arXiv:2610.32259v1 Announce Type: cross Abstract: Protection levels (PLs) bound position errors under specified fault hypotheses and risk budgets, but advanced re-ceiver autonomous integrity monitoring (ARAIM) is formulated for snapshot GNSS estimation rather than the correlated poste-rior of tightly coupled GNSS/IMU factor graph optimization (FGO). This paper formulates ARAIM solution separation and PL computation on the FGO posterior. Because current-epoch pseudorange factors enter only the current-state block of the fixed-lag information matrix, the fault-excluded position covari-ance, solution separation, and nominal-bias propagation follow exactly from the linearized current-state marginal, which re-tains correlations with velocity, IMU-bias, and clock states and with historical information. Woodbury updates with selected-output evaluation compute these quantities for fault-free, single-satellite, constellation-wide, and second-order hypotheses with-out repeated full-state inversion or graph re-optimization. Sur-rounding monitoring layers screen measurements, handle post-fit outliers, and determine PL validity and availability. In two road experiments, both nominal sequences achieve 100% hori-zontal and vertical empirical bounding over PL-valid epochs, with a maximum error-to-PL ratio of 0.96. Normalized errors show that the posterior covariance alone does not capture slowly varying ranging biases: a covariance-only bound computed from the same posteriors retains no resolvable margin, and strong temporal correlation limits the empirical evidence to consisten-cy checks rather than validation of the integrity budget. On identical Experiment A posteriors, the proposed method reduces fault-hypothesis evaluation and PL solving time by 65.2% rela-tive to direct full-state inversion with matching integrity deci-sions, and controlled fault injections demonstrate fail-safe PL invalidation while navigation continues.