Passive optical motion capture is one of the predominant technologies for capturing high fidelity human skeletal motion, and is a workhorse in a large number of areas such as bio-mechanics, film and video games. While most state-of-the-art systems can automatically identify and track markers on the larger parts of the human body, the markers attached to fingers provide unique challenges and usually require extensive manual cleanup. In this work we present a robust online method for identification and tracking of passive motion capture markers attached to the fingers of the hands. The method is especially suited for large capture volumes and sparse marker sets of 3 to 10 markers per hand. Once trained, our system can automatically initialize and track the markers, and the subject may exit and enter the capture volume at will. By using multiple assignment hypotheses and soft decisions, it can robustly recover from a difficult situation with many simultaneous occlusions and false observations (ghost markers). We evaluate the method on a collection of sparse marker sets commonly used in industry and in the research community. We also compare the results with two of the most widely used motion capture platforms: Motion Analysis Cortex and Vicon Blade. The results show that our method is better at attaining correct marker labels and is especially beneficial for real-time applications.