  The identification of distribution network topology and parameters is a
critical problem that lays the foundation for improving network efficiency,
enhancing reliability, and increasing its capacity to host distributed energy
resources. Network identification problems often involve estimating a large
number of parameters based on highly correlated measurements, resulting in an
ill-conditioned and computationally demanding estimation process. We address
these challenges by proposing two admittance matrix estimation methods. In the
first method, we use the eigendecomposition of the admittance matrix to
generalize the notion of stationarity to electrical signals and demonstrate how
the stationarity property can be used to facilitate a maximum a posteriori
estimation procedure. We relax the stationarity assumption in the second
proposed method by employing Linear Minimum Mean Square Error (LMMSE)
estimation. Since LMMSE estimation is often ill-conditioned, we introduce an
approximate well-conditioned solution based on eigenvalue truncation. Our
quantitative results demonstrate the improvement in computational efficiency
compared to the state-of-the-art methods while preserving the estimation
accuracy.
