## 6 Test Results  
Table 9 shows the detection results (recall, rate of false detection, and accuracy) of Tests 1, 2, 3, and 4. The results of Test 1 show that the trained detector can achieve a recall of 77-87% (i.e., detect about 80% multipath measurements) with a rate of false detection of about 16% in Test 1. The detection accuracy is about 80%. Unlike simulated data, available GPS L2C and L5 data in the real kinematic datasets are not sufficient for training. Only one GPS IIF satellite (i.e., with L5 signal) and two GPS satellites with L2C signal are available in kinematic Dataset KTR2. Therefore, L5 data and L2C and L5 data are not processed in Tests 3 and 4. In Tests 2 and 3, the results show that the trained detector can achieve accuracy of about 70%. Comparing with simulated data, the real data have higher rates of false detection (over 30%). This is because a real multipath signal may have small magnitudes of multipath errors labelled as direct-signal only; they are sometimes comparable to the carrier phase measurement noise. An example of this is shown in Figure 10, where red dots represent 'true' residuals of measurements detected as multipath, and blue dots represent those detected as direct-signal only. Squared boxes in Figure 10 show typical multipath signals with small magnitudes of multipath errors. Results of Test 4 in Table 9 show that the trained detector can still detect multipath errors with degraded recall of about 70% when the test dataset and training dataset are collected in different environments (near a wall on rooftop and near a building). The moving trajectories and positions of pegs are shown in Figure 11.  
Figure 10: ‘True’ double-differenced carrier phase residuals of detected multipath measurements (red dots) and direct-signal only measurements (blue dots) in Dataset KTR1 (GPS L1 C/A data). Red dots in the squared areas represent multipath errors with small magnitudes. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tests** & **Signal** & **Recall (\%)** & **Rate of False Detection (\%)** & **Accuracy (\%)** \\ \hline
1 & L1 C/A & 79.8 & 16.2 & 82.2 \\
1 & L2P(Y) & 77.7 & 16.4 & 81.2 \\
1 & L2 C & 82.2 & 25.8 & 76.8 \\
1 & L5 & 86.8 & 13.6 & 86.6 \\
2 & L1 C/A & 81.5 & 28.4 & 74.6 \\
2 & L2P(Y) & 80.2 & 34.4 & 69.1 \\
2 & L2 C & 74.5 & 34.4 & 67.7 \\
2 & L5 & 66.2 & 37.7 & 63.0 \\
3 & L1 C/A & 75.7 & 35.9 & 66.7 \\
3 & L2P(Y) & 81.9 & 35.0 & 68.9 \\
4 & L1 C/A & 73.8 & 31.1 & 61.5 \\
4 & L2P(Y) & 69.4 & 37.5 & 55.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results of Tests 1, 2, 3, and 4. Tables 10 and 11 show the Root Mean Square (RMS) positioning errors in horizontal and height components and 3D of the positioning solutions using simple elevation model, SIGMA-\(\varepsilon\) model, and new model based on down-weighting the detected multipath measurements (with Equation (10)). The improvements of percentage are relative to the standard least squares solution (i.e., without a stochastic model). The results in Table 10 show that SIGMA-\(\varepsilon\) model and the proposed method outperform the standard least squares method and simple elevation model. However, Table 11 shows that the performance of the simple elevation model in Dataset KTE3 is better than that in Dataset KTE1. This is because errors (excluding multipath error caused by walls) in Dataset KTE1 collected on the rooftop are less elevation dependent compared with errors in KTE1 collected on the ground with some trees nearby (see Figure 6). The positioning errors in Table 10 (KTE1) are generally larger than those in Table 11 (KTE3) as the environment of data collection of KTE3 is more difficult than that of KTE1 (as shown in Figure 6). The deterioration for SIGMA-\(\varepsilon\) and the proposed models are probably due to the weakened satellite geometry. Generally, all the multipath mitigation methods have better positioning accuracies when compared with the standard least squares method. The improved positioning accuracy validates the proposed multipath detection method in position domain.