Two novel dual quaternion Kalman filters for pose estimation in a satellite relative navigation problem are developed in this work. The satellites are assumed to be equipped with a vision navigation system that provides batches of intersatellite lines-of-sight. The measurements of the inertial angular velocities and the relative translation velocity are corrupted by additive biases and white noises and transferred over an intersatellite link for processing. Novel techniques of the dual quaternion nonlinear constraints are proposed: 1) a normalization and projection step along with a partial reset, and 2) pseudo-measurement updates. Extensive Monte-Carlo simulation results, along with a detailed numerical study of the observability Gramians, illustrate the relative advantage of the proposed dual quaternion filters over various state-of-the-art pose filters.