Posterior-Contact Soft-ZUPT for Foot-Mounted Inertial Navigation: Uncertainty-Aware Pseudo-Observation Modeling

Foot-mounted inertial navigation is an important option for pedestrian positioning when external localization infrastructure is limited, unavailable, or unreliable. Its performance, however, depends heavily on zero-velocity updates (ZUPTs), which can become overconfident during heel-strike, toe-off, and other non-ideal contact phases. This paper formulates ZUPT as probabilistic pseudo-observation modeling and introduces posterior-contact soft-ZUPT, in which update strength is controlled by a detector-derived contact prior and an innovation-conditioned posterior within a single error-state Kalman filter. Experiments on the 56-trial foot-mounted VICON benchmark under a two-fold development/evaluation protocol compare the method against hard-ZUPT, robust soft-ZUPT, contact soft-ZUPT, and a foot-instability-based adaptive covariance (FIBA)-like baseline. Posterior-contact soft-ZUPT improves difficult-trial robustness and upper-tail error suppression while remaining competitive in overall accuracy, achieving the best selected p95 and tail-risk values among the compared methods. These results indicate that probabilistic reliability modeling can soften ZUPT effectively while preserving a lightweight single-filter implementation.