# Accurate Collaborative Globally-Referenced Digital Mapping with Standard GNSS
## 3 GNSS Error Analysis
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In the case of averaging over 100 sessions, the standard deviation is computed based on 10 disjoint averaging ensembles of 100 sessions each. Note that because the simulation study was based on the same 1000 simulations for all averaging ensembles, the east, north, and up means taken across all averaging ensembles are equivalent to those shown in Figure 5. The more interesting trend is the decreasing standard deviation with increasing size of the averaging ensemble, as shown in Figure 6 for the case of NIS-based multipath rejection and for the east and north error components. As expected, the standard deviation of errors was higher at locations where the vehicle moved at low speed and multipath decorrelated slowly. Additionally, the standard deviation was larger at the beginning of the trajectory where the street was lined with tall buildings on both sides. Figure 6: Standard deviation of average position error in east and north directions for NIS-based multipath exclusion as a function of the number of sessions over which the errors are averaged. **Top panel**: standard deviation in the east direction. **Bottom panel**: standard deviation in the north direction. The standard deviation of the average east and north position error over 100 sessions was bounded below 15-20 cm. Thus, it is highly likely that the \(\sim\)40-cm error in the north direction between 15-20 s in Figure 5b is in fact a persistent non-zero bias. Table 3 summarizes the results of the multipath simulation study. It shows the 95-percentile horizontal error magnitude for increasing averaging ensemble sizes and for both ideal and NIS-based multipath exclusion. The 0-60 s average case lists the 95-percentile error over the entire trajectory, whereas the 13-19 s average case lists the 95-percentile error in the worst-case segment of the trajectory in terms of horizontal position bias and standard deviation. This challenging segment is illustrative of persistent problem spots that will arise in urban areas, within which multipath-induced biases will be larger than average. As expected, the 95-percentile error in Table 3 shrank as the averaging ensemble size became larger. For the urban corridor and vehicle dynamics considered in this simulation, NIS-based exclusion achieved 35 cm 95-percentile horizontal error with averaging over 100 sessions. Even in the worst-case region of the trajectory, the 95-percentile horizontal error remained below 50 cm. As multipath exclusion approaches the ideal case, with aid from other sensors or a 3D model of the surroundings, for example, the 95-percentile horizontal error could be reduced to as low as 25 cm for the simulated corridor. From the Section 3.3.3's analysis of asymptotic ionospheric errors, and from this section's multipath simulation study, one can draw the following conclusion: so long as the asymptotic horizontal position errors of the ionosphere corrections are below 5 cm, as is true for the Fast-PPP model, and assuming statistical independence of ionospheric and multipath errors, it appears feasible to achieve 50-cm horizontal positioning accuracy at approximately 95% by averaging over 100 mapping sessions.