1st Joint Commission 2 and IGFS Meeting
International Symposium on
Gravity, Geoid and Height Systems 2016

September 19-23, 2016
Thessaloniki, Greece

Accurate least squares collocation with no empirical covariance calculation

21/09/2016 | 10:45 | Session 3: Recent Development in Theory and Modelling


Wojciech Jarmołowski


The parametric modeling techniques like kriging or least squares collocation (LSC) use various analytical covariance models to represent data covariance. Usually, empirical covariance model is calculated and the parameters of the analytical model are determined empirically by the fitting one into another. It has been proved that parameters of the model can be also estimated by maximum likelihood (ML) technique. The Fisher scoring (FS) method is one of the analytical solutions of ML and probably one of the fastest. FS was often proposed in the form of limited efficiency, however the statisticians have found its' significantly more effective form with the Levenberg-Marquardt optimization. Such optimized method has been now tested with the planar covariance model and gravity anomalies. The results are promising. There is a need for some additional complementary research, however the method is simple, fast, accurate and enables estimation of covariance parameters with no empirical covariance calculation. Therefore LSC can now be more accurate, due to the ML estimation and faster, with quick solving of the parameters by the FS.

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