Using Curve Fitting to Remove Outliers From Altimeter Timeseries Data

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Using Curve Fitting to Remove Outliers From
Altimeter Timeseries Data Ellie Bramer
When the filtering process is applied to a data
set, any point more than a specified distance
from the curve is removed. This plot shows a data
set before and after filtering All the obvious
outliers have been removed. The original data set
is in blue, and the data set after filtering is
red
These are two examples of fits that didnt work.
On the left is the Gaussian fit and on the right
is the 9th degree Polynomial fit. The three best
fits were the Fourier fit y a0 a1cos(xw)
b1sin(xw) a8cos(8xw) b8sin(8xw),
the Smoothing Spline, and the Sum of Sins fit y
a1sin(b1x c1) a8sin(b8x c8)
The graph below is showing the altimeter
timeseries data in red, the fitted curve in
green, and the nearest corresponding gauge data
in blue. The timeseries data is closely following
the pattern of the gauge data, as is the fitted
curve for a short way each side of the timeseries
data.
The Sum of Sins fit was chosen for the following
reason. When the Smoothing Spline fit runs out of
data the fit goes to infinity, whereas the Sum of
Sins fit attempts to carry on the pattern of the
data.
The timeseries data is offset from the gauge
data, but the reference heights used for gauges
are often faulty
The RMSE was used to judge the goodness of
fit. The line graph above is showing the
differences between the RMSE values for the
Fourier, Smoothing Spline and Sum of Sin fits.
The Fourier fit has a consistently higher RMSE
than the other two, so the Fourier fit was
discarded