Research On Parameter Estimation Of Weak Signal In Chaotic Background

The chaotic signal is pseudo-random, and is generated by a deterministic dynamical system. Chaotic signal processing is an important branch of non-linear signal processing. It has broad applications in practical project fields such as meteorology, automatic control, seismology, biomedicine engineering, marine exploration, pattern recognition, secure communication, aerospace engineering and so on. By more and more profound studies, it is often found that a lot of weak signals are embedded in the strong chaotic background. So some researchers that work on the signal detection and estimation field are paying more attentions to the detection of the weak signals or estimation of the weak signals'feature parameters in the chaotic background at present.We take the topic of weak signal parameter estimation as the main object of study here. In this thesis, many new parameter estimation methods, which are used to estimate the weak signals'feature parameters from chaos backgrounds under different conditions such as signal to noise ratio, frequence ranges, have been put forward application of natures of chaos(time-frequence nature, statistical nature). Simulations by computer have proved effectiveness and usefulness of these methods.The main works are as follows:Firstly, the discriminate method between chaos signal and noise signal based on principal component analysis is researched. Some method of chaotic signal processing, empirical mode decomposition and chaotic synchronization are analyzed.Secondly, the limitations of empirical mode decomposition method which apply to estimate the weak signals'feature parameters in chaotic background are analyzed. A parameter estimation method for weak signal in chaotic background is presented. This method is based on combination of frequency multiplication method and empirical mode decomposition. First of all, the correlation method is applied to remove noise preliminarily, then the frequency multiplication method and the empirical mode decomposition method are used to decompose the mixed signal into many intrinsic mode functions (IMFs), among which one IMF is the recovered weak signal. By analyzing the cross power spectrum of the intrinsic mode function, we can easily estimate the weak signal parameters. The paper takes the signals are generated by Lorenz chaotic system and the Duffing chaotic system as background for example respectively and process with simulation experiments. Simulation results show that the method is simple and effective, and less complicated in calculation. Lastly, the theory of chaos synchronization and unidirectional coupling chaotic synchronization method are also introduced. The method is applied to estimate the weak signals'feature parameters in chaotic background, and a novel approach based on unidirectional coupling synchronization is proposed. The problem of parameter estimation in chaotic background is transformed into the parameter estimation in residual error using the method. This method can estimate weak signal parameter from background signal which includes strong noise. The paper takes the signals are generated by Lorenz chaotic system and the Chen chaotic system as background for example respectively and process with stimulation experiments. Simulation results show that the method is simple and effective besides less complicated.The research results of this thesis have certain theoretical and practical value in weak signal parameter estimation from chaotic background.