A fast satellite selection algorithm with floating high cut-off elevation angle based on ADOP for instantaneous multi-GNSS single-frequency relative positioning

With the Global Navigation Satellite System (GNSS) developing, the single-frequency single-epoch multiple GNSSs (multi-GNSS) relative positioning has become feasible. Since a larger number of the observed satellites make the instantaneous (single-epoch) positioning time-consuming, a proper satellite selection is necessary. Among the present methods, the satellite selection with a fixed high cut-off elevation angle (CEA) is least time-consuming. However, there is no criterion how large a fixed high CEA should be to achieve a high success rate and less time consumption. Besides, a fixed high CEA makes the number of visible satellites largely variable, which affects the success rate. Hence, a satellite selection strategy based on ambiguity dilution of precision (ADOP) is proposed. Firstly, the theoretical proof that the ADOP increases the least when removing satellites are all low-elevation-angle satellites is given, which is important to achieve the fast positioning with a high success rate. Then, the threshold $\beta$ is calculated for a different number of satellites and a given ADOP. The satellites are selected based on their elevation angles from high to low until $\beta$ of the selected satellites becomes smaller than the corresponding threshold; this method is called the extended floating CEA multi-GNSS (EF-multi-GNSS). The comparison of the single-frequency single-epoch positioning performance of the EF-multi-GNSS with the satellite selections based on a fixed low CEA (L-multi-GNSS) and a fixed high CEA (H-multi-GNSS) via the relative positioning experiments shows that: (1) the EF-multi-GNSS with a minimal number of satellites can achieve the fast positioning and a high success rate close to 100%. It can greatly reduce the time consumption of the L-multi-GNSS, by about 64.0%, by selecting 12.6 satellites of 23.4 satellites; (2) the floating CEA of EF-multi-GNSS eliminates the consideration how large a fixed high CEA should be, and a CEA larger than the fixed high CEA of the H-multi-GNSS makes it more suitable for different conditions.