# GPS Multipath Analysis Using Fresnel Zones
## 1 Motivation
Since the majority of the aforementioned mitigation techniques deal with signals that are already affected by multipath, the antenna environment and, especially, the Fresnel zones are seldom taken into account. Ray-tracing approaches use models of the antenna environment in order to analyze the signal paths between given satellite and antenna positions [21; 22]. By determining the reflection points on the reflecting surfaces in the antenna surroundings, possible paths of reflected signals can be identified from a geometrical point of view. Hence, ray-tracing enables an assessment of the multipath level at certain positions. Furthermore, based on additional knowledge of the dielectric properties of the reflecting materials, observation corrections can also be derived. Although the antenna environment, in terms of 3D point clouds or virtual city models, is integrated into the multipath analysis, usually only single reflection points are considered in the ray-tracing algorithms and the active scattering regions are not taken into account. One approach to minimize the influence of signal diffraction and NLOS reception is to replace the standard fixed-angle elevation mask with an azimuth-dependent elevation mask that represents the physical horizon from the antenna point of view. In [23], the azimuth-dependent elevation mask was determined using theodolite measurements and compared to a high fixed-angle elevation mask in mountainous regions. It was found that the azimuth-dependent elevation mask mitigates diffraction effects and leads to a higher positional accuracy, since the negative impact on the satellite geometry is lower compared to a high constant cut-off angle. In [24], the derivation of dynamic and azimuth-dependent elevation masks without terrestrial measurements directly from the measured SNR values was proposed. By comparing the SNR values to template functions generated under laboratory conditions, outliers can be erased and afterwards, the dynamic elevation mask can be determined by interpolating between the lowest elevations of the remaining SNR signals of the individual satellite tracks. The approach was tested in several urban scenarios, and it was shown that the quality of a network solution can be improved after application of the dynamic elevation masks to the carrier-phase observation. In [25], georeferenced 3D point clouds were used for the determination of obstruction adaptive elevation masks by extracting the upper borders of the obstruction sources in the antenna environment. After an adjustment of the elevation mask by considering the influence of the uncertainty of the initial antenna position, satellite signals that are subject to NLOS reception and signal diffraction were eliminated from the position estimation, leading to an improvement in the positional accuracy. However, Fresnel zones were not taken into account in any of the aforementioned approaches. In recent years, attempts to use multipath as the signal of interest increased. Especially in the GNSS reflectometry (GNSS-R) community, ground reflected satellite signals are utilized in order to derive information, such as soil moisture content, snow depth or sea water levels [26; 27]. In this context, Fresnel zones are used to identify and select the active scattering regions or sensing zones that contribute to the desired quantities. Furthermore, the Fresnel zones describe the spatial resolution of the GNSS-R experiments [28]. The basic idea is that the spectral content of signal-to-noise time series changes, if, for example, the soil moisture content changes in these regions [29]. The same holds for the sea level estimation. Here, the SNR time series of satellite signals, whose scattering regions are completely located on the water, are used to determine the height of the antenna above the water level [30]. In the context of GNSS-R, large Fresnel zones are preferred to increase the spatial sampling of the data retrieval.