Studying On Detection Of Small Signal In Chaotic Background

The chaotic signal is pseudo-random and generated by a deterministic dynamical system. By more and more profound studies of signal detection and chaotic dynamics, it is found that a lot of target signals are embedded in the strong chaotic background. So some researchers that work on the signal detection and estimation field are paying attentions to detection of the target signals or extraction of the target signals'feature parameters in the chaotic background at present.Based on the chaotic signals'geometric features, some studies on extracting the target signals and estimating the signals'parameters in the chaotic background are worked out. The main works are as followings:①After studying the features of the local-tangent space projection method, we do many numerical experiments on the harmonic signal's extraction from chaotic signal with the method, then analyze the experiments'results to research how the quality of the harmonic signal's extraction depends on the phase-space reconstruction parameters.②The local-tangent space projection method is used to detect the transient signals in the chaotic background, and many numerical experiments fully verify the validity of the method.③A novel method, named the Minimization of Relative Singular Value(MRSV) ,to extract useful signal in chaotic background is proposed, and the method is based on the mixed-signal's features of local singular value decomposition(SVD) on chaotic manifold. Simulations show that the method can effectively estimate the AR model's parameters and sine wave frequencies in chaotic background. The AR model's parameters can be estimated effectively with the short length of the data. The frequency of the sine signal not being distinguished by FFT can be estimated.The research results of this thesis have certain theoretical and practical value in detection weak signal from chaotic background.