Adaptive Regularized Particle Filter for Synchronization of Chaotic Colpitts Circuits in an AWGN Channel
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Adaptive Regularized Particle Filter for Synchronization of Chaotic Colpitts Circuits in an AWGN Channel Shaohua Hong · Zhiguo Shi · Lin Wang · Yujie Gu · Kangsheng Chen
Received: 3 July 2011 / Revised: 28 September 2012 / Published online: 20 October 2012 © Springer Science+Business Media New York 2012
Abstract For chaotic trajectories, when the system parameters are fixed, they are generally confined in a bounded state space. In this paper, we propose an adaptive regularized particle filter (RPF), which makes the best of this inherent characteristic, for identical synchronization of chaotic Colpitts circuits combating additive white Gaussian noise (AWGN) channel distortion. This proposed filter incorporates RPF that resamples from a continuous approximation of the posterior density to avoid sample impoverishment and then utilizes the revised Kullback–Leibler distance (KLD) sampling to adaptively select the number of particles used. Compared with the existing particle filters (PFs) with fixed large number of particles, this proposed adaptive RPF propagates less number of particles with similar performance and thus provides a much more efficient solution for this problem. Keywords Adaptive regularized particle filter · Chaos · Colpitts circuit · Synchronization S. Hong () · L. Wang Department of Communication Engineering, Xiamen University, Xiamen 361005, P.R. China e-mail: [email protected] L. Wang e-mail: [email protected] Z. Shi · K. Chen Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, P.R. China Z. Shi e-mail: [email protected] K. Chen e-mail: [email protected] Y. Gu School of Engineering, Bar-Ilan University, Ramat-Gan 52900, Israel e-mail: [email protected]
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Circuits Syst Signal Process (2013) 32:825–841
1 Introduction Since the work of Pecora and Carroll on chaos synchronization [15], considerable interest has been displayed in this research topic for its potential applications in radar, signal encryption, communications, etc. [9, 18]. As one of the standard oscillators, the synchronization of Colpitts circuit [8] is a hot research topic [2, 11, 17, 19, 23]. Both mathematical analysis and simulation results have confirmed that perfect synchronization can be achieved under ideal synchronization conditions [11, 19], and it was found that with minor parameter mismatch, chaos synchronization can still be obtained and maintained [2, 23]. However, in chaos synchronization with an additive white Gaussian noise (AWGN) channel, the traditional algorithms using the same or partly the same circuit in the receiver as a response system show unacceptable performance [17]. Recently, recursive Bayesian approaches used to construct a receiver posed another way for this problem [5, 10, 20, 21, 24, 25], especially the particle filters (PFs) that are the state-of-the-art solution to nonlinear and non-Gaussian problems [1, 16]. In 2006, Kurian and Puthusserypady investigated the unscented Kalman filter (UKF) and PF for chaotic synchronization, where the Lorenz and Mac
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