This thesis introduces a novel SLAM method based on Semidefinite Programming–Gradient Descent (SDP-GD) and compares it to a sonar-based SLAM algorithm and the ORB-SLAM2 visual SLAM algorithm for seabed reconstruction. All three algorithms were tested in Gazebo/ROS simulations using BlueROV2 and Desistek SAGA AUV models. A linear discrete time varying model is built and a PID controller is used for each AUV along straight trajectories while collecting measurement with among others a stereo-camera and sonar sensor. Across the various seabed profiles with increasing complexity, SDP-GD demonstrated reconstruction accuracy comparable to ORB-SLAM2. Furthermore, SDP-GD consistently achieved lower errors and exhibited greater robustness across different levels of seabed complexity when compared to the Sonar-Based SLAM algorithm. These findings suggest that SDP-GD matches the performance of with both sonar-based and visual SLAM methods in terms of performance, with the only downside being its higher computational cost.