The best fitting multi-Bernoulli filter

Abstract

Recent derivations have shown that the full Bayes random finite set filter incorporates a linear combination of multi- Bernoulli distributions. The full filter is intractable as the number of terms in the linear combination grows exponentially with the number of targets; this is the problem of data association. A highly desirable approximation would be to find the multi-Bernoulli distribution that is closest to the full distribution in some sense, such as the set Kullback-Leibler divergence. This paper proposes an approximate method for achieving this, which can be interpreted as an application of the well-known expectation-maximisation (EM) algorithm.