The accuracy of parameter estimation from noisy data, with application to resonance peak estimation in distributed Brillouin sensing


Distributed Brillouin sensing of strain and temperature works by making spatially resolved measurements of the position of the measurand-dependent extremum of the resonance curve associated with the scattering process in the weakly nonlinear regime. Typically, measurements of backscattered Stokes intensity (the dependent variable) are made at a number of predetermined fixed frequencies covering the design measurand range of the apparatus and combined to yield an estimate of the position of the extremum. The measurand can then be found because its relationship to the position of the extremum is assumed known. We present analytical expressions relating the relative error in the extremum position to experimental errors in the dependent variable. This is done for two cases: (i) a simple non-parametric estimate of the mean based on moments and (ii) the case in which a least squares technique is used to fit a Lorentzian to the data. The question of statistical bias in the estimates is discussed and in the second case we go further and present for the first time a general method by which the probability density function (PDF) of errors in the fitted parameters can be obtained in closed form in terms of the PDFs of the errors in the noisy data.

Uncontrolled Keywords: temperature sensor, optical fibers, scattering, spectroscopy, silica
Publication ISSN: 0957-0233
Last Modified: 23 Oct 2019 11:27
Date Deposited: 28 Apr 2011 08:58
Published Date: 1998
Authors: Pannell, C.N.
Dhliwayo, J.
Webb, David J.


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