  Virtual sensing techniques allow for inferring signals at new unmonitored
locations by exploiting spatio-temporal measurements coming from physical
sensors at different locations. However, as the sensor coverage becomes sparse
due to costs or other constraints, physical proximity cannot be used to support
interpolation. In this paper, we overcome this challenge by leveraging
dependencies between the target variable and a set of correlated variables
(covariates) that can frequently be associated with each location of interest.
From this viewpoint, covariates provide partial observability, and the problem
consists of inferring values for unobserved channels by exploiting observations
at other locations to learn how such variables can correlate. We introduce a
novel graph-based methodology to exploit such relationships and design a graph
deep learning architecture, named GgNet, implementing the framework. The
proposed approach relies on propagating information over a nested graph
structure that is used to learn dependencies between variables as well as
locations. GgNet is extensively evaluated under different virtual sensing
scenarios, demonstrating higher reconstruction accuracy compared to the
state-of-the-art.
