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A noise-adaptive variant of the Kalman filter is presented for the motion estimation and prediction of a free-falling tumbling satellite as seen from a satellite in a neighboring orbit. A complete dynamics model, including aspects of orbital mechanics, is incorporated for accurate estimation. Moreover, a discrete-time model of the entire system which includes the state-transition matrix and the covariance of process noise are derived effectively in a closed form, which is essential for the real-time implementation of the Kalman filter. We will show that the translational and rotational measurements are coupled and consequently derive the corresponding observation matrix. The statistical characteristics of the measurement noise is formulated by a state-dependent covariance matrix. This model allows additive quaternion noise, while preserving the unit-norm property of the quaternion. The estimator takes the noisy measurements from a laser vision system with unknown and possibly varying statistical noise properties, and subsequently the estimator adaptively estimates the full sates, i.e., the pose and the velocities, in addition to the covariance of the measurement noise and the inertial parameters of the target satellite. Simulations and experiments conducted will demonstrate the quality performance of the adaptive estimator.