## 3 Localisation of a City Bus with GNSS
### Performance Evaluation of the GNSS-Based Localisation System  
The overall performance of GNSS was evaluated on three different routes in Poznan during the regular operation of an electric bus in city traffic. The average distance and travel time of the analysed routes are presented in Table 1. This table contains also information about the number of RTK FIXED poses registered for each sequence, which translates into the overall reliability of the system. As mentioned before, the RTK FIXED poses indicate the high-precision mode of localisation with centimetre-level accuracy, that is necessary to perform manoeuvres, such as docking to a charging station. Based on these results, it can be stated that only a few percent (1.36%, 6.65%, and 4.14% accordingly) of registered poses are non-RTK ones. They are mainly caused by the poor visibility of the sky because of the roadside buildings and trees. However, it is worth noting that the GNSS signal was available throughout the whole sequences and there are no gaps (i.e., signal outages) in the recorded trajectories. To facilitate statistical analysis of the GNSS localisation performance, the metric of Absolute Trajectory Error (ATE) is introduced, which is a Euclidean distance between the positions of _moving_base_ and _rover_ receivers corresponding in time and averaged along the route (Table 2). In order to calculate the ATE metric in this scenario, the _rover_ coordinates were transformed to the _moving_base_ frame by performing a translation along the longitudinal axis of the bus (in a global coordinate frame) by a vector of length 4.96 m (distance between receivers). This vector corresponds to the exact distance between the two antennas mounted on the vehicle's roof. This translation, however, introduces an additional error to the position of a _rover_, as it depends on the accuracy of heading estimation, which is also provided by the _rover_ receiver. Unfortunately, in the real-world scenario followed in our tests, we have no possibility to measure the error of the heading estimation, as it would require either more precise ground-truth data or using an additional set of two GNSS receivers that would allow us to simply compare their measurements. Nevertheless, the results confirm that the smallest discrepancy between _moving_base_ and _rover_ positions was achieved for the Dworzec Zachodni-Kacza sequence, which is also characterised by the smaller number of non-RTK poses. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{1}{c}{**Sequence (Bus Stops)**} & \multicolumn{1}{c}{**Distance**} & \multicolumn{1}{c}{**Time**} & \multicolumn{1}{c}{**Num. of Precision**} & \multicolumn{1}{c}{**Num. of Poses in**} \\  & & & **RTK FIXED Poses** & **Low Precision Modes** \\ \hline Dworzec Zachodni–Kacza & 7.483 km & 34.77 min & 20,558 & 284 \\ Garbary PKM–Strzeszyn & 11.616 km & 42.42 min & 23,749 & 1691 \\ Garbary PKM–Os. Debina & 9.290 km & 43.93 min & 25,264 & 1090 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The routes of the city bus recorded for the analysis of the GNSS localisation reliability and performance. RTK FIXED poses denote the high-precision mode with centimetre-level accuracy, while low-precision modes include the standard FIX and RTK FLOAT modes, and they indicate the reduced precision of the system. Another factor that could potentially deteriorate localisation accuracy is the mobile network coverage. This is due to the fact that our system requires constant access to the internet in order to receive the differential correction for GNSS receivers. Without these corrections, the bus positioning would be too inaccurate for our system to work properly. Fortunately, this does not apply to our case, as the GSM/LTE network was available all the time during our tests. The described routes were also plotted on the map, as presented in Figure 4A-C. This allowed us to visualise and further analyse the fragments of the trajectories, where the GNSS localisation accuracy was reduced.