  Filtering and smoothing algorithms for linear discrete-time state-space
models with skew-t-distributed measurement noise are proposed. The algorithms
use a variational Bayes based posterior approximation with coupled location and
skewness variables to reduce the error caused by the variational approximation.
Although the variational update is done suboptimally using an expectation
propagation algorithm, our simulations show that the proposed method gives a
more accurate approximation of the posterior covariance matrix than an earlier
proposed variational algorithm. Consequently, the novel filter and smoother
outperform the earlier proposed robust filter and smoother and other existing
low-complexity alternatives in accuracy and speed. We present both simulations
and tests based on real-world navigation data, in particular GPS data in an
urban area, to demonstrate the performance of the novel methods. Moreover, the
extension of the proposed algorithms to cover the case where the distribution
of the measurement noise is multivariate skew-$t$ is outlined. Finally, the
paper presents a study of theoretical performance bounds for the proposed
algorithms.
