Tracking and data association procedures like the joint probabilistic data association filter (JPDAF) are not prone to the integration of additional information, such as shape constraints. A standard probabilistic framework is not suited to merging partially incoherent information sources. The theory of evidence, introduced by Shafer, describes a way to combine distinct "bodies of evidence" about the same phenomena. Under this framework we provide a rigorous derivation of the JPDAF as well as a procedure to integrate additional shape knowledge.