Book excerpt: This thesis presents algorithms that enhances the spatio-temporal observability of residential loads. This increased visibility in the load profiles is crucial for achieving secure and efficient operations in distribution systems, especially with the increasing penetration of distributed energy resources. The recovery formulation utilizes a joint inference framework by leveraging the spatial and temporal strengths of multiple data sources. More specifically, smart meter data is available for almost all residential households with low temporal resolution while distribution synchrophasor data is available at limited locations with very high temporal resolution. By combining the respective strengths of the two types of data, the load recovery problem is cast as a matrix recovery problem. Regularization terms are introduced to promote the underlying low-rank plus sparse structure characteristics of the load matrix to improve the recovery performance. As a result, the matrix recovery problem can be formulated as a convex optimization problem which can be solved using standard convex solvers. Numerical studies using real residential load data demonstrate the effectiveness of the proposed algorithms capability in identifying large appliance activities and recovering the irradiance pattern of rooftop solar output profiles. Furthermore, our numerical studies have suggested that the presence of periodic loading can degrade the recovery performance. To address this issue, we have explored the introduction of an additional sinusoidal wave component. Last, online implementations of the recovery algorithms are discussed to accelerate the computational speed and process the data streams in real-time, while a rectangular waveform model is considered to better represent the presence of periodic loads. The proposed methods discussed in this thesis serve to enhance the observability of residential distributed energy resources