# GPS Multipath Analysis Using Fresnel Zones
## 4 Multipath Analysis from a Spatially-Limited Reflector Using Fresnel Zones
### Measurement Concept and Data Preparation  
Empirical investigations on the relationship between the location and size of the Fresnel zones and the reflecting surface are not easy to realize. Generally, separating the multipath effects from several reflectors is a non-trivial problem, and thus, it seems to be straightforward to reduce the problem on \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Original Data Set**} & \multicolumn{4}{c}{**Classical OAEM**} & \multicolumn{4}{c}{**OAEM with Fresnel Zones**} \\ \hline  & & \(\Delta\mathbf{E}\)**[m]** & \(\Delta\mathbf{N}\)**[m]** & \(\Delta\mathbf{U}\)**[m]** & \(\Delta\mathbf{E}\)**[m]** & \(\Delta\mathbf{N}\)**[m]** & \(\Delta\mathbf{U}\)**[m]** & \(\Delta\mathbf{E}\)**[m]** & \(\Delta\mathbf{N}\)**[m]** & \(\Delta\mathbf{U}\)**[m]** \\ \hline \multirow{3}{*}{**(a)**} & **min** & \(-0.158\) & \(-0.197\) & \(-0.361\) & \(-0.056\) & \(-0.018\) & \(-0.255\) & \(-0.013\) & \(-0.019\) & \(-0.050\) \\  & **max** & 0.09 & 0.264 & 0.949 & 0.111 & 0.089 & 0.471 & 0.029 & 0.032 & 0.030 \\  & **RMS** & 0.003 & 0.004 & 0.008 & 0.003 & 0.004 & 0.008 & 0.003 & 0.004 & 0.007 \\ \hline \multirow{3}{*}{**(b)**} & \multicolumn{4}{c}{**Percentage of outliers** (total number of epochs: 17,128)} \\  & & \(1.0\%\) & \(0.9\%\) & \(1.2\%\) & \(0.9\%\) & \(0.8\%\) & \(1.0\%\) & \(0.6\%\) & \(0.6\%\) & \(0.5\%\) \\ \hline \multirow{3}{*}{**(c)**} & \multicolumn{4}{c}{**Percentage of epochs with fixed ambiguities** (total number of epochs: 17,128)} \\  & & \multicolumn{4}{c}{95.5\%} & \multicolumn{4}{c}{97.2\%} & \multicolumn{4}{c}{99.9\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: **(a)** Minimum and maximum coordinate differences for the East-, North- and Up-component time series and the respective root-mean-squared error (RMS). **(b)** Percentage of outliers with respect to the 3\(\sigma\) boundary. **(c)** Percentage of observation epochs with fixed carrier phase ambiguities. one single reflecting surface--the ground. However, since the ground is usually not spatially limited, it is difficult to answer the question of whether multipath effects will occur even though the Fresnel zones are not fully located on the reflector. Therefore, the field test was carried out on the roof of a building, which, due to its exposed position, was the only dominant reflector in the antenna environment and at the same time, was spatially limited by the roof edges. Due to security and privacy reasons, a UAV flight was not possible, and instead of an aerial image, a colored point cloud of the roof is shown in Figure 16. The point cloud was created using a Leica BLK360 imaging laser scanner and was georeferenced using control points determined via GPS-RTK. The roof has dimensions of 49 times 10.5 m and is covered by roofing felt. Although the roof is the highest point in the surroundings, it is not an completely ideal reflector. The six thin lightning rods shown in Figure 16 could not be removed during the measurements, since the metal wires were attached to a few small concrete brackets along the roof edges. Nevertheless, it can be assumed that their influence on the measurements should be small compared to the multipath effects. Furthermore, their locations are known and it should be possible to trace back anomalies in the observations that can not be explained by ground reflections. For about 24 h, two Leica AS10 GNSS antennas (A and B) in combination with Leica GS25 receivers were mounted on tripods with the same antenna height of \(1.84m\) and were placed at the positions shown in Figure 16. At both stations, dual frequency GPS observations were logged at a sampling rate of 0.2 Hz. After the measurements, the raw observations were synchronized between the two antennas using the GPS time stamps in the respective RINEX files, and the azimuth and elevation angles for all observed satellites were determined from the broadcast ephemeris.