Improved Frequency Estimation Algorithm by Least Squares Phase Unwrapping

Short Paper
  • 9 Downloads

Abstract

Among the frequency estimation methods, the least squares phase unwrapping estimator (LSPUE) that unwraps the phase in the least squares sense has a much better performance than other phase unwrapping estimators. In this paper, based on a more accurate phase model, an improved LSPUE is presented. Compared with other LSPUE, the performance is improved in two aspects. Firstly, when the number of samples is small, our estimator has a lower signal-to-noise ratio (SNR) threshold. Secondly, from the medium SNR, the LSPUE has an asymptotic mean square error (MSE) which is larger than the Cramer–Rao bound (CRB) but the MSE of our estimator converges to the CRB.

Keywords

Frequency estimation Least squares Phase unwrapping 

References

  1. 1.
    H. Fu, P.Y. Kam, Phase-based, time-domain estimation of the frequency and phase of a single sinusoid in AWGN the role and applications of the additive observation phase noise model. IEEE Trans. Inf. Theory 59(5), 3175–3188 (2013).  https://doi.org/10.1109/TIT.2013.2238604 MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    H. Fu, P.Y. Kam, MAP/ML estimation of the frequency and phase of a single sinusoid in noise. IEEE Trans. Signal Proces. 55(3), 834–845 (2007).  https://doi.org/10.1109/TSP.2006.888055 MathSciNetCrossRefGoogle Scholar
  3. 3.
    C.A. Haniff, Least-squares Fourier phase estimation from the modulo 2 bispectrum phase. J. Opt. Soc. Am. A 8(1), 134–140 (1991).  https://doi.org/10.1364/JOSAA.8.000134 CrossRefGoogle Scholar
  4. 4.
    S.M. Kay, A fast and accurate single frequency estimator. IEEE Trans. Acoust. Speech Signal Process. 37(12), 1987–1990 (1990).  https://doi.org/10.1109/29.45547 CrossRefGoogle Scholar
  5. 5.
    S.M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (PTR Prentice Hall, Upper Saddle River, 1993), p. 57MATHGoogle Scholar
  6. 6.
    R.G. Mckilliam, B.G. Quinn, I.V.L. Clarkson et al., Frequency estimation by phase unwrapping. IEEE Trans. Signal Proces. 58(6), 2953–2963 (2010).  https://doi.org/10.1109/TSP.2010.2045786 MathSciNetCrossRefGoogle Scholar
  7. 7.
    C. Qian, L. Huang, H.C. So et al., Unitary PUMA algorithm for estimating the frequency of a complex sinusoid. IEEE Trans. Signal Proces. 63(20), 5358–5368 (2015).  https://doi.org/10.1109/TSP.2015.2454471 MathSciNetCrossRefGoogle Scholar
  8. 8.
    D.C. Rife, R.R. Boorstyn, Single-tone parameter estimation from discrete-time observations. IEEE Trans. Inf. Theory 20(5), 591–598 (1974).  https://doi.org/10.1109/TIT.1974.1055282 CrossRefMATHGoogle Scholar
  9. 9.
    H.C. So, F.K.W. Chan, W.H. Lau, C.F. Chan, An efficient approach for two-dimensional parameter estimation of a single-tone. IEEE Trans. Signal Proces. 58(4), 1999–2009 (2010).  https://doi.org/10.1109/TSP.2009.2038962 MathSciNetCrossRefGoogle Scholar
  10. 10.
    S. Tretter, Estimating the frequency of a noisy sinusoid by linear regression (Corresp.). IEEE Trans. Inf. Theory 31(6), 832–835 (1985).  https://doi.org/10.1109/TIT.1985.1057115 CrossRefGoogle Scholar
  11. 11.
    Z. Xu, B. Huang, S. Xu, Robust phase unwrapping algorithm. Electron. Lett. 49(24), 1565–1567 (2013).  https://doi.org/10.1049/el.2013.2909 CrossRefGoogle Scholar
  12. 12.
    Z. Xu, T. Lu, B. Huang, Fast frequency estimation algorithm by least squares phase unwrapping. IEEE Signal Process. Lett. 23(6), 776–779 (2016).  https://doi.org/10.1109/LSP.2016.2555933 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Chinese Academy of SciencesBeijingChina
  2. 2.Technology and Engineering Center for Space UtilizationChinese Academy of SciencesBeijingChina

Personalised recommendations