FIM-based observability analysis for angles-only navigation of cooperative and non-cooperative spacecraft systems

Effective configuration selection for angles-only navigation of mixed cooperative and non-cooperative spacecraft systems requires fast and quantitative observability metrics applicable at both the mission design and in-orbit reconfiguration stages. However, existing Lie derivative criteria yield only binary observability, while Monte Carlo filter simulations are computationally prohibitive for systematic design or real-time onboard use. This paper proposes an observability analysis framework that bridges instantaneous pure measurement geometry and dynamic state estimation. A unified geometric Fisher Information Matrix (FIM) is first introduced to enable consistent and computationally efficient evaluation of formation configurations based on line-of-sight diversity. Building on this, a state transition matrix (STM)-based dynamic FIM is developed to propagate measurement information through nonlinear orbital dynamics, allowing rigorous assessment of initial-state observability, including the emergence of velocity observability. The framework is evaluated across three representative formation configurations: Triangular, Eccentricity-Inclination (EI), and In-Track (IT), and covers a two-orbital-period observation arc. Results show that the proposed approach achieves over 150×computational speedup compared to Monte Carlo filtering, while maintaining consistent observability ranking and providing additional insight into the underlying information structure. This makes it suitable both for systematic mission design and for lightweight onboard guidance in real-time formation reconfiguration.