# An Improved Single-Epoch Attitude Determination Method for Low-Cost Single-Frequency GNSS Receivers
## 4 Experiments and Results
### Dynamic Experiment  
In this sub-section, we demonstrate the performance of the proposed CLAMBDA-search method for a moving vehicle. The data are collected at the interval of 1 Hz and with a \(10^{\circ}\) elevation cutoff angle. The vehicle speed is about 30 km/h. The baseline lengths are (0.85 and 0.85), (0.85 and 0.85), and (0.83 and 0.85) m. The Taiyuan Street turntable is surrounded by high buildings whose multipath effect is severe, the Hep \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Baseline Length** & **CLAMBDA** & **MCLAMBDA** & \multicolumn{2}{c}{**CLAMBDA-Search**} & \multicolumn{1}{c}{**CLAMBDA-Search**} \\  & & & \(5^{\circ}\) & \(2.5^{\circ}\) \\ \hline
0.3 & 0.71 & 57.01 & 52.63 & 107.19 \\
0.5 & 0.72 & 67.81 & 65.09 & 111.58 \\
1.0 & 0.73 & 154.79 & 71.95 & 140.93 \\
1.5 & 1.34 & 315.64 & 85.14 & 161.82 \\
2.0 & 0.74 & 472.12 & 93.34 & 188.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Calculation time [ms] for each test in the degraded environment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Partition Accuracy** & **Euler Success Rate** & \multirow{2}{*}{\(\delta\overline{\psi}(\sigma_{\delta\overline{\psi}})[^{\circ}]\)} & \multirow{2}{*}{\(\delta\overline{\theta}(\sigma_{\delta\overline{\theta}})[^{\circ}]\)} & \multirow{2}{*}{\(\delta\overline{\gamma}(\sigma_{\delta\overline{\gamma}})[^{\circ}]\)} & **Mean Computing** \\
[\({}^{\circ}\)] & **(Correctly Fixed) [\%]** & & & **Time (ms)** \\ \hline
1.25 & 69.7 (68.4) & \(-0.00\) (0.15) & \(-0.17\) (0.57) & \(0.11\) (0.68) & 330.18 \\
2.5 & 68.4 (67.4) & \(-0.00\) (0.15) & \(-0.17\) (0.57) & \(-0.11\) (0.68) & 161.82 \\
5 & 68.0 (67.0) & \(-0.00\) (0.15) & \(-0.17\) (0.58) & \(0.011\) (0.68) & 85.14 \\
10 & 66.7 (65.7) & 0.00 (0.15) & \(-0.16\) (0.57) & \(-0.11\) (0.69) & 40.63 \\
20 & 61.1 (60.1) & \(-0.00\) (0.15) & \(-0.15\) (0.57) & \(-0.13\) (0.70) & 20.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Euler success rate with various steps for group 1.5 m in degraded environments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Euler Success Rate** & \multirow{2}{*}{\(\delta\overline{\psi}(\sigma_{\delta\overline{\psi}})[^{\circ}]\)} & \multirow{2}{*}{\(\delta\overline{\theta}(\sigma_{\delta\overline{\theta}})[^{\circ}]\)} & \multirow{2}{*}{\(\delta\overline{\gamma}(\sigma_{\delta\overline{\gamma}})[^{\circ}]\)} \\  & **(Correctly Fixed) [\%]** & & & & \\ \hline LAMBDA & \(0.0\) (0.0) & NaN & NaN & NaN \\ CLAMBDA & \(55.3\) (43.1) & \(3.14\) (\(21.80\)) & \(-0.16\) (\(3.41\)) & \(1.78\) (\(20.13\)) \\ MCLAMBDA & \(36.9\) (\(36.8\)) & \(-0.26\) (\(-0.29\)) & \(0.22\) (\(0.53\)) & \(-0.17\) (\(-0.16\)) \\ CLAMBDA-search & \(68.4\) (\(67.4\)) & \(-0.00\) (\(0.15\)) & \(-0.17\) (\(0.57\)) & \(-0.11\) (\(0.68\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: GPS/BDS attitude solution of group 1.5 m in degraded environments. Plaza turntable has tall trees beside the lane, and the open-sky scenario is for Development Avenue turntable, as it shows in Figure 7.  
Figure 8 demonstrates the correlation between the two baselines in the horizontal directions, with the turntable on Taiyuan Street, the Peace Square and the Development Avenue turntable, from top to bottom. It is quite clear that within a 10-min data collection period, the vehicle movement trajectory is very regular, resulting in 18, 9, and 13 circles for the three data sets, respectively. More specifically, we can obtain solutions of 336 epochs in data set 1, and the other two groups of 662 and 651, respectively. The relationship between the horizontal coordinates E and N conforms to a circular pattern, whose radius is the baseline length and origin is the base. When the coordinate in the up direction does not change too much, the projection should be a perfect circle, which means correct fixing. We judge the correctness of the solution subjecting to that the horizontal projection is on the circle and the up direction is equal to the mean value.