Particle Filter Applied to Noisy Synchronization in Polynomial Chaotic Maps
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.
[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
[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
@article{"International Journal of Electrical, Electronic and Communication Sciences:63351", author = "Moussa Yahia and Pascal Acco and Malek Benslama", title = "Particle Filter Applied to Noisy Synchronization in Polynomial Chaotic Maps", abstract = "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 = "Chaos synchronization, Saturation, Fast ExPKF, Particlefilter, Polynomial maps.", volume = "3", number = "11", pages = "2194-5", }
