Identification of linear systems driven by chaotic signals using nonlinear prediction

The problem of blind identification of a linear system driven by a discrete-time chaotic signal is considered in this paper. Based on the short-term predictability of a chaotic signal, an efficient inverse filtering identification method called the minimum nonlinear prediction error (MNPE) technique is proposed. The nonlinear prediction error (NPE) criterion is used as the objective function for inverse filtering. It is shown that the proposed MNPE inverse filtering method can identify linear autoregressive (AR) and moving average (MA) systems driven by chaotic signals accurately. In addition, the MNPE method is very robust in the sense that extra system parameters are estimated as zeros. In other words, the MNPE method does not require a separate order determination procedure for this chaotic system identification problem. Monte Carlo simulations are carried out to validate the efficiency of the MNPE method. Results show that the MNPE method is more effective than the optimal statistic-based identification method based on a white Gaussian driven signal and a least-square estimator. The proposed method is applied to design a novel receiver for a chaos shift keying communications system, which can equalize the channel effects.