Higher order loop corrections for short range magnetoquasistatic position tracking

Magnetoquasistatic position tracking has been shown to be an excellent technique to measure distances between an emitting and receiving loop for distances up to 50 m along a direction perpendicular to the surface normal of the loops. For short distances from the emitting loop (i.e., less than about ten loop radii) there is an error in the estimated distance. In this paper, we examine the cause of this error and show that a significant portion is due to the simplification of the emitting loop as a simple magnetic dipole. By including a more accurate expression of the source field, errors can be significantly reduced. We show that the first correction term results in a reduction in rms and peak distance estimation error of 12.51 cm (54.44 %) and 11.27 cm (44.72 %), respectively, for distances less than 1.5δ, where δ is the skin depth.