2Fast-2Lamaa: Large-Scale Lidar-Inertial Localization and Mapping with Continuous Distance Fields

This paper introduces 2Fast-2Lamaa, a lidar-inertial state estimation framework for odometry, mapping, and localization. Its first key component is the optimization-based undistortion of lidar scans, which uses continuous IMU preintegration to model the system's pose at every lidar point timestamp. The continuous trajectory over 100-200ms is parameterized only by the initial scan conditions (linear velocity and gravity orientation) and IMU biases, yielding eleven state variables. These are estimated by minimizing point-to-line and point-to-plane distances between lidar-extracted features without relying on previous estimates, resulting in a prior-less motion-distortion correction strategy. Because the method performs local state estimation, it directly provides scan-to-scan odometry. To maintain geometric consistency over longer periods, undistorted scans are used for scan-to-map registration. The map representation employs Gaussian Processes to form a continuous distance field, enabling point-to-surface distance queries anywhere in space. Poses of the undistorted scans are refined by minimizing these distances through non-linear least-squares optimization. For odometry and mapping, the map is built incrementally in real time; for pure localization, existing maps are reused. The incremental map construction also includes mechanisms for removing dynamic objects. We benchmark 2Fast-2Lamaa on 250km (over 10h) of public and self-collected datasets from both automotive and handheld systems. The framework achieves state-of-the-art performance across diverse and challenging scenarios, reaching odometry and localization errors as low as 0.27% and 0.06 m, respectively. The real-time implementation is publicly available at https://github.com/clegenti/2fast2lamaa.