System Identification And Application Based On Fractional Lower Order Cyclic Correlation

System identification aims at retrieving the unknown response of system using the input and the output signal and their statistics. The second-order statistics (SOS) method based on cyclostationary shows the superiority to the method based on higher statistics (HOS) in computations and convergence speeds. The system identification methods based on cyclostationary, which have been attracted much attention in recent years.Gaussian model is in dominant position of traditional signal processing field. This assumption is reasonable under many circumstances. It's easy to carry out theoretical analysis in designing signal processing methods using the Gaussian model. However, in fact there are a lot of non-Gaussian signals and noises with notable pulse characteristic, like underwater acoustic signals, low-frequency atmospheric noises and many other noises produced by human. If we still use Gaussian model to descript these processes, it will result in noticeable degradation of the algorithms, because the model doesn't match well with real signals or noises. Alpha-stable distribution is a very useful theoretical tool for this kind of process. So people usually use it to depict stochastic signals with a remarkable impulsive characteristic. Because alpha-stable distribution is generalized Gaussian distribution, which is to say Gaussian distribution is a special case of alpha-stable distribution. So alpha-stable model can be used in more widely range. But under noise model of the fractional lower order alpha-stable distribution, the system identification methods used the Gaussian model and based on second order statistics could not work properly for the second-order statistics become unbounded.In this thesis, we review the development of system identification. Considering the fractional lower order alpha-stable distribution model, we introduce the system identification method based on covariation and alpha spectrum. Considering the Gaussian model, we introduce the second order statistics method based on cyclostationary. Then combine the fractional low order correlation with second order cyclostationary correlation, we present the conception of fractional low order cyclostationary correlation (FLOCC). At the same time, we prove the property that the cyclic frequency of fractional low order cyclostationary correlation equals to the cyclic frequency of second order cyclostationary correlation. At last, drawing on existing second order algorithms based on cyclostationary, using fractional lower order correlation theory, the method of fractional lower order cyclic correlation is developed under the alpha-stable distribution noises. It shows that the new algorithm is robust for both Gaussian and non-Gaussian impulsive noise environment through theoretical analysis and computer simulations.