Low-Cost Sun Vector Estimation-Least Squares Optimization in Polyhedral Photodiode Arrays

Accurate and robust estimation of the Sun's direction is a critical requirement for attitude determination systems in small-scale aerospace platforms such as UAVs and CubeSats. This paper presents a low-cost Sun sensor design based on discrete photodiodes arranged over symmetric polyhedral geometries - specifically, the icosahedron and the truncated icosahedron. A simulation framework has been developed in MATLAB to evaluate Sun vector estimation using a least-squares method, incorporating realistic photodiode characteristics and system noise. Two sensor configurations, using 12 and 20 photodiodes respectively, are tested and compared in terms of accuracy, coverage, and a proposed optimization metric that quantifies performance per sensor. Monte Carlo simulations revealed that while the icosahedron configuration offers marginally higher efficiency, it suffers from larger worst-case errors. In contrast, the truncated icosahedron maintains bounded errors below 2°, providing more reliable performance across the entire field of view. The results highlight a practical trade-off between average efficiency and robustness in geometric sensor deployment for Sun sensing applications.