How Accurately Can We Determine Orthometric Height Differences from GPS and Geoid Data?

Abstract

The optimal combination of global positioning system (GPS) geometric heights with gravimetrically derived geoid undulations for the determination of orthometric heights above mean sea level (GPS/geoid leveling), or more precisely with respect to a vertical geodetic datum, requires the incorporation of a parametric corrector surface model. Such a parametric model is needed to absorb the datum inconsistencies and systematic distortions inherent among the different types of height data. An analysis for the achievable accuracy of relative GPS/geoid leveling is performed in this paper, using the covariance (CV) matrix of the estimated parameters in the corrector surface model, the standard measuring accuracy of GPS height differences, and the relative internal accuracy of a gravimetric geoid model. A test network of spirit leveled GPS control points located in the southwestern part of Canada has been used to perform a simulative integrated least-squares adjustment of all three types of height data, and to obtain the CV matrix of the parameters in the corrector surface model. The input CV matrices for the GPS and the orthometric height values at the control network points have been computed through separate simulative adjustments that take into account the measuring accuracy of GPS and spirit leveling. The input accuracy for the geoid undulation differences is based on the performance evaluation of the GSD95 Canadian geoid model in western Canada. The focus is placed on studying the effects of the combined relative accuracy of GPS and geoid data, in conjunction with a number of different parametric corrector surface models, for GPS/geoid leveling on new baselines within the test network area.