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

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

doi:10.1109/ICASSP.2011.5946255

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

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

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

4 Citations (Scopus)

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.

Original language	English
Title of host publication	2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
Place of Publication	Piscataway, N.J.
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	3592-3595
Number of pages	4
ISBN (Electronic)	9781457705397
ISBN (Print)	9781457705380
DOIs	https://doi.org/10.1109/ICASSP.2011.5946255
Publication status	Published - 2011
Event	36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Prague, Czech Republic Duration: 22 May 2011 → 27 May 2011

Other

Other	36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
Country/Territory	Czech Republic
City	Prague
Period	22/05/11 → 27/05/11

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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] Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/ICASSP.2011.5946255

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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",

year = "2011",

doi = "10.1109/ICASSP.2011.5946255",

language = "English",

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booktitle = "2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

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note = "36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 ; Conference date: 22-05-2011 Through 27-05-2011",

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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. et al.

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 proceeding › Conference proceeding contribution › peer-review

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N2 - 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.

AB - 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.

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BT - 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings

PB - Institute of Electrical and Electronics Engineers (IEEE)

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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

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

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