  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.
