Determining inter-system bias of GNSS signals with narrowly spaced frequencies for GNSS positioning

Relative positioning using multi-GNSS (global navigation satellite systems) can improve accuracy, reliability, and availability compared to the use of a single constellation system. Intra-system double-difference (DD) ambiguities (ISDDAs) refer to the DD ambiguities between satellites of a single constellation system and can be fixed to an integer to derive the precise fixed solution. Inter-system ambiguities, which denote the DD ambiguities between different constellation systems, can also be fixed to integers on overlapping frequencies, once the inter-system bias (ISB) is removed. Compared with fixing ISDDAs, fixing both integer intra- and inter-system DD ambiguities (IIDDAs) means an increase of positioning precision through an integration of multiple GNSS constellations. Previously, researchers have studied IIDDA fixing with systems of the same frequencies, but not with systems of different frequencies. Integer IIDDAs can be determined from single-difference (SD) ambiguities, even if the frequencies of multi-GNSS signals used in the positioning are different. In this study, we investigated IIDDA fixing for multi-GNSS signals of narrowly spaced frequencies. First, the inter-system DD models of multi-GNSS signals of different frequencies are introduced, and the strategy for compensating for ISB is presented. The ISB is decomposed into three parts: 1) a float approximate ISB number that can be considered equal to the ISB of code pseudorange observations and thus can be estimated through single point positioning (SPP); 2) a number that is a multiple of the GNSS signal wavelength; and 3) a fractional ISB part, with a magnitude smaller than a single wavelength. Then, the relationship between intra- and inter-system DD ambiguity RATIO values and ISB was investigated by integrating GPS L1 and GLONASS L1 signals. In our numerical analyses with short baselines, the ISB parameter and IIDDA were successfully fixed, even if the number of observed satellites in each system was small.