This letter introduces a sensory augmentation technique enabling a contact robot to understand its human user's control in real-time and integrate their reference trajectory information into its own sensory feedback to improve the tracking performance. The human's control is formulated as a feedback controller with unknown control gains and desired trajectory. An unscented Kalman filter is used to estimate first the control gains and then the desired trajectory. The estimated human's desired trajectory is used as augmented sensory information about the system and combined with the robot's measurement to estimate a reference trajectory. Simulations and an implementation on a robotic interface demonstrate that the reactive control can robustly identify the human user's control, and that the sensory augmentation improves the robot's tracking performance.