This paper presents a Bayesian model which is a unifying extension of many of the approaches to tracking multiple targets in clutter, when multiple sensors may also be present. The total number of potential targets dealt with in this problem is assumed in general to be finite. One of the results shown here connects this approach to the infinite target set Poisson arrival approach. Stochastic processes used in the model include target initialization and termination times, trajectories with maneuvers or types of motion changes, clutter, one time step Markovian detections, and measurements, including non-geolocation attributes. A number of analytic expressions is obtained for the posterior distribution of various parameters of interest, including present target sets, target initialization and termination times, number of targets present, and number of new targets present. Other results are more complicated in form and serve to indicate the inherent difficulties present in the problem.