融合激光雷达与视觉的实时三维建图，提升地图精度与稳定性

While 3D Gaussian Splatting (3DGS) enabled photorealistic mapping, its integration into SLAM has largely followed traditional camera-centric pipelines. As a result, they inherit well-known weaknesses such as high computational load, failure in texture-poor or illumination-varying environments, and limited operational range, particularly for RGB-D setups. On the other hand, LiDAR emerges as a robust alternative, but its integration with 3DGS introduces new challenges, such as the need for tighter global alignment for photorealistic quality and prolonged optimization times caused by sparse data. To address these challenges, we propose LIVE-GS, an online LiDAR-Inertial Visual SLAM framework that tightly couples 3D Gaussian Splatting with LiDAR-based surfels to ensure high-precision map consistency through global geometric optimization. Particularly, to handle sparse data, our system employs a depth-invariant Gaussian initialization strategy for efficient representation and a bounded sigmoid constraint to prevent uncontrolled Gaussian growth. Experiments on public and our datasets demonstrate competitive performance in rendering quality and map-building efficiency compared with representative 3DGS SLAM baselines.