Direct discrete variational curve reconstruction from derivatives and its application to track subsidence measurements

This paper presents a new direct discrete variational solution to curve reconstruction from derivatives. The formulation of basis functions and the variational problem in terms of matrix algebra has simplified many proofs; including the χ 2 confidence interval surrounding the reconstructed curve. Si...

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Bibliographic Details
Published in2011 IEEE International Instrumentation and Measurement Technology Conference pp. 1 - 6
Main Authors OaLeary, P., Harker, M., Golser, J.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2011
Subjects
admissible functions
covariance propagation
Gram polynomials
inclinometers
Least squares approximation
Mathematical model
Monitoring
Monte Carlo methods
Polynomials
rail-track subsidence
spectral regularization
Variational problems
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Summary:This paper presents a new direct discrete variational solution to curve reconstruction from derivatives. The formulation of basis functions and the variational problem in terms of matrix algebra has simplified many proofs; including the χ 2 confidence interval surrounding the reconstructed curve. Simultaneous spatial reconstruction and temporal filtering is implemented. The Method is verified via Monte-Carlo simulations and also applied to the real-time monitoring of rail-track subsidence. In this application a string of inclinometers are mounted along the stretch of track where it will be monitored. The curve representing the form of the track is reconstructed from the measured derivatives.
ISBN:1424479339
9781424479337
ISSN:1091-5281
DOI:10.1109/IMTC.2011.5944013