Observation of the human knee stiffness is known to be an important issue in rehabilitation robotics in order to consider biomechanical knee parameters of the individual patient. As in-vivo identification often is a complicated task, modeling of biomechanical processes always comes with uncertainties. Therefore, we present a new model-based estimation algorithm using generalized polynomial chaos expansion (gPCE) to minimize uncertainty of the model states. The joint kinematics of the human knee is restricted to the two-dimensional sagittal-plane to reduce model complexity. In addition, the muscle activation and contraction dynamics are mathematically described to drive the employed model by recorded EMG data of the knee attached muscle groups. With additionally considering the knee angle as a measurement value we further designed a Kalman-structured observer based on the derived nonlinear model. First, in comparison to well known derivatives of the Kalman filter the recently implemented gPCE filter is validated in a simple nonlinear system. Afterwards, the knee movements were tested in an in-silico study following different arbitrary activation patterns to evaluate the capability of the proposed estimation algorithm.