Here, we analyze and test two extensions required to record the full eye-head orienting range, well exceeding 90° from straight-ahead in all directions. (1) The use of mutually perpendicular magnetic fields allows for the disambiguation of the non-monotonic signal from the ring. (2) The application of an artificial neural network for offline calibration of the signals. The theoretical predictions are tested for horizontal rotations with a gimbal system. Our results show that the method is a promising alternative to the search coil technique.