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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Vydáno v:	IEEE transactions on signal processing Ročník 62; číslo 8; s. 1962 - 1975
Hlavní autoři:	McKilliam, Robby G., Quinn, Barry G., Clarkson, I. Vaughan L., Moran, Bill, Vellambi, Badri N.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 15.04.2014 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	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
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Popis
Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2014.2306178