An analysis on the optimal combination of geoid, orthometric and ellipsoidal height data

The main objective of this research is to present a detailed analysis of the optimal combination of heterogeneous height data, with particular emphasis on (i) modelling systematic errors and datum inconsistencies, (ii) separation of random errors and estimation of variance components for each height type, and (iii) practical considerations for modernizing vertical control systems. Specifically, vertical control networks consisting of ellipsoidal, orthometric and geoid height data are investigated. Although the theoretical relationship between these height types is simple in nature, its practical implementation has proven to be quite challenging due to numerous factors that cause discrepancies among the combined height data. To address these challenges a general procedure involving empirical and statistical tests for assessing the performance of selected parametric models is developed. In addition, variance component estimation is applied to the common adjustment of the heterogeneous heights. This leads to an in-depth analysis of the effects of correlation among heights of the same type, provisions for computing non-negative variance factors, and the intrinsic connection between the proper modelling of systematic errors and datum inconsistencies with the estimated variance components. Additional numerical studies include the calibration of geoid error models (both regional and global), scaling the GPS-derived ellipsoidal height covariance matrix, and evaluating the accuracy of orthometric heights obtained from national/regional adjustments of levelling data. Ultimately, one of the main motivations for this work is embedded in the eminent need to introduce modern tools and techniques, such as GNSS-levelling, in establishing vertical control. Therefore, part of this research is aimed at bringing to the forefront some of the key issues that affect the achievable accuracy level of GNSS-levelling. Overall, the analysis of the optimal combination of the heterogeneous height data conducted herein provides valuable insight to be used for a variety of height-related applications.