  In the case of a linear state space model, we implement an MCMC sampler with
two phases. In the learning phase, a self-tuning sampler is used to learn the
parameter mean and covariance structure. In the estimation phase, the parameter
mean and covariance structure informs the proposed mechanism and is also used
in a delayed-acceptance algorithm. Information on the resulting state of the
system is given by a Gaussian mixture. In on-line mode, the algorithm is
adaptive and uses a sliding window approach to accelerate sampling speed and to
maintain appropriate acceptance rates. We apply the algorithm to joined state
and parameter estimation in the case of irregularly sampled GPS time series
data.
