5DOF electromagnetic 3D tracking
A 5DOF (five-degree-of-freedom) electromagnetic tracker is a type of electromagnetic tracking system. It is useful for tracking a pen or stylus in 3D, where you get the direction the pen is pointed, as well as its position in 3D space.
The single coil is symmetrical about its axis, so orientation roll about the single coil's axis cannot be tracked. Orientation latitude and longitude can be tracked, and X, Y, Z position.
One method is to track a single dipole coil receiver against a spread-out array of transmitter coils.
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.
A company that sells 5DOF devices is NDI.[1]
Architectures[edit]
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 single coil. See the following paper for discussion and workarounds:
- [| Nara et. al., "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.
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).