  Limited measurement availability at the distribution grid presents challenges
for state estimation and situational awareness. This paper combines the
advantages of two sparsity-based state estimation approaches (matrix completion
and compressive sensing) that have been proposed recently to address the
challenge of unobservability. The proposed approach exploits both the low rank
structure and a suitable transform domain representation to leverage the
correlation structure of the spatio-temporal data matrix while incorporating
the power-flow constraints of the distribution grid. Simulations are carried
out on three phase unbalanced IEEE 37 test system to verify the effectiveness
of the proposed approach. The performance results reveal - (1) the superiority
over traditional matrix completion and (2) very low state estimation errors for
high compression ratios representing very low observability.
