LIMOncello: Iterated Error-State Kalman Filter on the SGal(3) Manifold for Fast LiDAR-Inertial Odometry

This work introduces LIMOncello, a tightly coupled LiDAR-Inertial Odometry system that models 6-DoF motion on the $\mathrm{SGal}(3)$ manifold within an iterated error-state Kalman filter backend. Compared to state representations defined on $\mathrm{SO}(3)\times\mathbb{R}^6$, the use of $\mathrm{SGal}(3)$ provides a coherent and numerically stable discrete-time propagation model that helps limit drift in low-observability conditions. LIMOncello also includes a lightweight incremental i-Octree mapping backend that enables faster updates and substantially lower memory usage than incremental kd-tree style map structures, without relying on locality-restricted search heuristics. Experiments on multiple real-world datasets show that LIMOncello achieves competitive accuracy while improving robustness in geometrically sparse environments. The system maintains real-time performance with stable memory growth and is released as an extensible open-source implementation at https://github.com/CPerezRuiz335/LIMOncello.