# Development of a Submillimetric GNSS-Based Distance Meter for Length Metrology +
## 3 GNSS Multipath Mitigation
For GPS satellites, the repeating time is one sidereal day, which makes the technique attractive to use if data from consecutive days are available, whereas for Galileo satellites the repeating time increases to 10 sidereal days and the use of the technique would require GNSS observation sessions 10 days apart, which is impractical. In what follows, we will restrict the application of the sidereal filtering technique to GPS observations only. In contrast, the SNR estimator does not provide a value for the multipath error [41]. By differencing SNR measurements on different frequencies and comparing the result with that obtained in a low-multipath environment, multipath can be detected. The result is a number that can be used, in theory, to identify the presence of multipath. To characterize a low-multipath environment, we opted for the VALE permanent station. It is only 100 m away from the UPV calibration baseline and its equipment (Leica GR10 receiver and Leica AR25.R3 antenna) is very similar to the equipment used in our experiment described in the next section. Figure 4 shows the SNR estimator for the Galileo satellite that was selected as a low-multipath reference. The line in black is the expected value, and in green, orange and red are respectively the \(1\sigma\), \(2\sigma\) and \(3\sigma\) thresholds. If the estimator is clearly above the red line, multipath is considered to be present. Both techniques, sidereal filtering and SNR estimator, may be complementary. This is important since each technique may on certain occasions yield null values even when multipath is present. Conversely, depending on some aspects of the PPP implementation, e.g., cycle-slip detection and correction strategies, the residuals obtained could be abnormally high with no relation to multipath. However, matching residuals by using azimuth and elevation has clear advantages over time. First, the technique is independent of the value of multipath and does not need to rely on the identification of the correct satellite  
Figure 4: Low-multipath function used as reference to compute the SNR estimator for Galileo satellites. Figure 3: Example of double difference (DD) residuals that were obtained using Bernese 5.2.  
repeat period (a significant problem so far, as pointed out in Reference [43]). Second, the multipath model could be eventually parameterised in terms of azimuth and elevation even for the satellites with low multipath. In summary, the whole process to mitigate multipath in the context of GBDM consists of the following four steps  
1. To obtain a PPP solution for each site and for every day using an ionosphere-free combination. 2. To match the ionosphere-free observation residuals on successive days using azimuth and elevation in order to obtain a site-specific and time-specific multipath model for an ionosphere-free combination. 3. To form ionosphere-free DDs using the obtained multipath models with the same DD scheme that will be eventually used in the final L1/E1 solution. 4. To determine the L1/E1 DD multipath corrections from the previous values by using DD residuals from an independent DD solution and the same ionosphere-free combination that was used to obtain the PPP solution. In the first step, the PPP solution is obtained with an epoch-wise processing strategy that uses an ionosphere-free combination with floating ambiguities. Some advantages of this straightforward approach are that the bulk of the ionosphere error is removed, the multipath error is amplified with respect to that of the original observed frequencies, and it can be implemented in real-time if desired. Nevertheless, part of the multipath error could slip into other parameters and errors caused by the imperfect modelling of other parameters (receiver clock, troposphere delay, phase ambiguities) could be wrongly considered as multipath. For that reason, it is relevant to look for a repeating pattern in the second step. Only the residuals that follow a sidereal pattern can be considered as multipath error.