  State-of-the-art LiDAR calibration frameworks mainly use non-probabilistic
registration methods such as Iterative Closest Point (ICP) and its variants.
These methods suffer from biased results due to their pair-wise registration
procedure as well as their sensitivity to initialization and parameterization.
This often leads to misalignments in the calibration process. Probabilistic
registration methods compensate for these drawbacks by specifically modeling
the probabilistic nature of the observations. This paper presents GMMCalib, an
automatic target-based extrinsic calibration approach for multi-LiDAR systems.
Using an implementation of a Gaussian Mixture Model (GMM)-based registration
method that allows joint registration of multiple point clouds, this
data-driven approach is compared to ICP algorithms. We perform simulation
experiments using the digital twin of the EDGAR research vehicle and validate
the results in a real-world environment. We also address the local minima
problem of local registration methods for extrinsic sensor calibration and use
a distance-based metric to evaluate the calibration results. Our results show
that an increase in robustness against sensor miscalibrations can be achieved
by using GMM-based registration algorithms. The code is open source and
available on GitHub.
