Gaussian profile estimation in one dimension

Nathan Hagen, Matthew A Kupinski, Eustace L. Dereniak

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

We present several new results on the classic problem of estimating Gaussian profile parameters from a set of noisy data, showing that an exact solution of the maximum likelihood equations exists for additive Gaussian-distributed noise. Using the exact solution makes it possible to obtain analytic formulas for the variances of the estimated parameters. Finally, we show that the classic formulation of the problem is actually biased, but that the bias can be eliminated by a straightforward algorithm.

Original languageEnglish (US)
Pages (from-to)5374-5383
Number of pages10
JournalApplied Optics
Volume46
Issue number22
DOIs
StatePublished - Aug 1 2007

Fingerprint

Maximum likelihood
profiles
estimating
formulations

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Gaussian profile estimation in one dimension. / Hagen, Nathan; Kupinski, Matthew A; Dereniak, Eustace L.

In: Applied Optics, Vol. 46, No. 22, 01.08.2007, p. 5374-5383.

Research output: Contribution to journalArticle

Hagen, Nathan ; Kupinski, Matthew A ; Dereniak, Eustace L. / Gaussian profile estimation in one dimension. In: Applied Optics. 2007 ; Vol. 46, No. 22. pp. 5374-5383.
@article{aa69f0d8d15545879b584e57fec46568,
title = "Gaussian profile estimation in one dimension",
abstract = "We present several new results on the classic problem of estimating Gaussian profile parameters from a set of noisy data, showing that an exact solution of the maximum likelihood equations exists for additive Gaussian-distributed noise. Using the exact solution makes it possible to obtain analytic formulas for the variances of the estimated parameters. Finally, we show that the classic formulation of the problem is actually biased, but that the bias can be eliminated by a straightforward algorithm.",
author = "Nathan Hagen and Kupinski, {Matthew A} and Dereniak, {Eustace L.}",
year = "2007",
month = "8",
day = "1",
doi = "10.1364/AO.46.005374",
language = "English (US)",
volume = "46",
pages = "5374--5383",
journal = "Applied Optics",
issn = "1559-128X",
publisher = "The Optical Society",
number = "22",

}

TY - JOUR

T1 - Gaussian profile estimation in one dimension

AU - Hagen, Nathan

AU - Kupinski, Matthew A

AU - Dereniak, Eustace L.

PY - 2007/8/1

Y1 - 2007/8/1

N2 - We present several new results on the classic problem of estimating Gaussian profile parameters from a set of noisy data, showing that an exact solution of the maximum likelihood equations exists for additive Gaussian-distributed noise. Using the exact solution makes it possible to obtain analytic formulas for the variances of the estimated parameters. Finally, we show that the classic formulation of the problem is actually biased, but that the bias can be eliminated by a straightforward algorithm.

AB - We present several new results on the classic problem of estimating Gaussian profile parameters from a set of noisy data, showing that an exact solution of the maximum likelihood equations exists for additive Gaussian-distributed noise. Using the exact solution makes it possible to obtain analytic formulas for the variances of the estimated parameters. Finally, we show that the classic formulation of the problem is actually biased, but that the bias can be eliminated by a straightforward algorithm.

UR - http://www.scopus.com/inward/record.url?scp=35448987653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35448987653&partnerID=8YFLogxK

U2 - 10.1364/AO.46.005374

DO - 10.1364/AO.46.005374

M3 - Article

C2 - 17676153

AN - SCOPUS:35448987653

VL - 46

SP - 5374

EP - 5383

JO - Applied Optics

JF - Applied Optics

SN - 1559-128X

IS - 22

ER -