Scale-Variant Robust Kernel Optimization for Non-linear Least Squares Problems

In this letter, we increase adaptivity of an existing robust estimation algorithm by learning two parameters instead of one to better fit the residual distribution. Our method uses these two parameters to calculate weights for Iterative Re-weighted Least Squares (IRLS). This adaptive nature of the weights is shown to be helpful in situations where the noise level varies in the measurements, and is shown to increase robustness to outliers. We test our algorithm first on the point cloud registration problem with synthetic data sets, where the truth transformation is known. Next, we also evaluate the approach with an open-source LiDAR-inertial SLAM package to demonstrate that the proposed approach is more effective than existing versions of the algorithm for the application of incremental LiDAR-inertial odometry. We also analyze the joint variability of the two parameters learned from the data sets.