In this paper, we propose an estimation method of human joint movements from measured EMG signals for assistive robot control. We focus on how to estimate joint movements using multiple EMG electrodes even under sensor failure situations. In real world applications, EMG sensor electrodes might become disconnected or detached from skin surfaces. If we consider EMG-based robot control for assistive robots, such sensor failures lead to significant errors in the estimation of user joint movements. To cope with these sensor failures, we propose a state estimation model that takes uncertain observations into account. Sensor channel anomalies are found by checking the covariance of the EMG signals measured by multiple EMG electrodes. To validate the proposed control framework, we artificially disconnect an EMG electrode or detach one side of an EMG probe from the skin surface during elbow joint movement estimation. We show proper control of a one-DOF exoskeleton robot based on the estimated joint torque using our proposed method even when one EMG electrode has a sensor problem; a standard method with no tolerability against uncertain observations was unable to deal with these fault situations. Furthermore, the errors of the estimated joint torque with our proposed method were smaller than the standard method or a method with a conventional sensor fault detection algorithm.