We consider state and parameter estimation in multiple target tracking problems with data association uncertainties and unknown number of targets. We show how the problem can be recast into a conditionally linear Gaussian state-space model with unknown parameters and present an algorithm for computationally efficient inference on the resulting model. The proposed algorithm is based on combining the Rao-Blackwellized Monte Carlo data association algorithm with particle Markov chain Monte Carlo algorithms to jointly estimate both parameters and data associations. Both particle marginal Metropolis-Hastings and particle Gibbs variants of particle MCMC are considered. We demonstrate the performance of the method both using simulated data and in a real-data case study of using multiple target tracking to estimate the brown bear population in Finland.
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