  Gaussian processes (GPs) are becoming a standard tool to build terrain
representations thanks to their capacity to model map uncertainty. This
effectively yields a reliability measure of the areas of the map, which can be
directly utilized by Bayes filtering algorithms in robot localization problems.
A key insight is that this uncertainty can incorporate the noise intrinsic to
the terrain surveying process through the GPs ability to train on uncertain
inputs (UIs). However, existing techniques to build GP maps with UIs in a
tractable manner are restricted in the form and degree of the input noise. In
this letter, we propose a flexible and efficient framework to build large-scale
GP maps with UIs based on Stochastic Variational GPs and Monte Carlo sampling
of the UIs distributions. We validate our mapping approach on a large
bathymetric survey collected with an AUV and analyze its performance against
the use of deterministic inputs (DI). Finally, we show how using UI SVGP maps
yields more accurate particle filter localization results than DI SVGP on a
real AUV mission over an entirely predicted area.
