The Multiple Object Tracking problem for a known and constant number of closely-spaced objects in a track-before-detect context is considered. The underlying problem of decomposing a data-association-free Bayes posterior density is analyzed. A previously proposed solution for two objects moving in one-dimensional space is generalized for higher dimensional problems where t objects move in a M-dimensional space. The underlying problem is solved with the proposed Cross Modeling Tracker by means of hypothesizing physical crosses between the objects for a general t–MD objects case. In particular, the mathematical definition of cross-between-objects is generalized from a meaningful interpretation of the problem in the low dimensional setting. A method to provide optimal references for evaluation of the Cross Modeling Tracker is also considered. The Cross Modeling Tracker algorithm is validated with the optimal references by simulating t–MD closely-spaced objects scenarios. Wider applicability of the Cross Modeling Tracker with respect to comparable reviewed solutions is demonstrated via simulation experiments.