A new state estimation method is proposed for power distribution networks that suffer from low-observability. The proposed distribution system state estimation (DSSE) method leverages the high reporting rate of only a small number of distribution-level phasor measurement units (D-PMUs), a.k.a., micro-PMUs, to unmask and characterize sparsity among the state variables. The DSSE problem is formulated over differential synchrophasors as an adaptive group sparse recovery problem to track the changes that are made in the states of the system due to the events that are captured in D-PMU measurements. The formulated DSSE is further augmented to use adequate side information on the support of the vector of unknowns that is obtained from the outcome of an event-zone identification analysis prior to solving the DSSE problem. The sufficient conditions for the uniqueness of the obtained sparse recovery solution are derived with respect to the available side information. Moreover, a calibration mechanism is developed to address drifting in the tracking state estimation to enhance robustness.