On the equivalence of ionospheric-free, differenced, and undifferenced, uncombined GNSS network processing

Global Navigation Satellite System (GNSS) observations are commonly processed using various established methods, including the processing of ionospheric-free (IF) linear combinations (LC), differences of observations as well as the processing of undifferenced, uncombined (UDUC) observations. The most general and flexible approach to GNSS processing is widely regarded to be the UDUC approach, as this approach is based on the raw observation equations of potentially all available observations. The IF approach uses IF-LC obtained by observations on different frequencies but the same receiver-satellite link to eliminate the ionospheric slant delay. The differencing approach also uses LC of observations, with the distinction that observations of the same signal but different receivers and/or satellites are being used. The purpose of differencing is the elimination of satellite/receiver clocks and biases and, in some cases, reducing or even eliminating atmospheric delays. We aim to uncover the implicit model assumptions made when using various IF and differencing approaches and in what case they are equivalent to the processing of the UDUC observations. This is achieved by introducing a reformulation method, which is then applied to the UDUC observations of code division multiple access GNSS to obtain the functional models of various IF and differencing approaches. The underlying assumptions in this reformulation can then be identified. The results of this theoretical contribution will provide insight into the most appropriate method for processing GNSS observations in different cases and what implicit assumptions are being made when the respective method is being used.