Realistic modeling and experimental validation of quadrant photodiode outputs for high-precision relative navigation in formation flying

Recent advances in space science have highlighted the demand for high-resolution astronomical and Earth observations. Achieving higher angular resolution and sensitivity requires longer focal lengths and larger apertures, which exceed the physical limits of a single satellite. Formation Flying (FF), wherein multiple satellites maintain precisely controlled relative states, offers a means to overcome these limitations and enable millimeter- to micrometer-level observation accuracy. Realizing such missions demands equally precise relative navigation and control. This study develops and validates a method for high-precision relative position and attitude determination using Quadrant Photodiode Sensors (QPS). A physics-based model of Quadrant Photodiode (QPD) outputs is constructed, and displacement estimation methods are proposed and evaluated. The approach is verified through hardware experiments and numerical simulations, which together assess the accuracy of QPS-based determination and its consistency with the developed model under realistic operating conditions. • Proposes a 6-DOF relative navigation system using QPS and CLR sensors. • Develops a realistic QPD model with beam growth and aperture effects. • Introduces range-aware bias compensation for lateral displacement. • Achieves ∼ 20–30 μ m (1 σ ) lateral accuracy near the sensor center.