An expectation-maximisation tracker for multiple observations of a single target in clutter

We consider the estimation the state of a discrete-time, linear stochastic system whose observation process consists of a finite set of known, linear measurement models with additive white noise. Unlike conventional data fusion and tracking problems, the correspondence between the measurements and the models is assumed to be unknown. In addition, some of the measurements may be false alarms which convey no information about the state of the system. The expectation maximisation (EM) algorithm is applied as a MAP estimator of the sequence of measurement-to-model associations, with state sequence estimates obtained through fixed-interval Kalman smoothing conditioned on the association sequence. Each pass uses a Viterbi algorithm to provide updated data association estimates. The new technique is called expectation maximisation data association and represents an optimal fusion of dynamic programming and Kalman smoothing for data association.