Three‐Dimensional Adjustment Computations Model

Abstract

A three‐dimensional (3‐D) model based on the connectivity of astronomic and geodetic coordinate systems is developed from basic principles. It provides for simultaneous adjustment of most conventional types of terrestrial surveying observations. Observation equations express observed quantities in 3‐D space and are referenced to the local vertical at the point of observation. Classical reductions of observations to the reference ellipsoid prior to adjustment are not necessary. A least squares solution yields adjusted geodetic rectangular coordinates from which geodetic latitude, longitude and height values may be found. For most networks, astronomic coordinate values will also be obtained, but these values are probably reliable only if astronomic observations are included in the survey. The 3‐D model should provide a sound theoretical basis for development of a fully‐integrated adjustment model that includes conventional, photogrammetric, inertial, satellite and other surveying system observations. Additional research is desirable to evaluate the 3‐D method's full potential for applications such as local densification and project control surveys.