  In this paper, we present an algorithm for learning time-correlated
measurement covariances for application in batch state estimation. We
parameterize the inverse measurement covariance matrix to be block-banded,
which conveniently factorizes and results in a computationally efficient
approach for correlating measurements across the entire trajectory. We train
our covariance model through supervised learning using the groundtruth
trajectory. In applications where the measurements are time-correlated, we
demonstrate improved performance in both the mean posterior estimate and the
covariance (i.e., improved estimator consistency). We use an experimental
dataset collected using a mobile robot equipped with a laser rangefinder to
demonstrate the improvement in performance. We also verify estimator
consistency in a controlled simulation using a statistical test over several
trials.
