Modelling residual systematic errors in GPS positioning: methodologies and comparative studies

Abstract

Since its introduction to civilian users in the early 1980s, the Global Positioning System (GPS) has been playing an increasingly important role in high precision surveying and geodetic applications. Like traditional geodetic network adjustment, data processing for precise GPS static positioning is invariably performed using the least squares method, which requires both functional and stochastic models. A double-differencing technique is commonly used for constructing the functional model in order to account for systematic errors in the observations. In current stochastic models, it is usually assumed that all the one-way measurements have equal variance, and that they are statistically independent. The above functional and stochastic models have therefore been used in standard GPS data processing algorithms. However, with the use of such GPS data processing algorithms, systematic errors in GPS measurements cannot be eliminated completely or accounted for satisfactorily. These residual systematic errors (remaining after double-differencing the observations) can have a significant effect on both the ambiguity resolution process and the GPS positioning results. This is a potentially critical problem for high precision GPS positioning applications. It is therefore necessary to develop an appropriate data processing algorithm, which can effectively deal with systematic errors in a nondeterministic manner. Recently, several approaches have been suggested to mitigate the impact of systematic errors on GPS positioning results: the semi-parametric model, the use of wavelets and new stochastic modelling methodologies. These approaches use different bases and have different implications for data processing. This paper aims to numerically compare the above three methods.