In this paper a new technique is introduced for bias compensation of gyroscopes with a focus on mobiles phones. The standard problem of using gyroscopes is that integration of raw angular rates with non-zero bias will lead to continuous drift of the estimated orientation. To examine the nature of this bias, a simple error model was constructed for the whole device in terms of inertial sensing. For eliminating the bias, a sensor fusion algorithm was developed using the benefits of optical flow from the camera of the device. Our orientation estimator and bias removal method is based on complementary filters, in combination with an adaptive reliability filter for the optical flow features. The feedback of the fused result is combined with the raw gyroscope angular rates to compensate the bias. Various measurements were recorded on a real device running the demanding optical flow onboard. This way a robust and reliable fusion was constructed, which matched our expectations, and has been validated with simulations and real world measurements.