The three-dimensional combination of absolute and relative coordinates derived from satellite and terrestrial methods

The problem of combining satellite and terrestrial data is approached and solved by utilizing rigorous least squares estimation techniques. The mathematical model used is developed based on a three-dimensional reference frame. Derived observables from satellite as well as terrestrial observations are conceptually referred to their pre-defined coordinate systems, the relationships between which may be unknown and may be determined simultaneously with the coordinate unknowns. This is in contrast to the currently often adopted classical solution model where a set of 3-D observables derived from space positioning techniques, such as Transit-Doppler and GPS, are transformed into a local coordinate system and then split into 2-D (horizontal) and 1-D (vertical) type of observables. Solutions are then carried out independently for the horizontal and vertical networks. This 3-D model not only unifies the classical 2-D and 1-D solutions of satellite and terrestrial derived data for position unknowns, but also solves the problems arising due to the different coordinate systems associated with the observables.

This 3-D approach is investigated by comparing its results against a classical model of solution implemented in a standard classical program. Perfect agreement is achieved when simulated and uncorrelated data are used, but investigation with real data has led to a discussion on the improper stochastic modelling in the classical solutions, even though the disagreements are within their standard errors. Investigation with another 3-D approach (GEOLAB program) and using real data has led to a perfect agreement.

Observables are erroneous and axiomatically survey results have to be accompanied by quality measures in order to assess their usefulness. These problems are resolved by applying the concept of data snooping, and of precision and reliability analyses.

This thesis describes the details of the investigation, development and implementation of the adopted 3-D model. The problems of combining data from various coordinate systems of the observables are also solved. A review of a classical model is included, and the basic concepts of data snooping, and of precision and reliability analyses are provided.