# GPS Multipath Analysis Using Fresnel Zones
## 5 Conclusions and Outlook  
In the context of GPS, Fresnel ellipsoids describe the region between the satellite and user antenna where most of the signal energy is transmitted. The intersection of the ellipsoid with a reflecting surface leads to Fresnel zones, the active scattering regions that cause signal reflection and, in turn, lead to multipath effects after the superimposition with the signal received on the direct signal path.  
Figure 22: Correlation of simulated and observed \(\delta\)-SNR time series for satellites G14 (**top** two panels) and G19 (**bottom** two panels). The grey shaded region represents the part of the observation duration where the Rayleigh criterion is fulfilled.  
Within this study, two aspects of using Fresnel zones in the context of GPS multipath were addressed. First, an algorithm for the identification of diffracted signals was proposed. Herein, Fresnel zones are determined for the line-of-sight transmission between the satellite and the user antenna. By comparing the borders of the Fresnel zone to an obstruction adaptive elevation mask, satellite signals that are potentially distorted by signal diffraction are identified and excluded from the position estimation process. The data of a field test was used to evaluate the proposed algorithm and it was found that both the positional accuracy and the percentage of epochs with fixed ambiguities improved.  
Second, theoretical prerequisites for the occurance of multipath that are related to the location and size of the Fresnel zones were assessed. Therefore, the simulated and observed SNR time series of two antennas on a building roof were compared and related to the size and location of the Fresnel zones with respect to the spatially limited horizontal reflector. The results reveal that in contrast to the theoretical assumptions, multipath already can occur if the percentage of overlap between a Fresnel zone and a reflecting surface is above 50% and the reflection point of the satellite signal is located on the reflecting surface.  
Although in most GNSS applications spatially limited reflectors are most often found in terms of buildings or other man-made objects, similar investigations in such environments are hard to realize. In particular, the separation of multipath effects induced from several reflectors is a non-trivial problem. Nevertheless, since Fresnel zones can also be determined on arbitrarily oriented reflectors, the findings of this study are transferable to more complex environments. In particular, the quality assessment of planned or already existing GNSS stations could profit from the enhanced detection of possible reflecting surfaces. This is subject to current research and is part of the further investigations in this context.  
[PERSON] conceived, designed and performed the experiments, analyzed the data and wrote the paper; [PERSON] implemented the determination of Fresnel zones and was involved in preparatory investigations; [PERSON] was involved in the data analysis of the SNR simulation; all authors read and improved the final manuscript.  
This research was funded by the DFG (Deutsche Forschungsgemeinschaft) under the project number 1505 \"Mapping on Demand\".  
The authors would like to thank [PERSON] and [PERSON] for their assistance during the UAV flights and TLS measurements.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} GNSS & Global Navigation Satellite System \\ GNSS-R & GNSS reflectometry \\ NLOS & Non-line-of-sight \\ OAEM & Obstruction adaptive elevation mask \\ RMS & Root-mean-square \\ RTK & Real Time Kinematic \\ SNR & Signal-to-Noise ratio \\ TLS & Terrestrial Laser Scanner \\ UAV & Unmanned Aerial Vehicle \\ VRS & Virtual Reference Station \\ \end{tabular}