Statistical approach to weak signal detection and estimation using Duffing chaotic oscillators

In this paper, we describe the statistical characteristics of weak signal detection by a chaotic Duffing oscillator, and present a new method for signal detection and estimation using the largest Lyapunov exponent. Previous research has shown that weak signals can be detected by a chaotic system. Many researchers use the Lyapunov exponent to flag the detection of a chaotic state, but our research shows that the Lyapunov exponent follows statistical characteristics, and therefore more factors should be considered in flagging chaotic weak signals. Here, we analyze the statistical characteristics inherent in the Lyapunov exponent calculation steps, and build up a statistical model for different chaotic states based on simulation data. Furthermore, we provide expressions for false-alarm and detection probabilities, selection of driving force threshold and detection of signal-noise-ratio. Finally, we summarize the method of signal amplitude estimation. Our research indicates that the performance of the detection system is related to sampling times and intervals, in accord with the theory of statistical signal detection.