### 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.

Language | English |
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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 | |

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 |
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Country | Czech Republic |

City | Prague |

Period | 22/05/11 → 27/05/11 |

### Fingerprint

### Cite this

*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

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*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.

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

TY - GEN

T1 - The asymptotic properties of polynomial phase estimation by least squares phase unwrapping

AU - McKilliam, Robby G.

AU - Clarkson, I. Vaughan L

AU - Quinn, Barry G.

AU - Moran, Bill

PY - 2011

Y1 - 2011

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.

UR - http://www.scopus.com/inward/record.url?scp=80051626337&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2011.5946255

DO - 10.1109/ICASSP.2011.5946255

M3 - Conference proceeding contribution

SN - 9781457705380

SP - 3592

EP - 3595

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

PB - Institute of Electrical and Electronics Engineers (IEEE)

CY - Piscataway, N.J.

ER -