This paper presents an adaptive observer-based navigation strategy for spacecraft in Circular Relative Orbit (CRO) scenarios, addressing challenges in proximity operations like formation flight and uncooperative target inspection. The proposed method adjusts observer gains based on the estimated state to achieve fast convergence and low noise sensitivity in state estimation. A Lyapunov-based analysis ensures stability and accuracy, while simulations using vision-based sensor data validate the approach under realistic conditions. Compared to classical observers with time-invariant gains, the proposed method enhances trajectory tracking precision and reduces control input switching, making it a promising solution for autonomous spacecraft localization and control.