Generating function derivation of the IPDA filter
Darko Mušicki, Taek Lyul Song, Roy L. Streit · 2014
The Integrated Probabilistic Data Association (IPDA) filter is derived using an analytic combinatorial method. The IPDA filter and the underlying discrete-continuous event space are unchanged. The feasible measurement assignments are encoded by a probability generating functional (PGFL). The probability distributions are decoded by the derivatives of the PGFL. The IPDA derivation is analytic in the sense that the enumeration of feasible assignments is implicit in the derivatives of the PGFL. The Joint IPDA (JIPDA) filter assumes-like its classical JPDA counterpart-that each target has its own state space. This important modeling feature distinguishes the JIPDA from a related family of filters based on multi-Bernoulli point processes that are superimposed in one targets state space.