Combination of Geometric and Orthometric Heights in the Presence of Geoid and Quasi-geoid Models

A generalization of the well-known relationship between geometric and orthometric heights is presented in this paper. The advantage of our revised formulation is that, instead of the non-determinable true orthometric heights, it employs the (most commonly used in geodetic practice) Helmert orthometric heights. Based on standard concepts from physical geodesy theory and straightforward analytical derivations, we obtain a set of linearized constraints relating the geometric and Helmert orthometric heights in the presence of a geoid or quasi-geoid model. These constraints should be theoretically satisfied in the case of errorless data and thus they provide a standard framework for the joint analysis and the quality testing of heterogeneous heights in a terrestrial network