Exact analysis of the least-mean-square algorithm with coloured measurement noise

作     者：Lara, Pedro Olinto, Karen da S. Petraglia, Felipe R. Haddad, Diego B. 

作者机构：CEFET RJ Rio De Janeiro RJ Brazil Univ Fed Rio de Janeiro Rio de Janeiro RJ Brazil 

出 版 物：《ELECTRONICS LETTERS》 (电子学快报)

年 卷 期：2018年第54卷第24期

页      面：1401-1402页

核心收录：

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 

基　　金：CNPq FAPERJ CAPES 

主　　题：least mean squares methods adaptive filters filtering theory stochastic processes statistical independence current adaptive coefficients input vectors simplification empirical results step-size parameter exact expectation analysis stochastic model above-mentioned independence assumption least-mean-squares authors analysis coloured additive noise exact analysis least-mean-square algorithm coloured measurement noise general analyses theoretical analyses adaptive filtering algorithms statistical approximations derivations tractable 

摘      要：In general, theoretical analyses of adaptive filtering algorithms employ statistical approximations in order to render the derivations tractable. Among such hypotheses, the statistical independence between the current adaptive coefficients and past input vectors is a very popular one. Unfortunately, this simplification gives rise to discrepancies with respect to empirical results, especially for large values of the step-size parameter. In this Letter, this issue is overcome by the usage of an exact expectation analysis (i.e. a stochastic model that does not employ the above-mentioned independence assumption) of the least-mean-squares adaptive algorithm. The authors analysis is also generalised in order to address the common case of coloured additive noise, an issue that is so far missing from the literature. The accuracy of the advanced model is verified through simulations.