Driver's steering torque is an essential signal for automated and assistance driving systems to interpret the human driver's intention. In a steer-by-wire (SBW) apparatus, due to the inevitable couplings between the driver steering, electrical motor, and viscous frictional torques, such a vital signal cannot be directly measured via a torque transducer. Instead, model-based estimators are considered a more practicable route. Toward this end, this paper introduces a novel mixed observer to achieve a robust estimation respecting the human driver's steering torque in human-alone and human-automation shared driving. On the one hand, the induced norm from the process disturbance to the estimation error is attenuated. On the other hand, the synthesis seeks to suppress the effects of measurement noises from the steering angle encoder and the motor's current sensor. Driving simulator human subject experiments are effectuated to justify the proposed strategy and manifest its superiorities over a benchmark method.