On the application of nonparametric regression methods to geodetic data
Fischer, Beat & Philipp Bruehlmann
The collocation and filtering method of geodesist H. Moritz not only estimates parameters but also separates signal from noise and provides prediction following the Wiener-Kolmogorov theory and treating the signal as a stochastic quantity. The statistic approach of nonparametric or semiparametric regression simplifies the theory of the method. The signal is treated as a deterministic quantity, and the Wiener-Kolmogorov prediction can be replaced by simple interpolation. In addition, several methods to determine the signal to noise ratio such as cross validation were developed. By applying these methods to the transformation of old coordinates from 1903 to new GPS-coordinates of 1995, systematic distortions of the old coordinates can be estimated besides the estimation of Helmert-transformation parameters. Mapping the derivative of the systematic distortions enabled the Swiss Canton of Basel-Stadt to choose appropriate triangles in order to define a triangulation for coordinate transformation which fulfilled precision requirements in each triangle separately. These statistical methods may also be applied to the estimation of locally different motions of sliding slopes.
Event: XXIII International FIG Congress : Shaping the change
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