## 3 Measurement Weighting and Exclusion (WE)
### Measurement Exclusion  
In order to evaluate the effects of multipath into the 2 pol antenna outputs, it is firstly important to analyze the benign scenario (see Figure 5a). This will give us an idea of how the antenna is behaving under nominal conditions. Then, any anomalous behavior departing from the nominal one will be associated to multipath. Specifically, the RLR in the benign scenario is used to determine three different zones as done in Ref. [11] and as shown in Figure 7a, namely  
* **Nominal** (green area): Above the fifth percentile of the RLR in the benign scenario. In this area the received multipath is considered to be the one received under nominal conditions and the measurements should be considered by themselves (or traditional weighting). * **Weighting area** (yellow area): In the range from 0 dB to the fifth percentile of the RLR in the benign scenario. In this area the received multipath is considered to be moderate (subject to a more severe multipath than in the benign scenario) and the measurements should be weighted down. * **Exclusion area** (red area): Below the exclusion threshold. Theoretically, the exclusion threshold should be a ratio equal to 0 dB. In practice, this threshold must be calibrated. In this area, the received measurements can be considered to be obtained under NLOS conditions, thus they should be excluded. Figure 6: Ratio between RHCP and LHCP components in a sky plot. (**a**) Benign test scenario, and (**b**) Urban test scenario together with the elevation masks corresponding to the buildings in the scenario (see Figure 5a). Results for GPS L1 (up), GPS L2 (middle) and GLO L1 (down). Furthermore, Figure 7b shows the three different zones together with the mean value of the RLR, as well as the 95- and fifth percentile curves of this ratio, as a function of the elevation angle for the data captured in the foliage scenario. The results clearly suggest the presence of multipath due to the fact that around half of the RLR (see solid black line) measurements lie in the weighting area (yellow area), which is an indicative that these data are contaminated by multipath. Moreover, more than the 5% of the data in the foliage scenario (see fifth percentile line) is in the exclusion area (red area), thus being an indicative of NLOS conditions and very large errors. These experiments verify the utility of the RLR to identify the presence of multipath on GNSS signals. Now, we have to fix the exclusion threshold used to exclude the measurements. This threshold is of particular interest because it denotes the bound between the cases in which it is useful to mitigate multipath or not. Often, the latter is associated with NLOS propagation for which mitigation has no sense. In Figure 7 this threshold is fixed to 0 dB, which is the ballpark figure for exclusion [11]. Nevertheless, due to the complexity of signal propagation, this threshold may be different. For instance, NLOS can have positive RLR (in dB units) if the reflection incidence angle is above the Brewster's angle. In addition, LOS may have negative ratio (in dBs) in case multiple LHCP multipath rays interfere constructively. With the aim of fine tuning the exclusion threshold, we will make use of the data collected at the urban scenario. This is so because this scenario includes two buildings in know locations that block the visibility of some satellites. Using the know locations of the buildings we can draw an elevation mask, as shown in Figure 8, in order to know when some satellite is completely blocked by the building, thus if received, it is likely to be received under NLOS conditions. In this way, taking the mean value of the RLR of those satellites obstructed by the buildings we can estimate the value of the exclusion threshold. For instance, we see in Figure 8a that the satellite G31 is obstructed by the southern building from an elevation of \(60^{\circ}\). Doing so, the selected threshold for the exclusion zone is equal to \(-1\) dB.