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Tethered capture of space debris is a promising method of Active Debris Removal, but has numerous well-known challenges in the post-capture phase. Control of the system in this phase is complicated by nonlinear dynamics with the potential of chaotic motion, unknown debris parameters, and debris tumbling. The inherent uncertainty present in the system and the need for control often necessitate the estimation of debris states and parameters such that the post-capture system can remain controlled. To this end, a relative distance Proportional-Integral-Derivative control and an Unscented Kalman Filter are implemented during the post-capture phase of an ADR mission. It is assumed that some debris (target) states and properties are unknown to the chaser, requiring the estimation of the attitude, angular rates, and principal moments of inertia of the target. For estimating these states, the UKF uses measurements of the tether tension magnitude and pixel coordinates of feature points on the target provided by a camera mounted on the chaser. Both estimation and control are done simultaneously, simulating online estimation and control of an ADR mission. The PID control was found to maintain safe conditions when using the estimated states in two separate Monte-Carlo simulations, differing in the measurement frequency of the pixel coordinates, while the estimation of the principal moments of inertia of the debris was satisfactory.