Integrity-Constrained Factor Graph Optimization for GNSS Positioning in Urban Canyons

Global navigation satellite system (GNSS) integrity monitoring (IM) has been introduced in aviation, but remains challenging for urban scenarios because of limited satellite visibility and strong multipath and non-line-of-sight effects. Consequently, factors such as limited measurement redundancy and inaccurate uncertainty modeling significantly compromise positioning and IM performance. To alleviate these issues, this paper proposes an integrity-constrained factor graph optimization model for GNSS positioning augmented by switch variables. In contrast to conventional IM methods, this method enhances redundancy through the factor graph structure. Instead of directly excluding measurements, the proposed method reweights the measurements by using switch variables to satisfy a chi-square test constraint within the optimization, ultimately yielding optimal positioning accuracy. Moreover, a proper protection level that conservatively bounds the positioning error can be derived by using the modified weighting matrix under a single-fault assumption. The effectiveness of the proposed method was verified based on data sets collected in open-sky and urban-canyon areas in Hong Kong.