ReNiL: Relative Neural Inertial Locator with Any-Scale Bayesian Inference

Pedestrian inertial localization is key for mobile and IoT services because it provides infrastructure-free positioning. Yet most learning-based methods depend on fixed sliding-window integration, struggle to adapt to diverse motion scales and cadences, and yield inconsistent uncertainty, limiting real-world use. We present ReNiL, a Bayesian deep-learning framework for accurate, efficient, and uncertainty-aware pedestrian localization. ReNiL introduces Inertial Positioning Demand Points (IPDPs) to estimate motion at contextually meaningful waypoints instead of dense tracking, and supports inference on IMU sequences at any scale so cadence can match application needs. It couples a motion-aware orientation filter with an Any-Scale Laplace Estimator (ASLE), a dual-task network that blends patch-based self-supervision with Bayesian regression. By modeling displacements with a Laplace distribution, ReNiL provides homogeneous Euclidean uncertainty that integrates cleanly with other sensors. A Bayesian inference chain links successive IPDPs into consistent trajectories. On RoNIN-ds and a new WUDataset covering indoor and outdoor motion from 28 participants, ReNiL achieves state-of-the-art displacement accuracy and uncertainty consistency, outperforming TLIO, CTIN, iMoT, and RoNIN variants while reducing computation. Application studies further show robustness and practicality for mobile and IoT localization, making ReNiL a scalable, uncertainty-aware foundation for next-generation positioning.