The Application Of Mixture Distribution Test In Signal Sorting

The mixture model has been widely used in data analysis and data mining in practice,especially in cluster algorithm.If the data can be described by a certain distribution,the cluster method based mixture model is better than the other based on distance.However,most current mixture distribution model are the mixture of the same family of distributions in practical application.The study of the heterogeneous distribution mixture model is still very little.In this paper,based on the characteristic of signal and clutter we use heterogeneous distribution mixture model to sort the signal to improve the accuracy of the signal sorting algorithm.As the electromagnetic environment is being more and more complex,it is not ideal that the single distribution fits the receiving clutter.We propose the mixture of normal and Rayleigh distribution model to fit clutter.The mixture model can more accurately fit the clutter data than the single distribution.To estimate the parameters of the mixture normal and Rayleigh distribution model,we use the moment estimation and the maximum likelihood estimation method based on EM algorithm,respectively.We derive the iterative expressions for the moment equations and the EM algorithm.For the complex signal,we consider applying the mixture normal and uniform distribution model to classify the signal.The parameter estimation based on EM algorithm is heavily rely on the initial iteration values,because of the particular probability density function of the uniform distribution.Moreover,this algorithm needs to traverse the entire data set,which lead to a large amount of problem,we propose a new method to estimate the parameters of the uniform distribution based on empirical cumulative distribution function.The algorithm flow is also given.Then we estimate the mixture proportion and the parameters of normal distribution through maximum likelihood estimation based on EM algorithm.The method has the advantages of low computational cost and high efficiency.We generate three class of six group simulated data respectively according three factors including the mixture ratio,the degree of overlap and the sample size.The proposed methods are applied to estimate the parameters.The simulation results show that the maximum likelihood estimation method based on EM algorithm is superior to the method of moment estimation for the mixture of normal and Rayleigh distribution model.To the mixture of normal and uniform distribution model,the proposed method can estimate the parameters of the model accurately without overlap,but the parameters estimation are biased with overlap.At last,we apply these two methods to the actual received signal,the fitting and sorting results are very satisfactory.