SonarReg-GS SLAM: Sparse Sonar-Guided Depth Regularization for Underwater Gaussian Splatting SLAM

3D Gaussian Splatting (3DGS) SLAM provides an explicit scene representation for dense tracking and mapping, which is useful for underwater robotic perception. However, underwater monocular 3DGS SLAM lacks reliable metric depth cues: monocular depth estimation can provide dense structural priors, but its scale and reliability often degrade under underwater appearance changes. Forward-looking sonar (FLS) provides range-azimuth acoustic measurements whose range coordinate is related to physical distance, but raw sonar observations are sparse, noisy, and ambiguous. Our key insight is that FLS returns can serve as sparse metric depth anchors when they are associated with visually detected object regions. Based on this insight, we propose SonarReg-GS SLAM, an underwater visual-acoustic 3DGS SLAM framework with sparse sonar-guided depth regularization. Given synchronized RGB and sonar inputs, SonarReg-GS SLAM uses object masks to constrain the search space for acoustic range association. Filtered sonar responses are selected as sparse metric anchors through object-aware sampling, bearing-to-beam gating, and valid-pair checking. These anchors regularize the scale of monocular depth and generate metric depth priors for Gaussian initialization and tracking. An object-aware RGB mask loss further increases supervision on detected object regions while preserving full-scene mapping. Experiments on two public RGB-sonar underwater datasets show that SonarReg-GS SLAM improves tracking accuracy and mapping quality compared with representative classical SLAM and Gaussian Splatting SLAM baselines. Compared with Splat-SLAM, our method reduces the average ATE RMSE from 0.1296 m to 0.1015 m on UXO and from 0.5687 m to 0.4640 m on OPTI, corresponding to relative reductions of 21.7% and 18.4%, respectively. For rendering-based mapping, it increases the average PSNR from 28.05 dB to 29.61 dB on UXO and from 20.91 dB to 28.63 dB on OPTI while reducing the average LPIPS from 0.345 to 0.173 and from 0.450 to 0.303, respectively.