# GPS Multipath Analysis Using Fresnel Zones
## 1 Motivation  
The signals from GNSS (Global Navigation Satellite Systems) satellites can be used to estimate the position of the user antenna. Especially in applications with high accuracy requirements, appropriate countermeasures have to be applied to account for the systematic observation errors, influencing the accuracy of the positioning solution. In differential approaches, the position of the user antenna is determined relative to a master antenna. By forming double-differences of the observations simultaneously received at the master and user antenna, the majority of systematic errors, such as orbital and atmospheric errors, can be eliminated or at least minimized. After this processing step, site-dependent effects remain accuracy-limiting factors, since these errors depend on the individual antenna environment and cannot be eliminated by differential techniques. Although site-dependent errors are often generalized as multipath, it is necessary to distinguish between four effects: (1) far-field multipath, (2) non-line-of-sight (NLOS) reception, (3) signal diffraction and (4) near-field effects. Far-field multipath occurs when the direct GNSS signal that has arrived through the line-of-sight (LOS) path is superimposed by a reflected signal that reaches the antenna on one or more indirect paths [1]. If the direct signal is completely blocked by an obstacle and only the reflected signal arrives at the antenna, one speaks of NLOS reception [2]. Signal diffraction describes the phenomena where the direct signal path is also blocked but the signal is diffracted, for example, at an edge of an obstacle [3]. Finally, near-field effects arise from the closest vicinity of the antenna and can lead to an altering of the electrodynamic properties of the antenna itself [4]. However, in thispaper, we focus on far-field multipath effects and signal diffraction, and for the sake of simplicity, far-field multipath is referred to as multipath hereafter. Besides the distinction between the aforementioned effects, it is also necessary to discriminate between code- and carrier-phase multipath. Depending on the severity of multipath conditions, the code-multipath error can range between several meters up to 100 m, while the carrier-phase multipath error is limited to a few centimeters [1]. Thus, in the case where both observation types are used, the code-multipath error will be the dominant influence. Especially for applications where an instantaneous carrier-phase ambiguity resolution is needed, this is a crucial factor. Since the dimensions of the search space for the ambiguity resolution usually depend on the accuracy of the code observations, the code-multipath can enlarge the search space, and thus, the ambiguity resolution can take longer [5]. As a consequence, positioning techniques that only use carrier-phase observations, e.g., as presented in [6], are of special interest, since such approaches eliminate the dominant influence of the code-multipath. The majority of multipath mitigation techniques are either data-driven approaches, or they are related to the receiver architecture or special antenna design. A detailed overview of multipath mitigation techniques can be found in [7]. Data-driven approaches, such as sidereal filtering [8; 9; 10; 11], multipath stacking maps [12; 13; 14] or signal-to-noise (SNR)-based filtering and modeling [3; 15; 16; 17], have been developed to minimize the influence of multipath interference. The purpose of receiver-internal techniques, such as different correlator spacings or the Multipath Estimation Delay-Lock-Loop [18], and special antenna designs, such as choke-rings or ground planes [19], is to identify or suppress reflected signals. However, multipath occurrence mainly depends on the roughness of the reflecting surface and the size of the active scattering region, which can be determined using the concept of Fresnel zones. That means, from a theoretical point of view, that only if the reflecting surface is smooth and large enough can multipath occur [20].