Reconstruction of piecewise chaotic dynamics using a multiple model approach

In this paper we propose using a multiple model (MM) predictor to reconstruct piecewise chaotic dynamic. The motivation relies on the observation that conventional single model is usually incapable of reconstructing the piecewise dynamic properly because a piecewise map is non-differentiable. In our approach, multiple radial basis function (RBF) neural nets are used to model the dynamic in different partition intervals. Switching between different intervals could be estimated by a nonlinear gate model. In particular, an Expectation-Maximization (EM) algorithm is employed to train the MM-RBF. Compared to the conventional approach, the proposed MM is shown to greatly improve the reconstruction performance for piecewise chaotic dynamic. We further apply it to combat channel distortions in an analog chaotic spread spectrum (SS) system. It is found that the proposed method has satisfactory equalization performance even when channel effect is strong.