We propose a fast and robust method to estimate the ground surface from LIDAR measurements on an automated vehicle. The ground surface is modeled as a UBS which is robust towards varying measurement densities and with a single parameter controlling the smoothness prior. We model the estimation process as a robust LS optimization problem which can be reformulated as a linear problem and thus solved efficiently. Using the SemanticKITTI data set, we conduct a quantitative evaluation by classifying the point-wise semantic annotations into ground and non-ground points. Finally, we validate the approach on our research vehicle in real-world scenarios.