Chaotic system reconstruction from noisy time series measurements using improved least squares genetic programming

The problem of chaotic system reconstruction in the presence of measurement noise is not only an important one from the viewpoint of communication systems and radar signal processing, but also a challenging one if one has no a priori knowledge of the system structure. In this paper, we propose a novel algorithm based on genetic programming to reconstruct not only the structure of the underlying chaotic dynamical system but also the optimal parameters of the dynamical system using time series measurements that are corrupted by additive Gaussian noise. We show via computer simulations that the proposed algorithm called improved least squares genetic program (ILS-GP) is able to reconstruct different kinds of chaotic systems from their noisy time series measurements even at low SNRs. We finally show the improved ability of the ILS-GP algorithm by applying it to predict the time series of airborne radar sea clutter.