The multisensor-multitarget Bayes filter is the foundation for multi-sensor-multitarget detection, tracking, and identification. This paper addresses the question of principled implementation of this filter. Algorithms can always be cobbled together using catch-as-catch-can heuristic techniques. In formal Bayes modeling one instead derives statistically precise, implementation-independent equations from which principle approximations can then be derived. Indeed, this has become the accepted methodology for single-sensor, single-target tracking R&D. In the case of the multitarget filter, however, partisans of a so-called "plain-vanilla Bayesian approach" have disparaged formal Bayes modelling, and have protrayed specific, ad hoc implementations as completely general, "powerful and robust computational methods." In this and a companion paper I expose the speciousness of such claims. This paper reviews the elements of formal Bayes modeling and approximation, describes what they must look like in the multitarget case, and contrasts them with the "plain-vanilla Bayesian approach."