## 4 Zero-Baseline Instantaneous RTK Positioning with Smartphones in Lying Down and Upright Positions
(**b**) Smartphones used in upright positions: with GP4 (left) and S20 (right column) using an external antenna. precise, as shown by the more peaked histograms, and the formal and empirical normal PDFs now fit the histograms very well (red lines are on top of the blue lines). On the other hand, for the S20 smartphones we can see an empirical normal PDF that does not fit the histograms of the correctly fixed solutions very well (top row, right column), which implies that the data are not normally distributed when the S20 smartphones are lying down. This improves, however, at the bottom row when the S20 smartphones are in an upright position, where we get more precise North errors with a good fit between the formal and empirical normal PDFs. To further investigate the problematic period for the S20 smartphones in the zero-baseline setup between epoch 13,800 and 25,000 (cf. dashed black lines in Figure 5), we show in Figure 7a the corresponding L1 GPS and L1 QZSS DD phase residuals with the smartphones in a lying down position in the left column and in an upright position in the right column. The selected zoom-in period at the bottom row depicts a transition period between epochs 19,800 to 23,400 (1 h of data), where it goes from having a poorer RTK positioning performance to a better one (cf. Figure 5). In Figure 7b, we show the corresponding GP4 results. We note that the L5 DD phase residuals show a similar pattern for all our results and are thus not shown for brevity, and that the depicted L1 DD phase residuals are expected to repeat between days as the GPS and QZSS constellation repeatability period was accounted for (cf. Table 2). Figure 7a shows, as expected (cf. RMSs in Table 3), that the S20 smartphones obtained larger magnitude of DD phase residuals when they were lying down (left column). In contrast, the S20 smartphones achieved smaller magnitude of DD phase residuals when they are in an upright position (right column), despite having fewer number of satellites (cf. Figure 5). This implies that the smartphone setup has played a significant role in the quality of the phase observations and that the S20 internal antennas seem more sensitive to interferences when the smartphones are lying down. We also remark that there are some large excursions in the DD phase residuals in the top row and right column of Figure 7, when there is also fewer number of satellites, which correspond to incorrectly fixed solutions (cf. Figure 5). More importantly, in Figure 7a and the left column, we can see that many of the DD phase residuals, when the smartphones are lying down, have a mean different from zero meters and several linear trends present. However, when the smartphones are in an upright position in the right column, we have a zero mean of all residuals and the linear trends become absent. Finally, we can see in Figure 7a that the mean RMS values of the L1 DD phase residuals decrease from 0.020 m and 0.024 m, for GPS and QZSS respectively, to 0.005 m and 0.006 m when the S20 smartphones are in an upright position. In comparison to the S20 results in Figure 7a, one can see in Figure 7b that the GP4 performance remains visually more or less unchanged between having the smartphones in a lying down and upright position (left vs. right column). Moreover, there are no apparent linear trends in the DD phase residuals at the bottom row present. However, it is evident that there is a small 2 mm increase in the average RMS values for the GPS L1 DD phase residuals when the smartphones are lying down (whereas the corresponding L1 QZSS RMS remains unchanged). Figure 7: **Zero baseline with S20 in (a) and GP4 in (b), both in a lying down (left column) and upright position (right column): the DD phase residual time series of the L1 signal (top row) is shown for epoch 13,800 and 25,000 (cf. dashed black lines in Figure 5). The DD phase residuals of GPS are depicted as blue dots and QZSS as cyan dots. The black dashed lines indicate the zoom-in period of the L1 DD phase residuals (bottom row) between the epochs 19,800 and 23,400.