  With the transition to a smart grid, we are witnessing a significant growth
in sensor deployments and smart metering infrastructure in the distribution
system. However, information from these sensors and meters are typically
unevenly sampled at different time-scales and are incomplete. It is critical to
effectively aggregate these information sources for situational awareness. In
order to reconcile the heterogeneous multi-scale time-series data, we present a
multi-task Gaussian process framework. This framework exploits the
spatio-temporal correlation across the time-series data to impute data at any
desired time-scale while providing confidence bounds on the imputations. The
value of the imputed data for distribution system operation is illustrated via
a matrix completion based state estimation strategy. Results on the IEEE 37 bus
distribution system reveals the superior performance of the proposed approach
relative to linear interpolation approaches.
