Constrained Smoothing of Noisy Data Using Splines in?Tension |
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Authors: | Nicholas A Teanby |
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Institution: | (1) Atmospheric, Oceanic & Planetary Physics, Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK |
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Abstract: | A method of fitting a smooth cubic spline curve through noisy data points is presented. Overshoots of the spline curve between
data points were prevented by applying tension to the fit using a quadratic spring approximation, which allowed a linear inverse
theory approach to be adopted. Error-bars in the measured data were mapped through the inversion process to give the covariance
of the fitted curve. This is an improvement over previous methods, which largely neglect the effect of data errors on the
fit. Another improvement is to impose fixed constraints on the fit by simultaneously applying the method of Lagrange multipliers.
The effect of these constraints on the covariance of the fitted curve is quantified using results from linear algebra. Example
applications to synthetic data and a record of magnetic inclination from Hawaii are given. |
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Keywords: | Curve fitting Data analysis Lagrange multipliers |
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