Frequency-domain Calibration of LiDARs: An online method for extrinsic calibration of LiDAR sensors on marine vessels using IMU data and frequency analysis

Abstract

LiDAR-based autonomous boat operations rely on accurate extrinsic calibration. Current practice requires manual measurement of each LiDAR’s position and orientation (pose), which is time-consuming and must be repeated if a sensor is displaced during operation. This thesis presents an online and target-less method for automatic extrinsic calibration of LiDARs mounted at arbitrary positions on a marine vessel. The proposed method uses the vessel’s rigid-body dynamics through a four-step pipeline based on data from the LiDAR’s internal IMU. First, the sensor’s roll and pitch offsets are determined using gravity projection. Second, a straight-line acceleration maneuver determines the yaw offset. Third, periodic yaw oscillations are analyzed in the frequency domain to estimate the longitudinal and lateral positions. Fourth, roll oscillations are used to estimate the vertical position. The output is a six degrees of freedom pose estimate that serves as an initial guess for a fine calibration using the Generalized Iterative Closest Point (GICP) algorithm. The method was tested in three environments: simulations with synthetic data, a controlled test rig and a 13 meter vessel. On the test rig, at a known sensor distance of 27.2 cm from the center of rotation (CoR), the longitudinal, lateral and vertical positions were estimated within 1 cm, 3 cm and 1.5 cm respectively. On the vessel, longitudinal position errors were 15-17% (1.04-1.19 m), lateral errors 3-10% (0.05-0.17 m) and vertical errors 23-29% (0.33-0.42 m), all relative to the distance from the CoR. The main limitations were gravity compensation, uncertainty in the estimated CoR and difficulty of producing sinusoidal maneuvers without dedicated maneuvering software. The fine calibration using GICP was demonstrated on a sensor pair with overlapping field of view of a nearby building. A convergence region test showed that the algorithm converges for initial guess errors below approximately 1.5 m per axis, confirming that the pipeline provides a sufficiently accurate starting point for relative calibration between LiDARs.