Magnetoquasistatic position measurement above earth using the exact integral solutions

Measurements of the magnetoquasistatic coupling between a co-polarized vertical emitting and receiving coil, both located above earth, is compared to calculations using complex image theory and the exact integral solutions along a direction perpendicular to the surface normal axes of the loops. Inverting the theoretical expressions of the exact integral solution to estimate distance from measured fields resulted in an RMS error of 0.089 m for distances between 1.3-29.4 m, which corresponds to a 21.9% reduction in RMS distance error over complex image theory.