Particle filter applied to polynomial chaotic maps

Yahia, Moussa; Acco, Pascal

doi:10.1109/ecctd.2009.5275041

Cited by 1 publication

(2 citation statements)

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“…An easy solution given in [21] is to saturate the posteriori state. The counterpart is that the new dynamic noise pdf is no longer Gaussian and no more uncorrelated to the state x k .…”

Section: 2mentioning

confidence: 99%

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Estimation of nonlinear systems via a Chebyshev approximation approach

Yahia

Acco

Benslama

2011

Int. J. Control Autom. Syst.

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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 computation 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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“…An easy solution given in [21] is to saturate the posteriori state. The counterpart is that the new dynamic noise pdf is no longer Gaussian and no more uncorrelated to the state x k .…”

Section: 2mentioning

confidence: 99%

“…Informally this ExPKF is just running in absence of dynamic noise or by a simple adaptation of the iterative chaotic map as we showed in [21]. In addition to this, the computational cost is so high that the ExPKF algorithm can hardly be developed for commercial real time applications.…”

Section: Introductionmentioning

confidence: 96%