Bayesian estimation of multi-object systems with independently identically distributed correlations

Recent generalisations of stochastic filtering methods to multi-object systems have become very popular for solving multi-target tracking problems over the last decade. However, there was previously no general means of introducing correlations between objects. In this article, we investigate generalisations of such multi-object filters for systems where there may be dependencies between objects. Determining probability and factorial moment densities is facilitated by the use of a recent result in variational calculus, a general form of Faà di Bruno's formula. The result is illustrated through the Probability Hypothesis Density (PHD) filter, as a first-order moment example of the general form.