Markov chain Monte Carlo data association for target tracking

We consider the estimation of the state of a discrete-time Markov process using observations which are sets of measurements from a finite number of known linear models. The measurement to model association is unknown and false measurements that do not yield any information about the Markov process are contained in the measurement set. The objective is to perform data association between the detected measurements and the models and determine optimal estimates of the state of the Markov process. The application of this problem is found in over the horizon target tracking. We derive iterative deterministic and stochastic algorithms based on Gibbs sampling. Rao-Blackwellisation allows us to solve the problem efficiently, yielding methods with computational complexity linear in the number of received data sets. Contrary to recent approaches based on the EM algorithm, the novel procedures we propose do not require an introduction of a missing data set and consequently their range of applicability is wider. A simulation study shows that the new algorithms are superior to previously proposed methods.