## 4 Zero-Baseline Instantaneous RTK Positioning with Smartphones in Lying Down and Upright Positions
This implies that GP4 have a better redundancy than that of the S20 smartphones, which, as we show in Table 3, positively affects the RTK positioning performance. To further investigate the dramatic drop in the ILS SR for S20 in Table 3 and to evaluate the corresponding RTK positioning performance, Figure 5 depicts the horizontal North/East positioning scatter and vertical Up error time-series for the zero-baseline with the smartphones in the lying down (top panels) and upright position (bottom panels). We employ a zoom-in window to depict the correctly fixed solutions that have mm-cm level positioning precisions and are shown as green dots. The incorrectly fixed and ambiguity-float solutions, shown as red and grey dots, respectively, have meter-level positioning precisions. The GP4 smartphones are shown in the left column and the S20 counterparts in the right column. For all these results, we use 12 h of data with a one second measurement interval, an elevation cut-off angle of 10\({}^{\circ}\), with GPS (L1 + L5), Galileo (E1 + E5a), QZSS (L1 + L5) and BDS (B1) observations, cf. Tables 1 and 2. The empirical and formal correctly fixed Up-error confidence intervals (CIs) and horizontal error ellipses, depicted as blue and red lines, respectively, have all been determined from the empirical and formal position VCV-matrices. We also depict at the bottom of the Up time-series in Figure 5 the number of satellites for all constellations as black lines, so as to demonstrate the model strengths of the two smartphone models GP4 and S20. On the right hand side \(y\)-axis we further depict the correctly fixed formal STDs for the Up-component, so as to measure the effect from the receiver-satellite geometry strength on the estimated positioning errors. Note that the lying down position for both GP4 and S20 smartphones achieved an ILS SR of 99.9% and 79.4%, respectively (Figure 5a, cf. Table 3), whereas the corresponding ILS SRs for when the smartphones are in an upright position read 99.9% and 97.8%, respectively (Figure 5b). Finally, we denote epochs 13,800 to 25,000 in Figure 5 with dashed black lines in the Up positioning error panel, since here the S20 smartphones seem particularly affected by the fact that the smartphones are lying down with many incorrectly fixed solutions at the meter level. This particular period will be further investigated in Figure 7.  
Figure 5 shows that the S20 smartphones (right column) have a better float precision, as shown as grey dots, compared to that of the GP4 counterparts (left column). The figure further shows that the repeatability of the correctly fixed solutions of the GP4 smartphones, in the left column, are more precise and that GP4 also have less incorrectly fixed solutions (red dots) when compared to that of S20. In particular, we note that less than 3500 out of 11,200 epochs, i.e., an ILS SR of about 31.0%, of the S20 positions were found correctly fixed between epochs 13,800 to 25,000 in Figure 5a, as indicated by the black dashed lines. Figure 5b shows that the S20 results improve when in an upright position with fewer incorrectly fixed solutions. This since the corresponding ILS SRs between epochs 13,800 to 25,000 are now 99.9% and 97.4% for GP4 and S20, respectively, which means that the ILS SR for GP4 remains unchanged but that the ILS SR for S20 has increased by 66.4%. This despite the fact that the mean number of satellites for the same period _decreased_ from 16 to 11 satellites when the S20 smartphones were in a lying down position and an upright position, respectively. This implies that the S20 internal smartphone antennas are more sensitive to interferences such as multipath, even inside the RF shielding box (cf. Figure 1). Furthermore, note in Figure 5a,b that the formal STDs of the vertical component of the GP4 is relatively consistent throughout the observation period between the two setups.