Detection Of Weak Signals In Chaos

Detections of weak signals in complicated background signal are mostly based on the statistic detection theory which regards the background signal as random signal and establishes a statistic model for it. The performance of detection is affected deeply by the model. And that it is difficult to establish a model for the complicated background signal. Recent researches have revealed some complicate signals are chaotic. So research on the detection of weak signals in complicated background signal based on its chaotic characteristics is significant both in theory and in application.The algorithms of phase space reconstruction based on the time series are studied firstly in this paper. After this, a method for detecting weak signals in chaos by neural networks is presented. It is based on the theory of phase space reconstruction of the complicated nonlinear system and the feature of chaos that can be forecasted in short term. One-step predictive model for chaotic background is built by neural network which possess powerful ability of studying and nonlinear processing. Then the weak transient signal or periodic signal which is embedded in the chaotic background can be detected from the predictive error. The signal-to-noise ration is improved with this approach. The difference of the detecting principle about the transient signal and periodic signal is pointed out. And the detecting ability of this method when the chaotic background includes white noise is studied. The experiment which takes the Lorenz system as chaotic background shows this method can detect out the very weak signal which is embedded in the chaotic background effectively.The theories of chaos are applied to the actual data of sea clutter. The correlation dimension and largest Lyapunov exponent of the sea clutter are calculated by different methods. Results show the sea clutter has chaotic character. After this, a method for detecting weak signals in sea clutter by neural networks is presented. And the detecting model of radar is introduced.