## 3 Data Processing and Analysis for Smartphone Real-Time Kinematic (RTK) Positioning
### Evaluation of Ambiguity Resolution for Different Observation Combinations
Therefore, for a suitable number of satellites, the cycle-slip satellites should be controlled to participate in positioning, and observations from the BDS GEO and GLONASS satellites should be avoided. Further analysis of the combinations that include dual-frequency observations and other satellites with single-frequency data was also performed. The corresponding solutions are listed in Table 7. The fixing rate of the GPS dual-frequency observations is only 22.4%, which is lower than the single-frequency result, and the fixing rate of G/E single-frequency observations is relatively high, but the dual-frequency fixing rate is only 10.6%, being lower than that of the single-GPS constellation. The positioning accuracy also fails to converge within 0.1 m. If band L5 or E5a is not fixed, the fixing rate increases to 59.1% and 88.0%, respectively, mainly because the cycle slips in bands GPS L5 and Galileo E5a are extremely frequent, with those of band Galileo E5a being more frequent. The cycle-slip ratios in bands GPS L5 and Galileo E5a are 5.2% and 8.2%, respectively. When a cycle slip occurs in RTK positioning, the ambiguity parameters should be reinitialised, and frequent initialisation reduces the ambiguity fixing rate. In Table 7, the number of satellites with simultaneous dual-frequency observations is low, and their cycle slips are frequent, further reducing the availability of dual-frequency observations. Therefore, these observations are limited for use in long-baseline RTK positioning or precise point positioning and other multi-frequency combination positioning strategies. Figure 11: Half-cycle jump of BDS GEO satellite observations acquired by smartphone. In the results reported above, the accuracy of fixed solutions using different observation combinations is consistent, and an accuracy of approximately 1 and 2 cm can be achieved along the horizontal and vertical directions, respectively. However, owing to the excessive noise in smartphone observations, even for a fixing rate above 90%, it is still difficult to obtain millimetre-level accuracy. For several combinations with a fixing rate higher than 88%, we compared the accuracy of the fixed solutions and their corresponding float solutions simultaneously after the fixed solutions converged, obtaining the results shown in Figure 12. After fixing the ambiguity, the accuracy along the three directions improves. The east direction shows the highest improvement, reaching approximately 80%, and the other two directions show improvements by more than 30%. Hence, ambiguity resolution is important for high-precision positioning in smartphones, and future work should pursue further improvements in the fixing rate while shortening the convergence time. The above analysis shows that the large difference in fixed rates for the different combinations is mainly due to the impact of the number of satellites, cycle slips, and observation accuracy. By considering the results above, the correct fixing rate, and a reasonable convergence time, we recommend using combination G/E/C (no GEO/float C) for poisoning based on smartphone observations when the number of satellites is sufficient.