Adaptive Neural Dynamics for Robust Geometric LiDAR-Inertial State Estimation on UAVs

This paper presents an enhanced LiDAR-inertial odometrysystem that addresses the challenge of spatiotemporal drift through anadaptive neural stochastic differential equation (SDE) framework. Tra-ditional IMU bias models based on random walk assumptions often failto capture the complex, high-order non-linearities inherent in low-costinertial sensors during high-dynamic UAV maneuvers. To bridge the gapbetween classical geometric constraints and deep learning, our approachintroduces three key innovations: an adaptive hybrid bias model that dy-namically integrates learned neural dynamics with linear motion priors;a neural SDE framework that explicitly models stochastic bias evolu-tion and heteroscedastic uncertainties; and a differentiable covariancepropagation mechanism that ensures consistency between learned repre-sentations and geometric state estimation within an invariant extendedKalman filter. Extensive evaluations on self-collected UAV datasets, val-idated by a Vicon motion capture system, demonstrate that our methodconsistently outperforms the baseline FAST-LIO2, providing superior ac-curacy in both position and orientation estimation. Furthermore, ourapproach offers reliable uncertainty estimates crucial for complex spatialperception and robust autonomous flight in challenging environments.