Unmanned ground vehicles (UGVs) require effective perception and analysis of their surrounding terrain for safe operation. This paper presents a novel approach to their local elevation mapping and traversability analysis using sparse data from a single LiDAR sensor, which can generate a dense local traversability map in real-time. By preserving ground height information, our method can differentiate between vertical obstacles, suspended objects and other terrains in the elevation map. The modified Bayesian generalized kernel elevation inference is utilized to predict and fill in sparse elevation maps to achieve local dense terrain traversability mapping. The system uses GPU parallel processing to accelerate calculations, ensuring real-time perception and dynamic processing. The proposed system was tested in both structured and unstructured environments, and achieved better performances in map filling and handling of suspended and vertical objects compared to other existing approaches.