This paper presents a measurement-based under-frequency load shedding scheme that considers time delays, measurement uncertainties, and communication network faults. Using a moving first-degree polynomial function, an iterative approach to estimate the frequency nadir and the associated frequency nadir time is proposed. Then, a novel method to simultaneously estimate the power imbalance and the system inertia constant is developed. According to an analytical basis, a base system is selected from a set of pre-defined base systems to guarantee accurate power imbalance estimation. Finally, a mathematical index is investigated to calculate a threshold for the generation-load power imbalance beyond which loads should be shed. Further, a systematic approach for specifying the amount of load to be shed in each transmission bus of the system is proposed. The effectiveness of the proposed methodologies is examined on both simulated and actual measured data from 9 historical power system disturbances in a national power grid.