The fields of bioinformatics and biotechnology rely on the collection, processing and analysis of huge numbers of biocellular images, including cell features such as cell size, shape, and motility. Thus, cell tracking is of crucial importance in the study of cell behaviour and in drug and disease research. Such a multitarget tracking is essentially an assignment problem, NP-hard, with the solution normally found in practice in a reduced hypothesis space. In this paper we introduce a novel approach to find the exact association solution over time for single-frame scan-back stem cell tracking. Our proposed method employs a class of linear programming optimization methods known as the Hungarian method to find the optimal joint probabilistic data association for nonlinear dynamics and non-Gaussian measurements. The proposed method, an optimal joint probabilistic data association approach, has been successfully applied to track hematopoietic stem cells.