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RISS 인기검색어
- 검색키워드
- 저자 : Moussa Yahia (검색결과 2 건)
- 무료
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Estimation of Nonlinear Systems via a Chebyshev Approximation Approach
Moussa Yahia,Pascal Acco,Malek Benslama 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.6
This paper proposes to decompose the nonlinear dynamic of a chaotic system with Chebyshev polynomials to improve performances of its estimator. More widely than synchronization of chaotic systems, this algorithm is compared to other nonlinear stochastic estimator such as Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Chebyshev polynomials orthogonality properties is used to fit a polynomial to a nonlinear function. This polynomial is then used in an Exact Polynomial Kalman Filter (ExPKF) to run real time state estimation. The ExPKF offers mean square error optimality because it can estimate exact statistics of transformed variables through the polynomial function. Analytical expressions of those statistics are derived so as to lower ExPKF algorithm compu-tation complexity and allow real time applications. Simulations under the Additive White Gaussian Noise (AWGN) hypothesis, show relevant performances of this algorithm compared to classical nonlinear estimators.
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Use of Chebyshev Polynomial Kalman Filter for Pseudo-blind Demodulation of CD3S Signals
Moussa Yahia,Valerio Freschi,Davide Radi,Laura Gardini 제어·로봇·시스템학회 2015 International Journal of Control, Automation, and Vol.13 No.5
Chaos based communication represents an attractive solution in order to design secure multiple access digital communication systems. In this paper we investigate the use of piecewise linear chaotic maps as chaotic generators combined, on the receiver side, with Chebyshev Polynomial Kalman Filters in a dual scheme configuration for demodulation purpose. Piecewise linear maps results into enhanced robustness properties of the spreading chaotic sequence, while approximation of nonlinear systems through Chebyshev polynomial series allows closed form estimation of mean and variance. Therefore, statistical moments can be computed by means of simple algebraic operations on matrices in compact form. In this work we extend these concepts to a dual Chebyshev Polynomial Kalman Filter scheme, suitable for signal recovery in chaos based spread spectrum systems. Numerical simulations show that the proposed method achieves lower error levels on a wide range of the bit-energy-tonoise- power-spectral-density ratio with respect to a state-of-the-art method based on unscented Kalman filters.
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