  In this article, we consider the problem of outlier-robust state estimation
where the measurement noise can be correlated. Outliers in data arise due to
many reasons like sensor malfunctioning, environmental behaviors, communication
glitches, etc. Moreover, noise correlation emerges in several real-world
applications e.g. sensor networks, radar data, GPS-based systems, etc. We
consider these effects in system modeling which is subsequently used for
inference. We employ the Expectation-Maximization (EM) framework to derive both
outlier-resilient filtering and smoothing methods, suitable for online and
offline estimation respectively. The standard Gaussian filtering and the
Gaussian Rauch-Tung-Striebel (RTS) smoothing results are leveraged to devise
the estimators. In addition, Bayesian Cramer-Rao Bounds (BCRBs) for a filter
and a smoother which can perfectly detect and reject outliers are presented.
These serve as useful theoretical benchmarks to gauge the error performance of
different estimators. Lastly, different numerical experiments, for an
illustrative target tracking application, are carried out that indicate
performance gains compared to similarly engineered state-of-the-art
outlier-rejecting state estimators. The advantages are in terms of simpler
implementation, enhanced estimation quality, and competitive computational
performance.
