Accurate satellite-based positioning has revolutionized several industries over the past two decades from agriculture to transportation. However, conventional GNSS receivers consume significant amounts of energy and are too large for many applications, including wildlife-tracking which is critical for conservation efforts and improving our understanding of the global climate. To address this capability gap, we propose a new positioning system to minimize the mass, power, and size of the terrestrial tracking device. We analyze, through extensive modeling and simulation, a mission concept that relies on space-based receivers hosted on a constellation of small satellites in low-Earth orbit (LEO) that detect and localize signals from very small transmitter tags. We compare a variety of positioning techniques, including both Doppler and time-of-arrival methods, and evaluate the achievable position accuracy across a wide range of design parameters. Our model also accounts for errors in satellite orbital state knowledge, clock offsets, frequency measurement errors, and ionospheric effects. This thesis will present the results of our extensive trade study along with the orbit determination methods used to obtain the satellite state uncertainty.