Noise reduction in chaotic timeseries

This paper describes the application of a nonlinear autoregressive (NLAR) modelling technique to three chaotic systems in order to estimate the underlying NLAR signal using causal data processing. The systems under consideration are the Henon map, the Lozi map, and a discrete generation insect predator-prey map. The noise reduction algorithm is assessed quantitatively using two fractal dimension estimates and the first Lyapunov exponent, and graphically by results depicting the improvement in strange attractor form and sharpness. Results for the classic chaotic system, the Henon map, show an improvement upon filtering of the order of 30% whilst results for the Lozi map demonstrate that this technique may, at least sometimes, be applied successfully to systems which are not autoregressive. Whilst filtering of the discrete insect population predator-prey map produced noticeable levels of improvement, the overall improvement in performance was less dramatic