The detection and characterization of a class of discrete time chaotic signals

The paper describes a simple method for detecting a class of first order or low dimensional discrete-time signals whose dynamical properties have the form of the logistic map. The authors have developed a maximum likelihood estimation (MLE) technique for the tuning parameter a and the initial condition of a logistic map embedded in zero-mean white Gaussian noise. They use the estimated values to determine the chaotic behavior of class of first order discrete time signals. They have also derived the recursive Cramer Rao lower bound (CRLB) for the tuning parameter a and the initial condition to characterize the performance of the developed estimators