## 5 Analyses
### Kinematic Data  
This section presents the analyses of the kinematic data comparing the proposed method with the existing method. These dual-frequency GPS data analyses aim to compare the estimation of the parameters of interest for geo-referencing, namely the heading and center point of the rotating frame. Figure 6 shows the satellite visibility: the skylpot, the number of satellites and the PDOP values. With a \(10^{\circ}\) elevation cut-off, we have a good GPS satellite geometry (PDOP \(\approx 2\)) during the experiment. Table 6 summarizes the root mean square (RMSE) values of the heading angle for all five rotations, where the ground truth is determined using the fact that the frame was rotating at a constant rate and synchronized though a GNSS receiver event marker. Since the precision of ambiguity-fixed attitude angles is driven by the high precision of the carrier phase observations, both the proposed method and \begin{table}
\begin{tabular}{c c} \hline \hline
**Heading** & **Elevation** \\ \hline
0.24 & 0.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Empirical angular standard deviation (deg) for the attitude determination using the epoch-by-epoch processing of the static data (0.6-m baseline). Figure 5: North-east scatter plot of the ambiguity-fixed baseline estimation using static data with epoch-by-epoch processing (20-m baseline). \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Processing Method** & **North** & **East** & **Up** \\ \hline Standard positioning & 3.4 & 2.1 & 5.1 \\ Array-aided positioning & 2.8 & 1.6 & 4.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Empirical position standard deviation (mm) for baseline estimation using the epoch-by-epoch processing of the static data (20-m baseline). the previous method [8] have a similar angular accuracy. Filtering further improves the estimates. Based on these analyses, the achievable heading angular accuracy using a \(0.6\)-m baseline on the rotating frame is about \(0.2^{\circ}\) RMSE. Baseline estimation errors of epoch-by-epoch processing and filtering for the first rotation are depicted in Figure 7, while the 3D position RMSE values for all five rotations are reported in Table 7. Here, smoothing estimates based on all five rotations are considered as the ground truth. The apparent improved performance of the proposed method is due to the use of novel integrated processing. Since the proposed integrated method naturally yields the estimates of the center point (see Section 4.2), the proposed filtering has a simple and strong dynamic model compared to the nonlinear, constrained filtering of the existing method [8] and, hence, yields improved estimates. Based on these analyses, the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Rotation**} & \multicolumn{2}{c}{**Epoch-by-Epoch**} & \multicolumn{2}{c}{**Filtering**} \\ \cline{2-5}  & **Previous** & **Proposed** & **Previous** & **Proposed** \\  & **Method** & **Method** & **Method** & **Method** \\ \hline
1 & 0.24 & 0.20 & 0.20 & 0.16 \\
2 & 0.26 & 0.23 & 0.24 & 0.20 \\
3 & 0.23 & 0.16 & 0.21 & 0.13 \\
4 & 0.20 & 0.15 & 0.16 & 0.11 \\
5 & 0.20 & 0.17 & 0.16 & 0.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Heading root mean square (RMSE) (deg) for kinematic data (0.6-m baseline). Figure 6: GPS satellite visibility during the kinematic experiment with a 10\({}^{\circ}\) elevation cut-off. (**a**) The number of satellites and PDOP; and (**b**) skylpot. achievable position accuracy using a \(20\)-m baseline with two antennas on the rotating frame is about \(3\) mm RMSE. Finally, we considered the determination of the center point using a reference station at about 6 km away. The baseline estimation results for this long baseline using the proposed method are provided in Table 8. The significant increase of the position RMSE of this baseline compared to the short baseline case in Table 7 is due to the presence of residual atmosphere delays for this long baseline. Hence, the achievable position RMSE for this baseline is about 20 mm.