Differential GPS: the Reduced Difference Approach

Abstract

In the traditional approach to differential GNSS, the satellite error terms are eliminated by forming the so-called single differences (SD). One then gets rid of the receiver error terms by computing, for each receiver to be considered, the corresponding double differences (DD): the discrepancies between the single differences (SD) and one of them taken as reference. To handle the SD's in a homogeneous manner, one may equally well consider the discrepancies between the SD's and their mean value. In this paper, these "centralized differential data" are referred to as "reduced differences" (RD). In the case where the GNSS devices include only two receivers, this approach is completely equivalent to "double centralization." More precisely, the information contained in the "double centralized observations" is then a simple antisymmetric transcription of that contained in the reduced differences. The ambiguities are then rational numbers which are related to the traditional integer ambiguities in a very simple manner. The properties established in this paper shed a new light on the corresponding analysis. (The extension to GNSS networks with missing data will be presented in a forthcoming paper.) The corresponding applications concern the identification of outliers in real time. Cycle slips combined with miscellaneous SD biases can thus be easily identified.