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Performance Evaluation of Gibbs Sampling for Bayesian Extracting Sinusoids

  • M. CevriEmail author
  • D. Üstündag
Chapter
  • 938 Downloads
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 307)

Abstract

This chapter involves problems of estimating parameters of sinusoids from white noisy data by using Gibbs sampling (GS) in a Bayesian inferential framework which allows us to incorporate prior knowledge about the nature of sinusoidal data into the model. Modifications of its algorithm is tested on data generated from synthetic signals and its performance is compared with conventional estimators such as Maximum Likelihood (ML) and Discrete Fourier Transform (DFT) under a variety of signal to noise ratio (SNR) conditions and different lengths of data sampling (N), regarding to Cramér–Rao lower bound (CRLB) that is a limit on the best possible performance achievable by an unbiased estimator given a dataset. All simulation results show its effectiveness in frequency and amplitude estimation of noisy sinusoids.

Keywords

Bayesian inference Parameter estimation Gibbs sampling Cramér–Rao lower bound and Power spectral density 

Notes

Acknowledgements

This work has been supported by the Research Fund of Istanbul University with project numbers are UDP-33672 and YADOP-19681.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of Science, Department of MathematicsIstanbul UniversityIstanbulTurkey
  2. 2.Faculty of Science and Letters, Department of MathematicsMarmara UniversityIstanbulTurkey

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