## 3 Data Processing  
The data processing chain implemented in this paper can be described as follows:  
* Analysis of data quality from different receivers operating in GNSS mode;
* Reference trajectory computation from MMS measurements;
* Trajectory computation from low-cost devices, namely u-blox ZED-F9P, ZED-F9R, and Xiaomi Miss, and Septentrio AsteRx-U professional geodetic receiver; and
* Evaluation of the performances of low-cost GNSS/INS devices compared to the professional MMS system and the Septentrio AsteRx-U geodetic receiver.  
The trajectories from all the receivers, including MMS, were computed by the post-processing relative double-difference carrier-phase technique. For the MMS, the Position and Orientation System Post-Processing Package (POSPac(tm) Mobile Mapping Suite (MMSTM) was used [45], which provides a deep level of sensor integration and error modelling and processing modes. For relative double difference positioning, the nearby Trieste reference station (the distance from the study area was around 11 km) belonging to the Antonio Marussi Friuli Venezia Giulia Region GNSS network was used [46]. Observations for geodetic and low-cost receivers, namely u-bloxes and Xiaomi Miss, were processed using RTKLIB software, demo 5, version b34d [47; 48].  
RTKLIB is an open-source program package for standard and precise positioning and consists of a portable program library and several APs (application programs). It supports: (1) standard and precise positioning algorithms with GPS, GLONASS, Galileo, QZSS, BeiDou, and SBAS; (2) single, DGPS/DGNSS, kinematic, static, PPP-kinematic and PPP-static positioning modes with GNSS for both real-time and post-processing. A number of features may contribute to its superior performance compared to the software, namely: (a) it is free, while commercial software comes with a cost that can be significant for some users; (b) flexibility in adjusting the processing parameters so that better results can be achieved; (c) possibilities to improve the current version of RTKLIB also by changing some algorithms.  
Since the MMS relay on GPS-only constellations, the initial processing strategy for all the used receivers was based only on GPS; successively, a multi-constellation solution using GPS, GLONASS, and Galileo was applied. For static mode ambiguity resolution, the \"fix-and-hold\" mode was used, which allows a GNSS receiver to maintain positioning even if the number of visible satellites decreases or the measurement quality degrades. In contrast, the \"continuous\" ambiguity mode was used for kinematic positioning because in this mode, ambiguities are resolved in real time and solutions are continuously updated as new observations become available. Since there were many obstacles along the roads, the lower obstacles were bypassed at the cut-off angle at 15\({}^{\circ}\).  
Observations were processed using broadcast ephemerides, ion-free mode, and [PERSON]'s tropospheric delay model. Unfortunately, there are no available antenna calibrations for the patch antennas of the u-blox receivers ZED-F9P and ZED-F9R and for the Xiaomi smartphones, as there were for the Septentrio AsteRx-U. However, in this research, an approximated antenna phase centre offset was calculated based on the procedure proposed by [PERSON] et al. (2019) [49], which is based on averaging post-processed coordinates in northing and easting (reference was added). This study was performed prior to this particular experiment in the static mode. All additional processing settings used are listed in Table 1.  
To investigate the benefits of multi-constellation, observations from the Septentrio AsteRx-U, the ZED-F9P and ZED-F9R u-bloxes and the Xiaomi Miss were also processed for GPS, GLONASS and Galileo, but without BeiDou, since the Marussi Network reference station, configured to collect observations from only three constellations, was used for relative positioning. Finally, the provided geographic coordinates were projected into the reference system UTM ETRS.