Autonomous Surface Vessels (ASVs) rely on advanced perception algorithms to accurately represent internal and external conditions. One of the most challenging tasks is tracking surrounding objects, especially in the presence of model and measurement uncertainties. In case of multiple dynamic obstacles, the tracking problem becomes highly important to guarantee safe navigation. Therefore, we propose a multi-target tracking algorithm based on Light Detection And Ranging (LiDAR) and Automatic Identification System (AIS) data. To estimate the shape of other vessels, a Numerically Stable Direct Least-Squares (NSDLS) ellipse fitting algorithm is applied to LiDAR point clouds. For that purpose, the point clouds are separated into clusters using a modified version of Density-Based Spatial Clustering of Applications with Noise (DBSCAN). To improve the robustness of the tracking algorithm, the LiDAR-generated estimations are fused with AIS measurements using a Kalman Filter (KF). The motion model used for the KF enables the prediction of dynamic obstacles surrounding the ASV. This proactive awareness can be used for predictive control concepts such as Model Predictive Control. However, testing such advanced algorithms on real systems can be dangerous. A Digital Twin (DT) allows for an extendable integration of physics-based models, sensor data, and intelligent algorithms, enabling simulations in a safe environment. This work demonstrates the proposed multi-target tracking approach in a DT of an ASV, which contains vessel dynamics, sensor models, and real-world AIS data streams.