## 5 Short-Baseline Instantaneous RTK Performance with Smartphones in Lying Down and Upright Positions
### Instantaneous RTK Positioning Performance for Short-Baselines with External and Internal Antennas
For GP4 we can see in Table 4 (similar to the zero-baseline in Table 3) that the ILS SR remains at 99.9% when external antennas are used and are in upright and lying down position, respectively. The situation changes entirely, however, when internal antennas are used. We then go from a GP4 ILS SR of 98.7% to 63.1%, which implies that the GP4 internal antennas also become more sensitive to interferences in the absence of the RF shielding box and the use of external antennas, when more multipath effects are present. Moreover, Table 4 shows that the correctly fixed positioning mean errors are at the mm level and the STDs are always at most one centimetre (in the Up component) when the smartphone are in an upright position rather than lying down. To further highlight the good instantaneous short-baseline RTK performance of the upright S20 and GP4 smartphones in Table 4 when using external antennas (cf. Figure 3), Figure 9 depicts the corresponding horizontal North/East positioning scatter and vertical Up error time-series (similar to zero-baseline results in Figure 5) for 8 h of data. The GP4 smartphones are again shown in the left column and the S20 counterparts in the right column. We only depict the results when the smartphones are in an upright position for brevity, because the poor fit of the empirical and formal confidence ellipses/intervals and PDFs are similar between these short-baseline results to that of the zero-baseline results in Figures 5 and 6, respectively. Figure 9: **Short-baseline with external antennas and smartphones in an upright position (cf. Figure 3):** Horizontal (N, E) positioning scatter (first row) and corresponding vertical (U) positioning error time-series (second row) for 8 h of data (cf. Table 2) with GP4 (left column): ILS SR 99.9% and S20 (right column): 99.2%. In this RTK model GPS + Galileo + QZSS + BDS L1 + L5, E1 + E5a, L1 + L5, B1 observations have been used. A zoom-in window is shown to depict the two order of magnitude improvement when going from incorrectly fixed (red dots) and ambiguity-float (grey dots), to correctly fixed solutions (green dots). The 95% empirical and formal confidence CIs and ellipses for the correctly fixed solutions are shown as blue and red lines, respectively. The number of visible satellites and the correctly fixed formal up STDs (bottom row) are shown as black and green lines, respectively. In Figure 9, we can see a good agreement between the formal and empirical confidence ellipses and intervals denoted as red and blue lines, respectively, which implies that the stochastic model settings in Table 2 are realistic. We can also see that the GP4 smartphones in the left column provides a single-epoch ILS SR of 99.9% even for this short-baseline, which implies that when external antennas are used it can give competitive performance to that of high-cost receivers and antennas with mm-cm level positioning performance. This is similar to the results shown in Odolinski and Teunissen [6] for another Android-based smartphone when connected to low-cost patch antennas. Figure 9 also shows that S20 can achieve an ILS SR 99.2% when external antennas are used and the smartphones are in an upright position. Finally, Figure 9 shows that when the correctly fixed Up formal STDs get larger, the corresponding Up errors also get larger for both smartphone models. This happens for instance at the end of the time-series for GP4 in the left column when there is almost a minimum number of tracked satellites over the observation time span, and just before epochs 7200 and 14,400 for S20 in the right column. To further investigate the instantaneous RTK positioning performance when using internal instead of the external antennas, we show in the top panel of Figure 10 the GP4 and S20 corresponding results when the smartphones are lying down (cf. Figure 4). In the bottom panel (Figure 10b), we also show the corresponding results when the smartphones are in an upright position.