Gaussian Process Regression under Location Uncertainty using Monte Carlo Approximation

Abstract

Gaussian Process Regression (GPR) is a commonstatistical framework for spatial function estimation. While itsflexibility and availability of closed-form estimation solutionafter training are its advantages, it suffers on applicabilityconstraints in scenarios with uncertain training positions. Thispaper presents the derivation of the exact GPR operating onuncertain training positions along with approximation of theresulting terms using Monte Carlo (MC) sampling. This methodis then implemented in a simulation environment and shown toimprove the estimation quality over the standard GPR approachwith uncertain training positions.