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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 Sinusoidal Order Estimation Using Angles between Subspaces | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2009 Article ID 948756 11 pages doi 10.1155 2009 948756 Research Article Sinusoidal Order Estimation Using Angles between Subspaces Mads Gnesboll Christensen 1 Andreas Jakobsson EURASIP Member 2 and Soren Holdt Jensen EURASIP Member 3 1 Department of Media Technology Aalborg University Niels Jernes Vej 14 9220 Aalborg Denmark 2 Department of Mathematical Statistics Lund University 221 00 Lund Sweden 3 Department of Electronic Systems Aalborg University Niels Jernes Vej 12 9220 Aalborg Denmark Correspondence should be addressed to Mads Grasboll Christensen mgc@imi.aau.dk Received 12 June 2009 Revised 2 September 2009 Accepted 16 September 2009 Recommended by Walter Kellermann We consider the problem of determining the order of a parametric model from a noisy signal based on the geometry of the space. More specifically we do this using the nontrivial angles between the candidate signal subspace model and the noise subspace. The proposed principle is closely related to the subspace orthogonality property known from the MUSIC algorithm and we study its properties and compare it to other related measures. For the problem of estimating the number of complex sinusoids in white noise a computationally efficient implementation exists and this problem is therefore considered in detail. In computer simulations we compare the proposed method to various well-known methods for order estimation. These show that the proposed method outperforms the other previously published subspace methods and that it is more robust to the noise being colored than the previously published methods. Copyright 2009 Mads Grasboll Christensen et al. 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 Estimating the order of a model is a central
