  In this paper, we consider the problem of blind estimation of states and
topology (BEST) in power systems. We use the linearized DC model of real power
measurements with unknown voltage phases (i.e. states) and an unknown
admittance matrix (i.e. topology) and show that the BEST problem can be
formulated as a blind source separation (BSS) problem with a weighted Laplacian
mixing matrix. We develop the constrained maximum likelihood (ML) estimator of
the Laplacian matrix for this graph BSS (GBSS) problem with
Gaussian-distributed states. The ML-BEST is shown to be only a function of the
states second-order statistics. Since the topology recovery stage of the
ML-BEST approach results in a high-complexity optimization problem, we propose
two low-complexity methods to implement it 1) Two- phase topology recovery,
which is based on solving the relaxed convex optimization and then finding the
closest Laplacian matrix, and 2) Augmented Lagrangian topology recovery. We
derive a closed-form expression for the associated Cramer-Rao bound (CRB) on
the topology matrix estimation. The performance of the proposed methods is
evaluated for the IEEE-14 bus test-case system and for a random network. It is
shown that, asymptotically, the state estimation performance of the proposed
ML-BEST methods coincides with the oracles minimum mean-squared-error (MSE)
state estimator, and the MSE of the topology estimation achieves the proposed
CRB.
