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

2026-03-26

AI Summary

This work addresses the persistent challenge of systematic position biases in loosely coupled INS/GNSS systems caused by raw GNSS measurements, which conventional model-driven smoothing approaches struggle to mitigate effectively. To this end, the authors propose BLENDS, a novel framework that integrates Bayesian learning with deep smoothing. Building upon the classical two-filter smoother, BLENDS incorporates a Transformer-based neural network within a Bayesian framework to directly refine the covariance matrix and apply additive corrections to the error states. A key innovation is the design of a Bayesian-consistent loss function that jointly supervises both smoothed means and covariances, ensuring statistical consistency while pursuing minimum-variance estimation. Evaluated on real-world datasets from mobile robots and quadrotors, BLENDS achieves up to a 63% improvement in horizontal positioning accuracy over the forward EKF baseline across all unseen test trajectories.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Bayesian Learning
• Search and Optimization: Learning to Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• inertial-aided navigation
• systematic position bias
• fixed-interval smoothing
• INS/GNSS
• post-processing navigation

Innovation

• Bayesian learning
• deep smoothing
• transformer-based neural network
• inertial-aided navigation
• covariance adaptation