Recovering undifferenced GNSS observations from double differences - use and limits

Double differences (DD) of GNSS phase observations are often used to eliminate or largely reduce systematic effects in the observations, especially the satellite and receiver clock errors. However, during this operation not only errors are eliminated but also information of four different lines-of-sights is combined into one DD observation. Consequently, specific effects of interest like e. g. multipath signatures or tropospheric slant delay variations can be hardly attributed to a specific line-of-sight. To overcome these problems, Alber et al. (2000) proposed a strategy to recover undifferenced observations (ZD) from DD which is now widely used in geodesy and GPS data assimilation in meteorology. In this paper, the explicit analytical solution of the strategy proposed by Alber et al. (2000) will be given. The findings describe directly the repartition of the information contained in the DD on the recovered ZD and the difference between the original ZD and the recovered one. Using simulated and real data the benefits and limitations of the strategy are discussed. It is shown that individual signatures cannot be completely recovered. ... mehrWe found that the success of recovering individual signatures and the degree of contamination of other observations by these signatures depend on the number of stations in the network, the number of satellites in common view, and the uniqueness of the signatures.