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

TL;DR

This paper introduces BLENDS, a novel data-driven post-processing framework that combines Bayesian learning with deep smoothing to significantly improve inertial-aided navigation accuracy, especially in challenging GNSS scenarios.

Contribution

BLENDS integrates transformer-based neural networks into classical smoothing, learning to adapt covariance matrices and correct errors within a Bayesian framework, addressing systematic biases in GNSS data.

Findings

Achieves up to 63% position accuracy improvement over baseline EKF.

Demonstrates effectiveness on real-world datasets with mobile robots and quadrotors.

Maintains statistical consistency through a Bayesian-supervised loss.

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.