{"title":"Particle Filter Applied to Noisy Synchronization in Polynomial Chaotic Maps","authors":"Moussa Yahia, Pascal Acco, Malek Benslama","volume":35,"journal":"International Journal of Electronics and Communication Engineering","pagesStart":2133,"pagesEnd":2138,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/14350","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.<\/p>\r\n","references":"[1] M. B. Luca, S. Azou, G. Burel, and A. Serbanescu, On Exact Kalman\r\nFiltering of Polynomial Systems, IEEE Trans. Circuits Syst. I, vol. 53,\r\nno. 6. pp. 1329-1340, 2006.\r\n[2] H. Fujisaka and T. Yamada, Stability Theory of Synchronized Motion in\r\nCoupled-Oscillator Systems, Prog. Theor. Phys., vol.69, pp. 32-47, 1983.\r\n[3] L. Pecora and T. Caroll, Synchronization in chaotic systems, Phys. Rev.\r\nLett., vol. 64, no. 2, pp. 821-823, 1990.\r\n[4] M. Hasler Synchronization of chaotic systems and transmission of information,\r\nInt. J. Bifurcation and Chaos, vol. 8, no. 4, pp. 647-659, 1998.\r\n[5] K. M. Cuomo, A. V. Oppenheim and S. H. Strogratz, Synchronization of\r\nLorenz-based chaotic circuits with application to communication, IEEE\r\nTrans. Circuits Syst. II, vol. 40, no. 10, pp. 626-633, 1993.\r\n[6] G. Kolumb'an, M. P. Kennedy, and L. O. Chua, The role of synchronization\r\nin digital communication using chaos \u00d4\u00c7\u00f6 Part I: Fundamentals od digital\r\ncommunications, IEEE Trans. on Circuits Syst. I vol 44, pp927-936, Oct\r\n1997\r\n[7] \u00d4\u00c7\u00f6- Part II: Chaotic modulation and chaotic synchronisation, IEEE Trans.\r\non Circuits Syst. I vol 45, pp 1129-1140, Nov 1998\r\n[8] \u00d4\u00c7\u00f6- Part III: Performance bounds for correlation receivers, IEEE Trans.\r\non Circuits Syst. I vol 47, pp1673-1683, Dec 2000\r\n[9] A. Gelb, Applied Optimal Estimation, MIT Press, Cambridge, 1974.\r\n[10] Y. Bar-Shalom and X.-R. Li, Estimation and Tracking: Principles,\r\nTechniques and Software. Artech House, Boston, 1993.\r\n[11] S. Julier, J. Uhlmann and H. F. Durrant-Whyte, A new method for\r\nthe nonlinear transformation of means and covariances in filters and\r\nestimators, IEEE Trans. Automat. Contr., vol. 45, no. 3, pp. 477-482,\r\n2000.\r\n[12] E. A. Wan and R. van der Merwe, Kalman Filtering and Neural\r\nNetworks, chap. 7 : The Unscented Kalman Filter, published by Wiley\r\nPublishing (editors S. Haykin), 2001.\r\n[13] M. Norgaard, N. K. Poulsen and O. Ravn, New developments in state\r\nestimation for nonlinear systems, Automatica, vol. 36, pp. 1627-1638,\r\n2000.\r\n[14] N. J. Gordon, D. J. Salmond and A. F. M. Smith, Novel approach to\r\nnonlinear\/NonGuassian Bayesian State Estimation, IEE Proc. vol. 140\r\nno. 2, pp107-113, 1993\r\n[15] M. S. Arulampalam, S. Maskell, N. Gordon and T. Clapp, Tutorial on\r\nparticle filter for online Nonlinear\/NonGaussian Bayesian Tracking IEEE\r\ntrans. Signal Processing, vol. 50, no. 2, pp 1174-188, Feb. 2002","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 35, 2009"}