Estimation of variance components through a combined adjustment of GPS, geoid and levelling data

The method of GPS-levelling for obtaining orthometric heights is not a new concept. In fact, many studies have proven its usefulness and the question of whether GPS-levelling can provide a viable alternative to traditional techniques is no longer an issue. An important question, however, that has yet to be satisfactorily solved is, 'What accuracy level can be achieved using this approach?' Over the past decade, numerous advances have been made which have placed us in a position where we can begin to address the issue with more confidence, namely (i) improved mathematical models/techniques for dealing with GPS and geoid data, (ii) increased data availability for gravimetric geoid models, and (iii) improved data processing capabilities. In this paper a statistical approach for estimating the variance components of heterogeneous groups of observations is used in the combined adjustment of GPS, geoid and levelling data. Specifically, the iterative minimum norm quadratic unbiased estimation algorithm is employed to determine the individual variance components for each of the three height types. The challenges encountered when implementing this well-known algorithm in practice with real data are discussed. The analysis provides some indication into the practicality and effectiveness of estimating variance components in mixed vertical networks. Notably, the estimation of realistic variance components provides us with important insight regarding the GPS-levelling problem in addition to other uses of combined GPS, geoid and levelling data, such as assessing the accuracy of a gravimetric geoid model.