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This paper presents a method for simultaneous classification and robust tracking of traffic participants based on the labeled random finite set (RFS) tracking framework. Specifically, a method to integrate the object class information into the tracking loop of the multiple model labeled multi-Bernoulli (MMLMB) filter, using Dempster-Shafer evidence theory is presented. The multi-object state is estimated using the detections from the sensors and by propagation of multi-object density in a Bayesian fashion. Parallelly, the object class information is also predicted and updated recursively. The underlying object class information required for this could typically be obtained from different types of sensor such as radar, lidar and camera, using classical perception or more recent deep learning methods. On one hand, this enables an unified classification and tracking of traffic participants. On the other hand, it also increases the robustness of multi-object tracking, as the parameters of the tracking algorithm could be adapted using the class information. Moreover, using the Dempster-Shafer method for fusing class information from different sensor sources improves the overall performance, especially when the sensors have contradicting classification.