# Development of a Submillimetric GNSS-Based Distance Meter for Length Metrology +
## 3 GNSS Multipath Mitigation  
The GNSS multipath error arises from the fact that the signal from a satellite arrives at the antenna via multiple paths due to reflection and diffraction. These indirect-path signals can distort the received signal by up to one quarter-cycle and this error does not cancel or mitigate when forming the double difference combination. Therefore, GNSSmultipath becomes a critical source of error in high precision applications [28; 35], and even more for length metrology because most of the current calibration baselines of reference, which were set up decades ago before the advent of the space geodesy era, are surrounded by objects such as trees, buildings or other facilities. Multipath interference can be separated into near-field and far-field effects, which do have different properties. Near-field multipath results from the closest vicinity of the antenna, i.e., the first 50 cm around the antenna, and mainly leads to a systematic bias that can be prevented by creating identical near-field situation in all stations which involves the same type of pillars, GNSS antenna model, antenna mounting, and routing of the antenna cable. However, the near-field can also change the electronic properties of the antenna and thus, individual antenna calibrations can be considered accurate as long as the actual near-field situation was reproduced during the calibration procedure. Nonetheless, this refinement is not usually included in the calibration process due to size and weight limitations and it would only make sense if each calibrated antenna was always setup in the same pillar [22; 35; 36; 37]. On the other hand, far-field effects arise from reflecting surfaces in the environment of the antenna such as trees or buildings, and for static surveys, which is the case at hand, lead to short periodic errors. Following the traditional geodetic approach, the far-field multipath is generally assumed to average out by sufficiently long observation times [35; 38; 39]. In consequence, this approach is particularly valid for permanent GNSS stations which have a favourable observational environment and 24-h sessions but cannot always be applied to calibration baselines and short time spans. Our initial approach to cope with multipath was based on the use of the signal-to-noise ratio flag and global robust estimation [40]. Interestingly for our study, the trees surrounding the UPV calibration baseline, which were young in 2012, are increasing in size as the years go by. As a consequence, our former approach to cope with multipath, based on the use of the signal-to-noise ratio flag and global robust estimation [40], cannot be successfully applied under these new conditions. To give a picture of the problem, some DD residuals which were obtained in our experiment are plotted in Figure 3. It can be clearly seen that the L1 DD residuals range from 0.04 m to \(-\)0.05 m and they cannot be considered Gaussian. Therefore, the obtained distance will be biased. In addition, the L2 DD residuals are bigger, as expected, and follow a different pattern than the L1 DD residuals. Similar residuals were found in other DD combinations. Over the last 10 years, the Space Geodesy and Navigation Laboratory of University College London (UCL) have developed and successfully applied techniques for GNSS multipath detection and mitigation, some of them suitable for GNSS processing for distance determination [31; 32; 41; 42]. Specifically, we have now implemented the observation-domain sidereal filtering technique and the signal-to-noise ratio (SNR) estimator. The sidereal filtering technique [31; 32] takes advantage of the consecutive passes of each satellite to predict the multipath error. As long as both azimuth and elevation repeat for the same satellite, the multipath effect can be considered similar, and subsequently corrected.