. S. Arulampalam, S. Maskell, N. Gordon and T. Clapp, Tutorial on particle filter for online Nonlinear/NonGaussian Bayesian Tracking IEEE trans. Signal Processing, vol. 50, no. 2, pp 1174-188, Feb. 2002