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.

翻译：精准的后处理导航对于测绘等应用至关重要，此类场景可利用全部历史观测量对过往状态估计进行精化。固定区间平滑算法在高斯假设下代表理论最优解。然而，松耦合惯导/全球卫星导航系统（INS/GNSS）本质上继承了原始GNSS测量的系统性位置偏差，导致基于模型的平滑器无法弥合持续存在的精度差距。为解决这一局限，我们提出BLENDS框架，该框架将贝叶斯学习与深度平滑相结合以增强导航性能。BLENDS是一种数据驱动后处理框架，通过基于Transformer的神经网络增强经典双向平滑器。该框架学习修正滤波协方差矩阵，并在贝叶斯框架内直接对平滑误差状态施加加性校正。一种新型贝叶斯一致性损失函数联合监督平滑均值与协方差，在确保统计一致性的同时实现最小方差估计。BLENDS在涵盖移动机器人和四旋翼飞行器的两组真实世界数据集上进行了评估。在所有未见测试轨迹中，BLENDS相比基线前向扩展卡尔曼滤波器（EKF）实现了最高63%的水平位置精度提升。