Problem
Consider the following data association problem. We track K moving objects u1, . . . , uK, using readings obtained over a trajectory of length T. Each object k has some (unknown) basic appearance Ak, and some position X(t)k at every time point t. Our sensor provides, at each time point t, a set of L noisy sensor readings, each corresponding to one object: for each l = 1, . . . , L, it returns B(t)l - the measured object appearance, and Y(t)l - the measured object position. Unfortunately, our sensor cannot determine the identity of the sensed objects, so sensed object l does not generally correspond to the true object l. In fact, the labeling of the sensed objects is completely arbitrary - all labelings are equally likely. Write down a DBN that represents the dynamics of this model.