## 4 Zero-Baseline Instantaneous RTK Positioning with Smartphones in Lying Down and Upright Positions
The mean was taken as an average RMS over all satellites for each GNSS, and the RMSs for the DD code residuals are shown within square brackets. The number of correctly fixed epochs was determined by the number of epochs where the estimated local North, East and Up coordinate errors are all below or equal 0.05 m. The ILS success rate was then computed as follows,  
\[P_{S_{E}}=\frac{\text{\# of correctly fixed epochs}}{\text{total \# of epochs}}\times 100\%. \tag{2}\]  
In other words, the single-epoch ILS SR in Table 3 shows the availability of correctly fixed solutions with mm level positioning STDs. In Table 3, we can see an identical ILS SR of 99.9% for the GP4 smartphones in the lying down and upright positions. We can also see that these results are impressive indeed, since they resemble that of the high-cost Trimble NetR9 and ulox ZED-F9P receivers and antennas with an ILS SR of 99.9% and 100.0%, respectively. However, for the S20 smartphones there is a significant worsening of the performance, where we go from 97.8% to 79.4% ILS SR when the smartphones are upright and in lying down positions, respectively. This despite the fact that the mean number of satellites _increased_ from 13 when upright to 17 when lying down. The drop in the number of satellites for when the S20 smartphones are in an upright position implies that there is possibly an outlier rejection threshold now activated to remove low-quality raw GNSS measurements internally in the S20 GNSS logger, similar to the findings in [PERSON] et al. (2020) and [PERSON] et al. (2020) for other Android-smartphones. If we further inspect the mean RMSs of the DD phase and code residuals in Table 3, we can see a slight increase in RMS values for GP4 when going from an upright to a lying down position for all frequencies (with also the L1 phase QZSS RMS increasing at the sub-mm level). For S20 the code RMSs are all increasing significantly when going from an upright to a lying down position, with the maximum increase in RMS value for L5 GPS increasing from about 1.1 m to 2.0 m. The S20 phase RMSs are also increasing dramatically when going from an upright to a lying down position, where again the largest increase is observed for L5 GPS of 0.005 m to 0.016 m. We also note that all L5 code RMSs are more precise than that of L1 for GP4 and S20, respectively, similar to ([PERSON] et al., 2020). We can further compare the obtained code and phase RMSs to that of the geodetic (Trimble) and low-cost (ulbox) receivers in Table 3, where we can see that all L1 code observations are much less precise for the smartphones. For instance, the L1 code RMS for the GP4 smartphones is about 2.5 m, which can be compared to the Trimble and ulbox L1 GPS RMSs of approximately 0.6 m and 0.3 m, respectively. It is worthwhile to note that the ulbox ZED-F9P receivers and antennas were also found to have a better L1 code precision than that of Trimble R10 receivers and antennas in [PERSON] and Teunissen (2019). Most importantly we can see that the GP4 and S20 smartphones have comparable carrier-phase L1 RMSs and correctly fixed position STDs at the mm level to that of the Trimble and ulbox receivers, respectively, when in an upright position. In addition, we can see that the mean positioning errors generally decrease by a few millimetres when going from lying down to an upright position for both smartphone models. Table 3 shows further that the float mean positioning errors and STDs are different between when the smartphones are lying down and are upright, respectively, which is likely related to the earlier mentioned outlier rejection threshold activated differently for the two cases ([PERSON] et al. (2020) and [PERSON] et al. (2020), see also the average number of satellites). We can also note in Table 3 that the mean number of satellites of GP4 is 21 and S20 is 13 when in an upright position, whereas the Trimble and ulbox receivers both tracked 25 satellites while L2 observations were collected rather than the L5 GPS.