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 illconditioned, 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.