Gaussian profile estimation in one dimension

Nathan Hagen, Matthew Kupinski, Eustace L. Dereniak

Research output: Contribution to journalArticle

36 Scopus citations

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

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Engineering (miscellaneous)
  • Electrical and Electronic Engineering

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