The Study On The Dynamic Parameter Estimation Of Stable Distribution

Non-Gaussian signal processing has called more and more attentions with the development of signal processing techniques. Alpha stable distribution is a typical non-Gaussian signal model. After it was first used in signal processing, large numbers of researchers domestic and overseas have thought much of it. But being a statistical model, Alpha stable distribution has its characteristic. How to do the theory study of the distribution under these restrict and expand it to the practice applications, has very important meanings. The task do the research of properties of stable distribution and its applications, the main job of the thesis is below.First it gives the research meaning of alpha stable distribution, as well as its relational definitions, properties, theorems. And detailed analyzes the interrelated statistics of stable distributions.Due to the characteristics of alpha stable distributions themselves, parameters estimation is a difficult problem. The thesis summarizes the frequently used parameters estimation methods after alpha stable distribution was put forward. Especially the latest fast estimation method, then expands it on this base, ratiocinates the recursive algorithm based on extreme order statistics, realizing the dynamic estimation of parameters.Considering the characters of the waveform of impulsive noise, on the base of robust statistics, the thesis uses the robust statistical function mending the customary adaptive algorithm based on second order statistic, applies it to the system identification problem. This algorithm can suppress the negative effect that the impulsive noise brings to the weight coefficients effectively.Finally, the thesis gives a brief summary of the job as well as the future expectations.