This paper proposes a sensor fusion algorithm to determine the motor torque for power-assist electric bicycles. Instead of using torque sensors to directly measure the pedaling torque, outputs from a wheel encoder and a six-axis inertial measurement unit (IMU) are processed by the fusion algorithm to estimate the slope angle of the road and the longitudinal acceleration of the bicycle for conducting mass compensation, gravity compensation, and friction compensation. The compensations allow the ride of the electric bicycle on hills to be as effortless as the ride of a plain bicycle on the level ground regardless of the weight increase by the battery and the motor. The sensor fusion algorithm is basically an observer constructed on the kinematic model which describes the time-varying characteristics of the gravity vector observed from a frame moving with the bicycle. By exploiting the structure of the observer model, convergence of the estimation errors can be easily achieved by selecting two constant, subgain matrices in spite of the time-varying characteristics of the model. The validity of the sensor fusion is verified by both numerical simulations and experiments on a prototype bicycle.

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