5DOF Electromagnetic Tracker Notes
5DOF (five-degree-of-freedom) electromagnetic trackers track a single dipole coil receiver against a spread-out array of transmitter coils. Because the single coil is symmetrical about its axis, orientation roll about the single coil's axis cannot be tracked. Orientation latitude and longitude can be tracked, as can X Y Z position.
The single receiver coil does not need to be characterized, as long as the coil is small enough to be a dipole, as the coil's gain is tracked as part of the position-and-orientation algorithm.
The single coil can be used as a transmitter, and the array as receivers, though it can be difficult to get enough signal.
There are many choices for the spread-out array:
1. Six or more coils pointed in various directions. Any particular arrangement needs to be analyzed and simulated for trackability.
2. Twelve coils in a field-and-gradient array. Think of the single coil as a transmitter. The twelve-coil array then measures the field and gradient from the single coil. By electromagnetic reciprocity, single coil as receiver works the same. There is a direct analytic solution for position using this array. One problem is that the gradient matrix is singular when the array is in the equatorial plane of the array. See the following paper for discussion and workarounds:
- [| Nara etal, "Moore-Penrose generalized inverse of the gradient tensor in Euler's equation for locating a magnetic dipole"][| J. Appl. Phys. 115, 17E504 (2014)] on field-and-gradient single-coil 5DOF tracking closed-form algorithm.
3. Array of spiral coils on a printed-circuit board. This has the advantage of precisely-known locations of coil turns.
4. Array of three or more 6DOF three-orthogonal-coil transmitters. The positions and orientations of the transmitters are tracked using a 6DOF three-orthogonal-coil receiver, so the positions and orientations of the transmitters can be permitted to change while tracking a single-coil receiver.
As mentioned above, the 5DOF tracker has an unmeasurable degree of freedom, single-coil roll. If the tracking algorithm is calculated in the coordinate system of the single-coil receiver, the unmeasurable degree of freedom is explicitly present, and its effects can be evaluated when converting from receiver coordinates to transmitter coordinates. If the tracking algorithm is calculated directly in the transmitter coordinates, the unmeasurable degree of freedom is hidden, and its effects can come as a surprise (as discussed in 2. above).
