tailieunhanh - báo cáo hóa học:" Research Article Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation"

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 Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2009 Article ID 178785 19 pages doi 2009 178785 Research Article Semidefinite Programming for Approximate Maximum Likelihood Sinusoidal Parameter Estimation Kenneth W. K. Lui EURASIP Member and H. C. So Department of Electronic Engineering City University of Hong Kong Tat Chee Avenue Kowloon Hong Kong Correspondence should be addressed to H. C. So hcso@ Received 19 February 2009 Revised 8 September 2009 Accepted 20 November 2009 Recommended by . Li We study the convex optimization approach for parameter estimation of several sinusoidal models namely single complex real tone multiple complex sinusoids and single two-dimensional complex tone in the presence of additive Gaussian noise. The major difficulty for optimally determining the parameters is that the corresponding maximum likelihood ML estimators involve finding the global minimum or maximum of multimodal cost functions because the frequencies are nonlinear in the observed signals. By relaxing the nonconvex ML formulations using semidefinite programs high-fidelity approximate solutions are obtained in a globally optimum fashion. Computer simulations are included to contrast the estimation performance of the proposed semi-definite relaxation methods with the iterative quadratic maximum likelihood technique as well as Cramer-Rao lower bound. Copyright 2009 K. W. K. Lui and H. C. So. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The problem of sinusoidal parameter estimation in additive noise has been an important research topic because of its numerous applications in science and engineering 1-5 . The typical parameters of interest are frequencies amplitudes and phases. As the frequencies are nonlinear functions in the .