Generating function derivation of the PDA filter

The classic probability data association filter is derived using generating functions. It is shown that there is a one-to-one correspondence between the terms of the cross-derivative of the generating function and the collection of assignments of measurements to target or clutter. Thus, the probability of a given set of assignments is a term in the derivative of the generating function, and conversely. In other words, the generating function encodes the feasible assignments and differentiation decodes their probabilities. The technique can be extended to the classic joint probability data association filter. The potential use of automatic differentiation for exact weight calculation with particle filters is also discussed.