# GNSS Code Multipath Mitigation by Cascading Measurement Monitoring Techniques
## 6 Field Data Analysis
### Static Test
#### 6.1.2 Position Results
It was generally observed that CMC-based error corrections effectively smooth position errors except during intervals when cycle-slips degrade the performance of the monitoring approach. Numerical results are presented in Table 1 and Figure 13a (labeled as A3). Based on the corresponding 3D RMS values, the CMC-based error correction shows a 18% improvement over a C/N\({}_{0}\)-based LS solution with no correction. Lower performance is expected as the multipath environment worsens. The combination of CMC error corrections and GF detection and exclusion was investigated next. Referring to the discussion in Section 5, due to the good visibility of satellites on different frequencies (mostly on L1 and L2C), the first cascading approach was used. Multipath errors were first alleviated by applying CMC-based error corrections on pseudoranges and then the GF detection metrics were performed on L1-L2C and L1-L5 combinations using the (partially) corrected measurements. Detection results are then exploited to exclude affected measurements in the consecutive exclusion approach discussed in Section 4.2. For included measurements, the C/N\({}_{0}\)-based stochastic model is applied to determine the corresponding variance factors. Results have been plotted in green in Figure 12. Numerical results have been presented in Table 1 and Figure 13a (labeled as A4). It is observed that positioning performance improved by 38% for 3D positioning RMS values which is higher than those resulting from the single detection/exclusion or CMC-based error correction techniques. This confirms the effectiveness of cascading monitoring techniques presented in Section 5, resulting in additional performance for multipath mitigation. Figure 12: GPS L1 frequency position errors—Red: C/N\({}_{0}\)-based LS solution with no correction or exclusion (benchmark)—Blue: C/N\({}_{0}\)-based LS solution with CMC-based error correction—Green: Combination of a preceding CMC-based error correction followed by the GF-based multipath detection and exclusion in a C/N\({}_{0}\)-based LS solution. For L2C and L5 positioning, a similar procedure was used (as with the L1 frequency) but based on their corresponding detection metrics. The only major difference was in the L5 case where due to low satellite visibility, the iterative change of measurement weights (de-weighting approach) was used (instead of excluding measurements) to keep all measurements. Referring to Section 4.2, a linear function of iteration number was used to de-weight detected measurements with the maximum number of iterations set to 100 and observed enough to reach the predefined geometry threshold. Table 1 shows the corresponding position errors for L1, L2C and L5 signals. The graphical presentations are shown in Figure 13. The number of satellites broadcasting signals on L2C and L5 frequencies is generally lower than L1, hence geometry is poorer in the former case and position errors are higher; the detection/exclusion or detection/de-weighting techniques therefore yield a lower performance compared to the GPS L1 positioning solution. The mean and RMS values have been extracted for the intervals where the number of satellites is four or more and the position solution has converged. It was also observed that for L2C and L5 positioning (compared to L1), the position results are more biased during several intervals of the data sets due to poorer geometry. While these positive and negative sign biases partly cancel out their effects on the overall mean value, they limit improvement in the RMS values when CMC corrections smooth position results. In general, the lowest RMS values relate to the proposed combined method where multipath errors are first alleviated by applying CMC-based error corrections and then the corresponding GF detection metrics are used to detect and exclude (or de-weight) remaining multipath errors. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Signal**} & \multirow{2}{*}{\ \begin{tabular}{c} **Positioning** \\ **Approach** \\ \end{tabular}