  Accurate and globally referenced global navigation satellite system (GNSS)
based vehicular positioning can be achieved in outlier-free open areas.
However, the performance of GNSS can be significantly degraded by outlier
measurements, such as multipath effects and non-line-of-sight (NLOS) receptions
arising from signal reflections of buildings. Inspired by the advantage of
batch historical data in resisting outlier measurements, in this paper, we
propose a graduated non-convexity factor graph optimization (FGO-GNC) to
improve the GNSS positioning performance, where the impact of GNSS outliers is
mitigated by estimating the optimal weightings of GNSS measurements. Different
from the existing local solutions, the proposed FGO-GNC employs the non-convex
Geman McClure (GM) function to globally estimate the weightings of GNSS
measurements via a coarse-to-fine relaxation. The effectiveness of the proposed
method is verified through several challenging datasets collected in urban
canyons of Hong Kong using automobile level and low-cost smartphone level GNSS
receivers.
