Three-dimensional magnetic tracking of biaxial sensors

We present an analytical (noniterative) method for tracking biaxial magnetic sensors. Low-resolution regions (LRRs) of a biaxial transmitter are determined for the tracking of a triaxial sensor. These regions represent the reciprocal LRRs of a biaxial sensor that is tracked with a triaxial transmitter. The LRRs' configuration suggests that at least four triaxial transmitters should be used to track a biaxial sensor. At least one of the transmitters will always avoid the sensor's reciprocal LRRs. We show, on the other hand, that there are no LRRs for estimations of distance between the transmitter and the sensor. This makes it possible to triangulate a biaxial sensor with a triad of transmitters, instead of four. Thanks to a better distance resolution, compared to the resolution of coordinates, the triangulation provides practically the same location resolution and update rate as those reached by conventional methods of tracking triaxial sensors. This is true despite the need to operate a greater number of transmitting coils.