  Continuous-time trajectory representations are a powerful tool that can be
used to address several issues in many practical simultaneous localization and
mapping (SLAM) scenarios, like continuously collected measurements distorted by
robot motion, or during with asynchronous sensor measurements. Sparse Gaussian
processes (GP) allow for a probabilistic non-parametric trajectory
representation that enables fast trajectory estimation by sparse GP regression.
However, previous approaches are limited to dealing with vector space
representations of state only. In this technical report we extend the work by
Barfoot et al. [1] to general matrix Lie groups, by applying constant-velocity
prior, and defining locally linear GP. This enables using sparse GP approach in
a large space of practical SLAM settings. In this report we give the theory and
leave the experimental evaluation in future publications.
