Tomographic principles offer a unique opportunity for sensor fusion, contributing to a better understanding of specific sensor characteristics and maximizing their potential for sensing the three-dimensional atmospheric state. However, a key challenge in converting integral measurements into three-dimensional images lies in the limited number of radio sources and detectors relative to the object's size. Nanosatellite technology is paving the way to overcome this problem and enable groundbreaking Earth observation opportunities. As we anticipate the emergence of large satellite constellations comprising hundreds to thousands of satellites in low Earth orbit, a significant number of these satellites will be equipped with cost-effective sensors, such as GNSS receivers, for Earth's atmosphere monitoring. This study focuses on utilizing dense nanosatellite formations equipped with GNSS receivers to reconstruct the 3D ionospheric structure, offering promising advancements in atmospheric science. A demonstration campaign was conducted in December 2022 using four satellites from the Astrocast nanosatellite fleet. The campaign showcased a novel tomography-based modeling approach based on four nanosatellites arranged in a "string-of-pearls" formation. The GNSS signals observed from such a formation enter the atmosphere at similar locations, resulting in spatially close radio occultation signals suitable for accurately reconstructing the electron density distribution from high-rate GNSS radio occultation measurements. The analysis revealed up to 1800 radio occultation events within the 14-hour observation period. A subset of these events demonstrated favorable observation geometry for tomographic processing, especially during the initial days post-satellite launch. Data analysis involved extracting the ionospheric excess phase from the GPS L1 code and phase observations and integrating them into a tomographic system alongside ray-traced signal paths to estimate electron density fields. The results from this first demonstration campaign exhibit the potential of this cutting-edge observation technique for comprehensive three-dimensional sensing of the ionosphere, presenting promising prospects for future atmospheric studies.