SαS PROCESS LOCATION PARAMETER ADAPTIVE ESTIMATOR BASED ON DATA CENSORING

摘要

The models with symmetric α-stable (SαS) distributions are widely used for describing non-gaussian noise arising in radars, sonars, multimedia applications, communications [1]. Such a situation takes place due to the generalized central limit theorem (GCLT). According to it, the limit distribution of the sum of independent and identically distributed random variables regardless of thear variances is the α-stable. It is worth noting that in case of finite variance values GCLT converges to the central limit theorem and the limit distribution becomes Gaussian. Processes with SαS distributions are uniquely characterized by two parameters α and γ [2]. A parameter α usually called exponent characteristic or index defines the tail heaviness of a probability density function (pdf) (the smaller the α values the heavier tails are). A parameter γ, referred to as dispersion describes data scale. One of the main features of SαS processes is the absence of the second order central moments [1] and this leads to impossibility to apply linear filters. Effective data processing in such a situation can be achieved using robust procedures and methods among which one can mention the sample median, the alpha-trimmed mean, the Wilcoxon and Hodges-Lehman estimators. It is known that each aforementioned robust non-adaptive estimator effectively determines a SαS distribution location parameter only in some range of α values [3]. However, in many practical tasks the only available a priori information about noise statistical characteristics is that noise pdf is symmetric with respect to location parameter (usually zero) and it can possess heavy tails. In such a situation the location parameter estimation quality provided by aforementioned robust procedures can be inappropriate. In this case the task of design and applying the estimates adaptive to a distribution tail heaviness (e.g. parameter α) and data scale (γ) is of great interest. To solve it, a new adaptation method for the estimator based on the sample data censoring [4] is proposed in the second part of this article. The comparative analysis of location parameter determination accuracy by means of the proposed and known robust and adaptive estimators is provided in the third part.