# An Improved Single-Epoch Attitude Determination Method for Low-Cost Single-Frequency GNSS Receivers
## 4 Experiments and Results
### Static Experiment

Table 1: SFSE (single-frequency single epoch) ambiguity fixing rate and correct fixed rate of various designed and actual baseline lengths (GPS-only observations, open sky), LAMBDA (approach I), CLAMBDA (approach II), MCLAMBDA (approach III) and CLAMBDA-search (approach IV). The column in the table is the designed baseline length. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Method**} & **0.3** & **0.5** & **1.0** & **1.5** & **2.0** \\ \hline \multirow{3}{*}{I} & b1 & 63.0(63.0) & 12.4(11.2) & 44.9(44.4) & 0.0(0.0) & 19.3(19.3) \\  & b2 & 82.9(82.9) & 9.7(0.0) & 4.8(4.8) & 0.0(0.0) & 1.1(0.0) \\ \cline{1-1}  & b1 & **100(100)** & **99.3**(98.3) & **97.9**(97.2) & 75.0(73.3) & 97.4(97.4) \\ \cline{1-1}  & b2 & **99.4**(99.2) & **98.9**(**98.7**) & 71.6(67.9) & 71.2(57.5) & 51.2(21.3) \\ \cline{1-1}  & b1 & 98.79(78.7) & 98.6(98.6) & 81.8(81.8) & 44.1(44.1) & 37.2(37.2) \\ \cline{1-1}  & b2 & 98.7(98.7) & 96.9(96.9) & 78.6(78.6) & 37.1(36.1) & 26.9(26.1) \\ \cline{1-1}  & b1 & **100(100)** & **99.3**(**98.9**) & **97.9**(**97.9**) & **81.9**(**81.9**) & **99.3**(**99.3**) \\ \cline{1-1}  & b2 & **99.4**(**99.4**) & **98.9**(**98.7**) & **78.2**(78.0) & **73.6**(**71.1**) & **56.7**(**56.0**) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: SFSE ambiguity fixing rate and correct fixed rate of various designed and actual baseline lengths (GPS + BDS observations, degraded). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Method**} & **0.3** & **0.5** & **1.0** & **1.5** & **2.0** \\ \hline \multirow{3}{*}{I} & b1 & 63.0(63.0) & 12.4(11.2) & 44.9(44.4) & 0.0(0.0) & 19.3(19.3) \\  & b2 & 82.9(82.9) & 9.7(0.0) & 4.8(4.8) & 0.0(0.0) & 1.1(0.0) \\ \cline{1-1}  & b1 & **100(100)** & **99.3**(98.3) & **97.9**(97.2) & 75.0(73.3) & 97.4(97.4) \\ \cline{1-1}  & b2 & **99.4**(99.2) & **98.9**(**98.7**) & 71.6(67.9) & 71.2(57.5) & 51.2(21.3) \\ \cline{1-1}  & b1 & 98.79(78.7) & 98.6(98.6) & 81.8(81.8) & 44.1(44.1) & 37.2(37.2) \\ \cline{1-1}  & b2 & 98.7(98.7) & 96.9(96.9) & 78.6(78.6) & 37.1(36.1) & 26.9(26.1) \\ \cline{1-1}  & b1 & **100(100)** & **99.3**(**98.9**) & **97.9**(**97.9**) & **81.9**(**81.9**) & **99.3**(**99.3**) \\ \cline{1-1}  & b2 & **99.4**(**99.4**) & **98.9**(**98.7**) & **78.2**(78.0) & **73.6**(**71.1**) & **56.7**(**56.0**) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: SFSE ambiguity fixing rate and correct fixed rate of various designed and actual baseline lengths (GPS-only observations, degraded). As for the open-sky environment, i.e., Tables 1 and 2, the LAMBDA method has a poor fixing performance in the case of the low-cost receiver SFSE. It is difficult to fix the ambiguity with GPS-only observations, and this may be due to the SFSE solution strategy and fewer satellites. The GPS + BDS solution only obtains satisfactory results in group 1.0 m. This is due to the large pseudorange observation noise of the low-range receiver. The CLAMBDA method with the GPS-only observations does not perform as well as that with the dual-system observations. There is a lot of wrong fixing in the single-system solution. When dual systems are used, the wrong fixing rate is significantly reduced. However, the CLAMBDA method does not show obvious ambiguity fixing improvements with the different baseline lengths. This finding is consistent with that in [PERSON] [28]. The MCLAMBDA method shows reliable results. At last, the CLAMBDA-search method proposed in this paper shows the best performance in both the single-system and dual-system scenarios for all baseline lengths. More importantly, there is no wrong fixing for the dual-system test. This is a remarkable feature for navigation applications with low-cost receivers. As for the degraded environment, i.e., Tables 3 and 4, the LAMBDA method still shows the worst performance. Similarly, the CLAMBDA method has a lot of wrong fixing results, especially in the single-system solution. The MCLAMBDA method still shows reliable results, but the number of solutions is insufficient.