Research On Alpha Stable Distribution Model And Its Applications

The statistics of the real signals does not always subject to the normal distribution. The alpha stable (αS) distribution has attracted considerable attention since it describes the non-Gaussian and heavy-tail characteristics of some random signals. Unfortunately, the closed-form expression for the pdf (probability density function) of the generalαS signal does not exist, and the characteristic function for the probability distribution of theαS signal is discontinuous at some points. These will bring inconvenience to the signal analysis and the actual application. This dissertation undertakes some work on the generator of random variables subject to theαSdistribution, the estimation methods of model parameters and the applications of signal models based onαS distribution.Firstly, the definitions and basic theories of theαS distribution are discussed. Then four parameters that control the distribution are introduced. The properties and backgrounds of theαS distribution are studied, the Fractional Lower Order Statistics are given, and the comparison between .theαS Statistics and the normal Statistics is presented.Simulating random variable (r.v.) subject to theαS distribution with arbitrary parameters in the standard parameterization is the foundation to perform some research on signal processing. Currently, in most of research, the noise or interference is assumed to subject to the Symmetric Alpha Stable ( SαS) distribution. However, in some areas (for example, the amplitude distribution of radar clutter), the statistics conforms to the skew distribution. There are different parameterizations for the Alpha stable distribution, which are easy to cause confusion. For this reason, the r.v. subject to theαS distribution is more difficult to generate than that with SαS. Based on the concepts and properties of the Alpha stable distribution, four parameterizations are discussed. Furthermore, we propose and proof the proposition to accurately generate the r.v. subject to theαS distribution. The Probability Density Functions (PDF) of the different parameterizations are compared by Monte-Carlo simulation. The simulations for the Pearson sea-clutter show that our method is valid and the method of Chambers has a certain error for location.We next discuss the joint parameter estimation of the random sequences that subject to theαSdistribution. Currently, the research on joint parameter estimation approach, which has high accuracy, low computation amount and may be widely used, is still a challenging work. We firstly estimated the parametersαandσby means of the character function (CF) method for the samples. Based on the bias-removed transform for the Alpha stable distribution, we nextly propose a fast method to estimate the location parameterμ. And then, using the estimation ofμand the Fractional Lower Order Moment (FLOM) method, new estimator for skew parameterβis proposed. Furthermore, with the estimations forβandμin the case ofα=1, a joint estimation method for four parameters is presented. The simulation results show that the proposed new method has higher precision and better robustness on wide region ofαin comparison with traditional CF method.To meet the goal of multi-clutter recognition in the Constant False Alarm Rate (CFAR) processing, the Alpha stable distribution is introduced to distinguish five traditional kinds of clutters, including Rayleigh, Weibull, Log-normal, K and Rice clutter. We show that these five clutter distributions can be described by uniform model, the alpha stable distribution. Furthermore, we propose a new method for recognizing different radar clutters, which relies on the estimated model parameters for Alpha stable distribution. Simulation results show that the proposed new method has higher precision and less calculation burden in comparison with traditional KS testing.Finally, we discuss a kind of multi-scale self-similar signal model. The self-similarity of the natural surface is not always so perfect. It may reveal multi-scale self-similarity rather than keeping invariable in whole scale space. We have analyzed the increment of several standard textures and the results show that their distributions are non-Gaussian. Consequently, the traditional FBM model is not suitable for modeling texture. Based on the above analysis, we proposed a multi-scale self-similar random field, Multi-scale Fractional Lévy Stable Motion (MFLSM), and used it to construct isotropic texture. As most of the real textures are anisotropic, a structure filter, which transforms an isotropic field to an anisotropic one, is introduced. The anisotropic multi-scale self-similar textures are generated by means of MFLSM and the anisotropic structure filter.