  In order for robots to safely navigate in unseen scenarios using
learning-based methods, it is important to accurately detect
out-of-training-distribution (OoD) situations online. Recently, Gaussian
process state-space models (GPSSMs) have proven useful to discriminate
unexpected observations by comparing them against probabilistic predictions.
However, the capability for the model to correctly distinguish between in- and
out-of-training distribution observations hinges on the accuracy of these
predictions, primarily affected by the class of functions the GPSSM kernel can
represent. In this paper, we propose (i) a novel approach to embed existing
domain knowledge in the kernel and (ii) an OoD online runtime monitor, based on
receding-horizon predictions. Domain knowledge is provided in the form of a
dataset, collected either in simulation or by using a nominal model. Numerical
results show that the informed kernel yields better regression quality with
smaller datasets, as compared to standard kernel choices. We demonstrate the
effectiveness of the OoD monitor on a real quadruped navigating an indoor
setting, which reliably classifies previously unseen terrains.
