Noise Reduction of Chaotic Systems by Kalman Filtering and by Shadowing

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.