  We present parameter learning in a Gaussian variational inference setting
using only noisy measurements (i.e., no groundtruth). This is demonstrated in
the context of vehicle trajectory estimation, although the method we propose is
general. The paper extends the Exactly Sparse Gaussian Variational Inference
(ESGVI) framework, which has previously been used for large-scale nonlinear
batch state estimation. Our contribution is to additionally learn parameters of
our system models (which may be difficult to choose in practice) within the
ESGVI framework. In this paper, we learn the covariances for the motion and
sensor models used within vehicle trajectory estimation. Specifically, we learn
the parameters of a white-noise-on-acceleration motion model and the parameters
of an Inverse-Wishart prior over measurement covariances for our sensor model.
We demonstrate our technique using a 36~km dataset consisting of a car using
lidar to localize against a high-definition map; we learn the parameters on a
training section of the data and then show that we achieve high-quality state
estimates on a test section, even in the presence of outliers. Lastly, we show
that our framework can be used to solve pose graph optimization even with many
false loop closures.
