BiLi: Bridging the Last Mile in LiDAR Localization

In large-scale outdoor LiDAR localization, Scene Coordinate Regression (SCR) achieves sub-meter accuracy, but its deployment in high-precision autonomous driving is hindered by a "last-mile" problem: the point-wise prediction paradigm causes unphysical trajectory jittering, rendering localization kinematically discontinuous despite low mean errors. To bridge the gap between high-precision localization and temporal kinematic consistency, we propose BiLi, a spatiotemporal synergistic relocalization framework. Spatially, BiLi utilizes Implicit Manifold Regularization (ISR) driven by an offline neural implicit field. Formulated as a novel point-to-manifold projection constraint, ISR strictly anchors predicted coordinates to continuous physical zero-level sets. Temporally, to bypass computationally heavy implicit optimization, we distill the teacher's kinematics into a lightweight feed-forward network, compelling it to learn robust, equivariant physical priors. Finally, a Differentiable Robust Manifold Gating mechanism dynamically fuses the global spatial predictions with the temporal kinematic states via adaptive state updating, facilitating efficient real-time deployment. Extensive experiments demonstrate that BiLi fundamentally resolves the "last-mile" challenge. Our method outperforms state-of-the-art approaches by 25% and 65% on the Oxford and NCLT benchmarks, respectively, delivering drift-free, kinematically coherent, and highly accurate real-time localization.