Matched Forward-Processing Comparison of EKF and Incremental FGO for Smartphone Carrier-Phase Differential GNSS Positioning

This study compares an extended Kalman filter (EKF) and incremental factor graph optimization (FGO) for smartphone carrier-phase differential global navigation satellite system (GNSS) positioning with float ambiguities. Both receive identical physical observation candidates from a common front end but retain distinct state parameterizations, screening, weighting, ambiguity handling, and update procedures. Forward-only offline replay uses measurements available up to each epoch without revising previous outputs. Twelve auxiliary-observation configurations are evaluated across 154 route–phone pairs and 59 equally weighted driving sessions. Under Base, FGO has a higher mean Google Smartphone Decimeter Challenge score than EKF (3.600 versus 2.825 m). Combining all auxiliary observations (All) reduces the FGO mean score by 8.4% relative to EKF (2.622 versus 2.864 m), but this advantage comes from a few influential sessions: FGO wins only 29 of 59 sessions, and the exploratory 95% confidence interval of the paired mean difference (−1.427 to +0.599 m) includes zero. Removing time-differenced carrier phase (TDCP) from All improves EKF but worsens FGO, and this opposite response strengthens when both estimators use the same TDCP acceptance rule and uncertainty. Including a separately reported case with asymmetric estimator-output support reverses the All ranking. The results characterize the tested implementations, not general FGO superiority.