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While global navigation satellite system (GNSS) technologies have always been the go-to solution for localization problems, they may not be the best choice for some Internet-of-Things (IoT) applications due to the incurred power consumption and cost. In this paper, we present an alternative satellite-based localization method exploiting the signature of Doppler shifts and angle-of-arrival measurements as seen by a low-Earth-orbit (LEO) satellite. We first derive the joint likelihood function of the measurements, which is represented as a combination of three Gaussian distributions. Then, we show that the maximum likelihood problem reduces to a more-efficient mean squared error minimization in the Gaussian case as inferred from real measurements we collected from low-Earth-orbit satellite using a tracking ground station. Thus, we propose utilizing a stochastic optimizer to search for the global minimum of the mean squared error, which represents the location of the ground IoT device as estimated by the satellite platform. The emulated results show that the IoT device localization, in such a realistic model, can be performed with sufficient accuracy for IoT applications. [ABSTRACT FROM AUTHOR]