Accurate attitude determination is crucial for satellites and spacecraft. Among attitude determination devices, star sensors are the most accurate. Solving the lost-in-space problem is the most critical function of the star sensor. Our research introduces a novel star-identification system that utilizes a polygon-recognition algorithm to assign a unique complex number to polygons created by stars. This system aims to solve the lost-in-space problem. Our system includes a full solution with a lens, image sensor, processing unit, and algorithm implementation. To test the system’s performance, we analyzed 100 night sky images that resembled what a real star sensor in orbit would experience. We used a k-d tree algorithm to accelerate the search in the star catalog of complex numbers. We implemented various verification methods, including internal polygon verification and a voting mechanism, to ensure the system’s reliability. We obtained the star database used as a reference from the Gaia DR2 catalog, which we filtered, to eliminate irrelevant stars, and which we arranged by apparent magnitude. Despite manually introducing up to three false stars, the system successfully identified at least one star in 97% of the analyzed images.