Incremental-Smoothing-Based ARAIM Protection Levels for Tightly Coupled GNSS/IMU Integration in Urban Canyons

Protection levels (PLs) bound position errors under specified fault hypotheses and risk budgets, but advanced receiver autonomous integrity monitoring (ARAIM) is formulated for snapshot GNSS estimation rather than the correlated posterior 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 covariance, 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 reoptimization. Surrounding monitoring layers screen measurements, handle post-fit outliers, and determine PL validity and availability. In two road experiments, both nominal sequences achieve 100% horizontal 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 consistency 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% relative to direct full-state inversion with matching integrity decisions, and controlled fault injections demonstrate fail-safe PL invalidation while navigation continues.