Joint Treatment of Random Variability and Imprecision in GPS Data Analysis

In the geodetic applications of the Global Positioning System (GPS) various types of data uncertainty are relevant. The most prominent ones are random variability (stochasticity) and imprecision. Stochasticity is caused by uncontrollable effects during the observation process. Imprecision is due to remaining systematic deviations between data and model due to imperfect knowledge or just for practical reasons. Depending on the particular application either stochasticity or imprecision may dominate the uncertainty budget. For the joint treatment of stochasticity and imprecision two main problems have to be solved. First, the imprecision of the original data has to be modelled in an adequate way. Then this imprecision has to be transferred to the quantities of interest. Fuzzy data analysis offers a proper mathematical theory to handle both problems. The main outcome is confidence regions for estimated parameters which are superposed by the effects of data imprecision. In the paper two applications are considered in a general way: the resolution of the phase ambiguity parameters and the estimation of point positions. The paper concludes with numerical examples for ambiguity resolution.