Bayesian Learning-Enhanced Navigation with Deep Smoothing for Inertial-Aided Navigation

arXiv cs.RO / 3/27/2026

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Key Points

The paper introduces BLENDS, a data-driven post-processing navigation framework that combines Bayesian learning with deep smoothing to improve inertial-aided navigation accuracy beyond classical smoothers under Gaussian assumptions.
BLENDS augments a two-filter smoother with a transformer-based neural network that learns to adjust filter covariance matrices and apply an additive correction to the smoothed error-state within a Bayesian-consistent estimation loop.
It proposes a novel Bayesian-consistent loss that jointly supervises the smoothed mean and covariance to enforce minimum-variance estimates while maintaining statistical consistency.
Experiments on two real-world datasets (mobile robot and quadrotor) show BLENDS delivers up to 63% horizontal position improvement over a baseline forward EKF across unseen trajectories.

Abstract

Accurate post-processing navigation is essential for applications such as survey and mapping, where the full measurement history can be exploited to refine past state estimates. Fixed-interval smoothing algorithms represent the theoretically optimal solution under Gaussian assumptions. However, loosely coupled INS/GNSS systems fundamentally inherit the systematic position bias of raw GNSS measurements, leaving a persistent accuracy gap that model-based smoothers cannot resolve. To address this limitation, we propose BLENDS, which integrates Bayesian learning with deep smoothing to enhance navigation performance. BLENDS is a a data-driven post-processing framework that augments the classical two-filter smoother with a transformer-based neural network. It learns to modify the filter covariance matrices and apply an additive correction to the smoothed error-state directly within the Bayesian framework. A novel Bayesian-consistent loss jointly supervises the smoothed mean and covariance, enforcing minimum-variance estimates while maintaining statistical consistency. BLENDS is evaluated on two real-world datasets spanning a mobile robot and a quadrotor. Across all unseen test trajectories, BLENDS achieves horizontal position improvements of up to 63% over the baseline forward EKF.