Automatic radar based classification of automotive targets, such as pedestrians and cyclist, poses several challenges due to low inter-class variations among different classes and large intra-class variations. Further, different targets required to track in typical automotive scenario can have completely varying dynamics which gets challenging for tracker using conventional state vectors. Compared to state-of-the-art using independent classification and tracking, in this paper, we propose an integrated tracker and classifier leading to a novel Bayesian framework. The tracker's state vector in the proposed framework not only includes the localization parameters of the targets but is also augmented with the targets's feature embedding vector. In consequence, the tracker's performance is optimized due to a better separability of the targets. Furthermore, the classifier's performance is enhanced due to Bayesian formulation utilizing the temporal smoothing of classifier's embedding vector.