Recent advancements in monocular neural depth estimation, particularly those achieved by the UniDepth network, have prompted the investigation of integrating UniDepth within a Gaussian splatting framework for monocular SLAM. This study presents UDGS-SLAM, a novel approach that eliminates the necessity of RGB-D sensors for depth estimation within Gaussian splatting framework. UDGS-SLAM employs statistical filtering to ensure local consistency of the estimated depth and jointly optimizes camera trajectory and Gaussian scene representation parameters. The proposed method achieves high-fidelity rendered images and low ATERMSE of the camera trajectory. The performance of UDGS-SLAM is rigorously evaluated using the TUM RGB-D dataset and benchmarked against several baseline methods, demonstrating superior performance across various scenarios. Additionally, an ablation study is conducted to validate design choices and investigate the impact of different network backbone encoders on system performance.