Doppler positioning methods for ground terminals are well established for dedicated satellite constellations. Newer research also demonstrates that large, not purpose-built constellations with sophisticated models can achieve sub-meter positioning results. Lesser is known about small satellite constellations, such as the Astrocast nanosatellite constellation. This master thesis examines the usability of said constellation using only seven satellites on two orbital planes.To analyze the data, a simple least-squares adjustment model was implemented. Instead of incorporating multiple error terms (such as relativistic or atmospheric effects), only a single, per flyover constant term, was added to model most error sources. The foundation of this thesis are three datasets: one consisting of frequency measurements taken during January 2022 to March 2022 in Lausanne, Switzerland; one consisting of simulated data obtained from a modified GPSSIM package in the Bernese v5.4 software; and the last one being orbital positions and velocities of the satellites.The results show that with just 10 flyovers solutions on a city-scale are possible. With 100-300 flyovers the precision increases to better than 50 m. Additional flyovers improve the quality very slowly and show diminishing returns. A systematic error causing all solutions to be located around 500 m south of the ground truth could not be eliminated.It was shown that even using a small satellite constellation, in combination with a simple model, achieve reliable results over longer measurement periods. Due to being on two orbital planes meaning that only around four measurement windows are available every day, this constellation is not suited for real-time applications. If, however, necessitating daily solutions on a city-scale, the Astrocast nanosatellite constellation is at the lowest limit, with around half of the days providing enough data (10 flyovers) for a sufficient quality.