SPATIAL MODELING AND ANALYSIS OF ADJUSTED RESIDUALS OVER A NETWORK OF GPS-LEVELLING BENCHMARKS

摘要

The idea of using a parametric surface to spatially model the datum discrepancies and systematic effects inherent when combining GPS, geoid, and orthometric heights has become standard practice. The types of parametric models used vary from simple planar surfaces to more complex polynomial type surfaces of higher degree, to name a few. In general, the process applied for selecting the best model in a particular region suffers from a high degree of arbitrariness both in choosing the model type and in assessing its performance. In order to address these issues, several statistical and empirical tests are applied to the results of the combined least-squares adjustment of ellipsoidal, orthometric, and geoid heights. This procedure also helps to evaluate the significance of the estimated parameters for a general surface, which can be used to form a more simplified trend model. It is assumed throughout the process that reliable information for the statistical behaviour of the GPS, geoid, and orthometric data is available in order for the results to be meaningful. In this paper, a detailed description of a semi-automated program designed for implementing the aforementioned approach is provided. Specifically, the operation of the program requires the user to select between two pre-specified families of parametric surfaces, namely (i) polynomial models up to 4th degree and (ii) similarity-based transformation model and its more simplified forms. Numerical tests of this methodology are demonstrated through the use of regional height data from Switzerland and Canada. Overall, this procedure proves to reduce some of the arbitrariness associated with selecting parametric surfaces for GPS-levelling.