Noise Reduction of Chaotic Systems by Kalman Filtering and by Shadowing
David M. Walker, Alistair Mees · International Journal of Bifurcation and Chaos · 1997
We investigate two techniques for filtering signals from noisy nonlinear systems. Both the dynamics and the observed signals may be subject to noise. The first technique is a modified Kalman filter which accounts for the noise-amplification properties of chaotic systems and has less tendency to diverge than the usual Kalman filter. The second is the noise-reduction algorithm of Hammel, based on the concept of shadowing from dynamical systems theory.