# Three-Dimensional Dead-Reckoning Based on Lie Theory for Overcoming Approximation Errors
## 4 Experiments and Results
### Speed Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Stat**} & \multirow{2}{*}{**Ti.**} & \multirow{2}{*}{**Md.**} & \multicolumn{5}{c}{**Speed Error (m/s)**} \\ \cline{4-7}  & & & **(I)** & **(2)** & **(3)** & **(4)** \\ \hline \multirow{8}{*}{Mn} & \multirow{2}{*}{0.1 (s)} & Conv. DR & 28.7996 & 34.1915 & 26.7012 & 548.2722 (W) \\  & & Proposed & 20.7235 (**B**) & 41.1633 & 24.3850 & 384.1330 \\  & & Conv. DR & 265.8342 & 379.7410 & 412.9848 & 1845.6265 (W) \\  & & Proposed & 85.4411 (**B**) & 108.0631 & 196.7227 & 1082.5576 \\  & & 1 (s) & Conv. DR & 2160.5948 (**W**) & 1932.6978 & 656.9144 & 2047.2024 \\  & & Proposed & 1716.4039 & 679.1729 & 101.4829 (**B**) & 1394.4212 \\ \hline \multirow{8}{*}{Std} & \multirow{2}{*}{0.1 (s)} & Conv. DR & 20.7475 & 28.2561 & 22.5549 & 367.4999 (W) \\  & & Proposed & 14.5014 (**B**) & 41.6856 & 20.2872 & 219.8812 \\ \cline{1-1}  & & Conv. DR & 204.8562 & 306.3114 & 318.4042 & 1253.6116 (W) \\ \cline{1-1}  & & Proposed & 89.4406 & 80.5588 (B) & 116.8470 & 76.27432 \\ \cline{1-1}  & & Conv. DR & 1402.8605 (W) & 1310.4113 & 542.7032 & 1234.7650 \\ \cline{1-1}  & & Proposed & 1191.4488 & 381.7053 & 54.9646 (**B**) & 795.9201 \\ \hline \multirow{8}{*}{RMS} & \multirow{2}{*}{0.1 (s)} & Conv. DR & 35.4947 & 44.3561 & 34.9525 & 660.0443 (W) \\ \cline{1-1}  & & Proposed & 25.2934 (**B**) & 58.5842 & 31.7206 & 442.6126 \\ \cline{1-1}  & & Conv. DR & 335.6079 & 487.8831 & 521.4764 & 2231.1162 (W) \\ \cline{1-1}  & & Proposed & 123.6324 (**B**) & 134.8025 & 228.0809 & 1324.2764 \\ \cline{1-1}  & & Conv. DR & 2576.0799 (**W**) & 2335.0586 & 852.0935 & 2390.7493 \\ \cline{1-1}  & & Proposed & 2089.4001 & 779.0858 & 115.4118(**B**) & 1605.5838 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Analysis of the speed error in the ENU coordinate frame. Figure 16: Comparison of speed error, mean, and standard deviation in region (1): (**a**) has a data reception period of 0.1 s; (**b**) has a data reception period of 0.5 s; and (**c**) has a data reception period of 1 s.  
Figure 17: Comparison of speed error, mean, and standard deviation in region (2): (**a**) has a data reception period of 0.1 s; (**b**) has a data reception period of 0.5 s; and (**c**) has a data reception period of 1 s.  
Figure 18: Comparison of speed error, mean, and standard deviation in region (3): (**a**) has a data reception period of 0.1 s; (**b**) has a data reception period of 0.5 s; and (**c**) has a data reception period of 1 s.  
Figure 21: Comparison of speed error, including RMS, in region (2): (**a**) has a data reception period of 0.1 s; (**b**) has a data reception period of 0.5 s; and (**c**) has a data reception period of 1 s.  
Figure 23: Comparison of speed error, including RMS, in region (4): (**a**) has a data reception period of 0.1 s; (**b**) has a data reception period of 0.5 s; and (**c**) has a data reception period of 1 s.  
Figure 20: Comparison of speed error, including RMS, in region (1): (**a**) has a data reception period of 0.1 s; (**b**) has a data reception period of 0.5 s; and (**c**) has a data reception period of 1 s.