An Adaptive Graduated Nonconvexity Loss Function for Robust Nonlinear Least-Squares Solutions

Many problems in robotics, such asestimating the state from noisy sensor data or aligning two point clouds, can be posed and solved as least-squares problems. Unfortunately, vanilla nonminimal solvers for least-squares problems are notoriously sensitive to outliers and initialization errors. The conventional approach to outlier rejection is to use a robust loss function, which is typically selected and tuned a priori. A newly developed approach to handle large initialization errors is graduated nonconvexity (GNC), which is defined for a particular choice of a robust loss function. The main contribution of this article is to combine these two approaches by using an adaptive kernel within a GNC optimization scheme. This brings a solution to least-squares problems that is robust to both outliers and initialization errors, without the need for model selection and tuning. Simulations and experiments demonstrate that the proposed method is more robust compared to non-GNC counterparts and performs on par with other GNC-tailored loss functions.