Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Sequential and Adaptive Learning Algorithms for M-Estimation | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2008 Article ID 459586 13 pages doi 2008 459586 Research Article Sequential and Adaptive Learning Algorithms for M-Estimation Guang Deng Department of Electronic Engineering Faculty of Science Technology and Engineering La Trobe University Bundoora VIC 3086 Australia Correspondence should be addressed to Guang Deng Received 1 October 2007 Revised 9 January 2008 Accepted 1 April 2008 Recommended by Sergios Theodoridis The M-estimate of a linear observation model has many important engineering applications such as identifying a linear system under non-Gaussian noise. Batch algorithms based on the EM algorithm or the iterative reweighted least squares algorithm have been widely adopted. In recent years several sequential algorithms have been proposed. In this paper we propose a family of sequential algorithms based on the Bayesian formulation of the problem. The basic idea is that in each step we use a Gaussian approximation for the posterior and a quadratic approximation for the log-likelihood function. The maximum a posteriori MAP estimation leads naturally to algorithms similar to the recursive least squares RLSs algorithm. We discuss the quality of the estimate issues related to the initialization and estimation of parameters and robustness of the proposed algorithm. We then develop LMS-type algorithms by replacing the covariance matrix with a scaled identity matrix under the constraint that the determinant of the covariance matrix is preserved. We have proposed two LMS-type algorithms which are effective and low-cost replacement of RLS-type of algorithms working under Gaussian and impulsive noise respectively. Numerical examples show that the performance of the proposed algorithms are very competitive to that of other recently published algorithms. Copyright 2008 Guang Deng. This is an open access article distributed under the Creative Commons .
