Dynamic tracking of sparse targets has been one of the important topics in array signal processing. Recently, compressed sensing (CS) approaches have been extensively investigated as a new tool for this problem using partial support information obtained by exploiting temporal redundancy. However, most of these approaches are formulated under single measurement vector compressed sensing (SMV-CS) framework, where the performance guarantees are only in a probabilistic manner. The main contribution of this paper is to allow deterministic tracking of time varying supports with multiple measurement vectors (MMV) by exploiting multi-sensor diversity. In particular, we show that a novel compressive MUSIC (CS-MUSIC) algorithm with optimized partial support selection not only allows removal of inaccurate portion of previous support estimation but also enables addition of newly emerged part of unknown support. Numerical results confirm the theory.