Traditional aerospace navigation often decouples attitude (orientation) from position (translation), using quaternions for the former and Cartesian vectors for the latter. However, in modern proximity operations such as autonomous docking, satellite servicing, and formation flying, the physical coupling between these two motions becomes significant. Our research proposal addresses the critical challenge of precise relative navigation within large-scale distributed spacecraft systems, where traditional decoupled representations of translation and rotation often fail to capture the complex kinematic coupling inherent in six-degree-of-freedom (6-DOF) maneuvers. In others words, our project aims to exploit the algebraic properties of dual quaternions to directly model these coupled dynamics, thereby improving the accuracy, computational efficiency, and robustness of state estimation in large space systems. The first phase of the project involves the rigorous formulation of a relative state error model. By applying the dual velocity transformation, we combine angular velocity and linear velocity into a single dual vector. The second task focuses on the development of a Multiplicative Extended Kalman Filter (MEKF) adapted specifically for the dual quaternion manifold. Unlike standard Euclidean filters, this architecture preserves the unit constraint of the dual quaternion through an error-state approach, facilitating distributed state estimation across large swarms. The final task establishes theoretical rigor through a stochastic stability analysis. By constructing a Lyapunov-like candidate function based on the dual quaternion geodesic distance, we prove that the estimation-control loop remains bounded under Gaussian perturbations. The proposed result is a robust, computationally efficient estimation framework that achieves a notable improvement in convergence rates and significantly lower steady-state error compared to traditional decoupled Extended Kalman Filter methods, providing a scalable solution for autonomous proximity operations in complex satellite constellations.