Changes

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:

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:

*[[http://scitation.aip.org/content/aip/journal/jap/115/17/10.1063/1.4861675 | Nara etal, "Moore-Penrose generalized inverse of the gradient tensor in Euler's equation for locating a magnetic dipole"]][[http://dx.doi.org/10.1063/1.4861675 | J. Appl. Phys. 115, 17E504 (2014)]] on field-and-gradient single-coil 5DOF tracking closed-form algorithm.

*[[http://scitation.aip.org/content/aip/journal/jap/115/17/10.1063/1.4861675 | Nara et. al., "Moore-Penrose generalized inverse of the gradient tensor in Euler's equation for locating a magnetic dipole"]][[http://dx.doi.org/10.1063/1.4861675 | 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.

3. Array of spiral coils on a printed-circuit board. This has the advantage of precisely-known locations of coil turns.