Three-Dimensional Model Based on Hotine’s “Mathematical Geodesy”

Abstract

Three-dimensional model in essence means employing all possible observables within a unified solution. However, in the context of application to the redefinition of North American networks, we are speaking primarily about the classic observables over intervisible distances, and the ensuing discussion is limited to this application. In addition to the observation equations produced by Hotine, the observation equation for spirit level rise is derived. It is concluded that, owing to the lack of vertical angles and level differences, the three-dimensional approach would not appear practical for the redefinition in North America. However, the three-dimensional approach should be used in selected areas, where there are enough required observations available.