# Accurate Collaborative Globally-Referenced Digital Mapping with Standard GNSS
## 2 Previous Work  
Improving the accuracy of maps by averaging GPS/GNSS tracks has been explored previously using a variety of approaches. An early effort, detailed in [8], proposed the precise determination of lane centerlines by clustering and averaging the GNSS tracks of probe vehicles. The accuracy of the estimated centerline was assessed in terms of the spread of GNSS tracks, assuming, without analysis, that the error was zero-mean at every location. Likewise, [9] invoked the zero-mean assumption without examination. More recently, [10] proposed vehicle lane determination via PPP on a rural road under open-sky conditions. The current paper aims to perform localization at a similar accuracy level, but in urban and suburban areas and with the aid of a digital mapping sensor. Minimizing the difference between GNSS measurements and the assigned map coordinates of locations visited multiple times by probe vehicles has been a common feature of the seminal works on map-based precise localization in urban environments for automated driving [4; 5], but no analysis of the accuracy of the resulting map in the global coordinate system was provided. The effect of multipath on measured pseudoranges was studied extensively for various signal types in [11]. However, this study was done under open-sky conditions with a static survey-grade antenna, hardly representative of a mass-market receiver in an urban environment. The effect of multipath from a single large reflector on a static receiver was studied in [12], where it was shown that the position solution of the receiver was significantly biased when tracking multipath-afflicted signals. However, no details were provided about the tracking strategy and navigation filter. Multipath characterization for a dynamic receiver in an urban area was performed in [13], but the study was carried out for a single run through the test area, and many of the important error sources (e.g., atmospheric modeling errors), were assumed to be negligible. A detailed study on the distribution of code-phase and Doppler offsets of the multipath components from individual satellites in a dynamic urban setting was carried out in [14]. However, the error was characterized as the combined distribution of code phase delays over the entire duration of the run, which marginalizes over the temporally- and physically-local biases. On the contrary, this paper explores the errors in the position domain for repeated sessions through a given realization of an urban corridor. Other GNSS error sources such as errors in modeling of ionospheric [15] and tropospheric [16] delay have been studied extensively over many decades, and their long-term error characteristics have also been reported in the literature. However, the impact of these errors on the asymptotic statistics of code-phase-based GNSS position estimates has not been previously presented. To the authors' best knowledge, despite the apparent simplicity of the problem, no prior work has studied the long-term statistics of GNSS errors in an urban environment representative of the conditions to be encountered by consumer vehicles creating digital maps anchored by code-phase-based GNSS positioning. One of this paper's primary contributions is to address this gap in the literature. Sensor fusion of visible-light cameras and GNSS has been extensively studied [17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28]. Some of these works [26; 27; 28] have proposed visual odometry as a replacement for, or an augmentation of, the traditional GNSS/INS architecture. Visual data from cameras are exploited to perform dead reckoning in a visual odometry pipeline, wherein an important distinction from the current paper is that the 3D map points do not persist after a window of time has elapsed--that is, no map of feature points is maintained. Clearly, such an approach does not allow improvement of the 3D map point positions over multiple mapping sessions.