A Decoupled Variational Bayesian Adaptive Kalman Filter for MEMS INS/GNSS Integrated Navigation under Time-Varying Noise Covariances

We evaluate a decoupled variational Bayesian adaptive Kalman filter (D-VBAKF) for MEMS INS/GNSS navigation, combining bounded fading-memory covariance matching for R with motion-regularized Bayesian model averaging over scaled Q candidates. In 50 paired trials of a 15-state, 120 s prescribed-noise simulation, 3D position RMSE reductions versus EKF-Fixed were 2.94 m (nominal paired 95% interval [1.59, 4.29] m) for 10 s outages and 7.76 m ([1.51, 14.02] m) for 30 s outages. At 60 s, intervals versus EKF-Fixed and joint-VB VBAKF included zero; all 90 s intervals included zero. In the separate no-outage simulation, Q-KL was 0.011, and the R relative error was 0.173. On one 1617 s ICM20602 drive with deterministic GNSS perturbations, full-route 3D RMSE was 27.19 m versus 30.77 m for EKF-Fixed. Across twelve repeated outage windows on that drive, the R-only variant yielded 28.19 m versus 28.86 m for the full method; BMA-Q only yielded 33.98 m versus 33.23 m for EKF-Fixed. Thus, the real-data experiment did not demonstrate an incremental accuracy benefit from adding BMA-Q to R-only adaptation, and validation on a single drive limits the generalizability of the findings. NIS coverage was 0.636 for D-VBAKF and 0.626 for EKF-Fixed, both below the nominal 0.95.