Polynomial Phase Estimation by Least Squares Phase Unwrapping

Estimating the coefficients of a noisy polynomial phase signal is important in fields including radar, biology and radio communications. One approach 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 must be...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 62; no. 8; pp. 1962 - 1975
Main Authors: McKilliam, Robby G., Quinn, Barry G., Clarkson, I. Vaughan L., Moran, Bill, Vellambi, Badri N.
Format: Journal Article
Language:English
Published: New York, NY IEEE 15.04.2014
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Asymptotic properties
Computer simulation
Detection, estimation, filtering, equalization, prediction
Econometrics
Economic models
Estimating
Estimators
Exact sciences and technology
Image processing
Information, signal and communications theory
Lattices
Least squares approximations
Least squares method
nearest lattice point problem
Phase estimation
phase unwrapping
polynomial phase signals
Polynomials
Radio communications
Regression
Signal and communications theory
Signal processing
Signal processing algorithms
Signal to noise ratio
Signal, noise
Telecommunications and information theory
Performance evaluation
Monte Carlo method
Parameter estimation
State of the art
Phase measurement
Polynomial phase signal
Phase unwrapping
Image processing
Asymptotic properties
Theoretical study
Image restoration
Algorithm
nearest lattice point problem
polynomial phase signals
Phase estimation
Least squares method
Radar
Signal processing
Numerical simulation
Radio communication
Polynomial regression
Number theory
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:Estimating the coefficients of a noisy polynomial phase signal is important in fields including radar, biology and radio communications. One approach 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 must be unwrapped before regression can be performed. In this paper, we consider an estimator that performs phase unwrapping in a least squares manner. We call this the least squares unwrapping (LSU) estimator. The LSU estimator can be computed in a reasonable amount of time for data sets of moderate size using existing general purpose algorithms from algebraic number theory. Under mild conditions on the distribution of the noise we describe the asymptotic properties of this estimator, showing that it is strongly consistent and asymptotically normally distributed. A key feature is that the LSU estimator is accurate over a far wider range of parameters than many popular existing estimators. Monte-Carlo simulations support our theoretical results and demonstrate the excellent statistical performance of the LSU estimator when compared with existing state-of-the-art estimators.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2014.2306178