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Open Access

Sinusoidal Order Estimation Using Angles between Subspaces

  • Mads Græsbøll Christensen1Email author,
  • Andreas Jakobsson2 and
  • Søren Holdt Jensen3
EURASIP Journal on Advances in Signal Processing20092009:948756

Received: 12 June 2009

Accepted: 16 September 2009

Published: 8 November 2009


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.


Information TechnologyComputer SimulationWhite NoiseQuantum InformationOrder Estimation

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Authors’ Affiliations

Department of Media Technology, Aalborg University, Aalborg, Denmark
Department of Mathematical Statistics, Lund University, Lund, Sweden
Department of Electronic Systems, Aalborg University, Aalborg, Denmark


© Mads Græsbøll Christensen et al. 2009

This article is published under license to BioMed Central Ltd. 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.