On the aliasing problem in the spherical harmonic analysis |
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| Authors: | F Sansò |
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| Institution: | (1) Istituto di Topografia, Politecnico di Milano, Piazza Leonardo da Vinci 32, I 20133 Milano, (Italy) |
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| Abstract: | To apply the least squares method for the interpolation of harmonic functions is a common practice in Geodesy. Since the method
of least squares can be applied only to overdetermined problem, the interpolation problem which is always under-determined,
is often reduced to an overdetermined form by truncating a series of spherical harmonics. When the data points are the knots
of a regular grid it is easy to see that the estimated harmonic coefficients converge to the correct theoretical values, but
when the observation density is not constant a significant bias is introduced. The result is obtained by assuming that the
number of observations tends to infinity with points sampled from a given distribution. Under the same conditions it is shown
that quadrature and “collocation-like” formulas displays a statistically consistent behaviour. |
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