The asymptotic properties of polynomial phase estimation by least squares phase unwrapping

Robby G. McKilliam, I. Vaughan L Clarkson, Barry G. Quinn, Bill Moran

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionResearchpeer-review

    Abstract

    Estimating the coefficients of a noisy polynomial phase signal is important in many fields including radar, biology and radio communications. One approach to estimation attempts to perform polynomial regression on the phase of the signal. This is complicated by the fact that the phase is wrapped modulo 2π and therefore must be unwrapped before the regression can be performed. A recent approach suggested by the authors is to perform the unwrapping in a least squares manner. It was shown by Monte Carlo simulation that this produces a remarkably accurate estimator. In this paper we describe the asymptotic properties of this estimator, showing that it is strongly consistent and deriving its central limit theorem. We hypothesise that the estimator produces very near maximum likelihood performance.

    LanguageEnglish
    Title of host publication2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
    Place of PublicationPiscataway, N.J.
    PublisherInstitute of Electrical and Electronics Engineers (IEEE)
    Pages3592-3595
    Number of pages4
    ISBN (Electronic)9781457705397
    ISBN (Print)9781457705380
    DOIs
    Publication statusPublished - 2011
    Event36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Prague, Czech Republic
    Duration: 22 May 201127 May 2011

    Other

    Other36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
    CountryCzech Republic
    CityPrague
    Period22/05/1127/05/11

    Fingerprint

    Polynomials
    Radio communication
    Maximum likelihood
    Radar
    Monte Carlo simulation

    Cite this

    McKilliam, R. G., Clarkson, I. V. L., Quinn, B. G., & Moran, B. (2011). The asymptotic properties of polynomial phase estimation by least squares phase unwrapping. In 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings (pp. 3592-3595). [5946255] Piscataway, N.J.: Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/ICASSP.2011.5946255
    McKilliam, Robby G. ; Clarkson, I. Vaughan L ; Quinn, Barry G. ; Moran, Bill. / The asymptotic properties of polynomial phase estimation by least squares phase unwrapping. 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings. Piscataway, N.J. : Institute of Electrical and Electronics Engineers (IEEE), 2011. pp. 3592-3595
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    title = "The asymptotic properties of polynomial phase estimation by least squares phase unwrapping",
    abstract = "Estimating the coefficients of a noisy polynomial phase signal is important in many fields including radar, biology and radio communications. One approach to estimation attempts to perform polynomial regression on the phase of the signal. This is complicated by the fact that the phase is wrapped modulo 2π and therefore must be unwrapped before the regression can be performed. A recent approach suggested by the authors is to perform the unwrapping in a least squares manner. It was shown by Monte Carlo simulation that this produces a remarkably accurate estimator. In this paper we describe the asymptotic properties of this estimator, showing that it is strongly consistent and deriving its central limit theorem. We hypothesise that the estimator produces very near maximum likelihood performance.",
    author = "McKilliam, {Robby G.} and Clarkson, {I. Vaughan L} and Quinn, {Barry G.} and Bill Moran",
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    McKilliam, RG, Clarkson, IVL, Quinn, BG & Moran, B 2011, The asymptotic properties of polynomial phase estimation by least squares phase unwrapping. in 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings., 5946255, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, N.J., pp. 3592-3595, 36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011, Prague, Czech Republic, 22/05/11. https://doi.org/10.1109/ICASSP.2011.5946255

    The asymptotic properties of polynomial phase estimation by least squares phase unwrapping. / McKilliam, Robby G.; Clarkson, I. Vaughan L; Quinn, Barry G.; Moran, Bill.

    2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings. Piscataway, N.J. : Institute of Electrical and Electronics Engineers (IEEE), 2011. p. 3592-3595 5946255.

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionResearchpeer-review

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    McKilliam RG, Clarkson IVL, Quinn BG, Moran B. The asymptotic properties of polynomial phase estimation by least squares phase unwrapping. In 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings. Piscataway, N.J.: Institute of Electrical and Electronics Engineers (IEEE). 2011. p. 3592-3595. 5946255 https://doi.org/10.1109/ICASSP.2011.5946255