# Accurate Collaborative Globally-Referenced Digital Mapping with Standard GNSS
## 5 Empirical Results
### Empirical GNSS Error Analysis  
Figure 13 shows the error in the enhanced code-phase GNSS position solutions with respect to the ground truth. The error is plotted versus the distance along the 1-km loop. The beginning of this loop was taken to be immediately after the overhead pedestrian bridge along the Dean Keeton corridor. It is observed that the enhanced code-phase GNSS errors are clustered separately for each of the campaigns, and that each cluster is offset from zero by as much as 1 m in the horizontal plane. Such error characteristics are representative of ionospheric modeling errors, which have a long decorrelation time. It is also evident that the error variance was larger as the receiver exits the challenging portion of the loop at which point the tracking loops were recovering from signal loss under the bridge. The effect was especially pronounced in the vertical direction. Figure 14 shows similar errors for the commercial ublox M8T receiver. The error traces from the ublox receiver show a wider spread than the enhanced code-phase receiver, likely due to lack of precise orbit and clock corrections. Figure 12: Different visual conditions on two days of data collection. (**a**) An image captured on the first day of data collection. Note the sharp shadows and absence of parked cars. (**b**) An image captured on the second day of data collection. Note the absence of sharp shadows and complete blockage of curb due to parked cars. On the basis of Figures 13 and 14, one might be tempted to conclude that errors in enhanced code-phase and stand-alone GNSS navigation solutions are substantially non-zero-mean, especially in the  
Figure 14: Errors in ublox M8T position estimates with respect to ground truth in the east, north, and up directions. Different colors distinguish data from six different campaigns. Dashed reference lines are drawn at \(\pm\) 50 cm. The solid black lines show the mean positioning error over the six campaigns. The error standard deviation in the east is \(\sim\)1.5 m over the first 100 m along the path and \(\sim\)0.7 m over the rest; \(\sim\)0.9 m in the north; and \(\sim\)2.7 m over the first 400 m and \(\sim\)2 m over the rest in the up direction. Figure 13: Errors in enhanced code-phase position estimates with respect to ground truth in the east, north, and up directions. Different colors distinguish data from six different campaigns. The dashed reference lines are drawn at \(\pm\) 50 cm. The solid black lines show the mean positioning error over the six campaigns. The error standard deviation is nearly constant along the path in the horizontal plane at \(\sim\)0.6 m in the east and \(\approx\)0.4 m in the north direction. In the up direction, the standard deviation is \(\sim\)2.1 m for the first 400 m along the path, and \(\approx\)1.3 m for the rest. north and up directions, despite the overhead GNSS constellation changing substantially between sessions. It certainly appears that the permanent structures (buildings, bridge) along the test loop left a bias in the vertical direction during the first 400 m along the loop. However, the bias in the north direction, and to a lesser extent in the east, may only be an artifact of the small sample size: ionospheric modeling errors were not yet averaged down to nearly zero in the east and \(\sim\)30 cm in the north, as one would expect from the WAAS ionospheric model (see Table 1). Given that the asymptotic properties of ionospheric modeling errors are better understood than those of multipath errors, it is instructive to eliminate, insofar as possible, all ionospheric modeling errors from the along-track error histories. To this end, a differential code phase GNSS technique was applied whereby the navigation solution was based on double-difference pseudorange measurements using data from a nearby reference station at a precisely known location. Such double differencing over a short 1-km baseline eliminates virtually all ionospheric and tropospheric errors, but does nothing to reduce vehicle-side multipath.