Bidirectional Joint State–Memory Deep Bayesian Smoother for Motion Estimation

Capturing the mutual dependencies among states is crucial for practical fixed-interval smoothing problems in motion estimation. However, the resulting noncausal properties present significant challenges for recursive Bayesian estimation. In this article, we propose a bidirectional joint state–memory deep Bayesian smoother, specifically designed for motion estimation under the leave-one-out all-state (LOOAS) model. The LOOAS model is first transformed into an equivalent bidirectional memory model, enabling the capture of bidirectional state evolution dynamics while supporting recursive Bayesian smoothing. By incorporating offline data, we derive a deep Bayesian smoothing framework that integrates bidirectional information under Bayesian estimation theory, ensuring consistency between memories. The Gaussian point estimation implementation of the proposed framework is derived, and the internal networks are designed with a cross-attention mechanism to enable bidirectional memory interaction. Both the recursive and gated structures of the method are derived from Bayesian theory, offering interpretability by integrating prior model knowledge with offline data. Experiments on real-world aircraft and vehicle datasets evaluate the proposed method in terms of smoothing performance, parameter utilization, and data efficiency.