Fitting AUSGeoid98 to the Australian Height Datum Using GPS-Levelling and Least Squares Collocation: Application of a Cross-Validation Technique

Abstract

In an absolute sense and over long (>100 km) baselines, the AUSGeoid98 gravimetric-only geoid model does not always allow the accurate transformation of Global Positioning System (GPS)-derived ellipsoidal heights to Australian Height Datum (AHD) heights in all regions of Australia. This is due predominantly to the well-known biases and distortions in the AHD, but long-wavelength errors in the gravimetric geoid model or GPS errors cannot be ruled out. Until the AHD is rigorously redefined, an interim solution is sought where co-located GPS and AHD heights are used to distort AUSGeoid98 such that it provides a better model of the separation between the base of the AHD and the GRS80 reference ellipsoid. This data combination was implemented using least squares collocation (LSC) gridding. Importantly, GPS-AHD data not used in the LSC combination were used to assess the improvement using a cross-validation technique. Using this cross-validation, RMS noise of 14 mm and correlation length of 2500 km for the LSC covariance function were optimised empirically. The standard deviation of the differences between the final combined model and the unused GPS-AHD data is ±156 mm, compared to ±282 mm for AUSGeoid98 alone. It is anticipated that the same technique will be used to produce a new Australian "geoid" model.