<title>Magnetic dipole localization using the gradient rate tensor measured by a five-axis magnetic gradiometer with known velocity</title>

Abstract

The use of the magnetic gradient tensor in the point-by-point localization of a magentic dipole was first demonstrated by Wynn in 1971, with a more explicit solution derived by Frahm in 1972. This algorithm maps the five independent components of the magnetic gradient tensor at a point into the dipole bearing vector and the dipole moment vector scaled by the inverse fourth power of the range to the dipole. This inversion produces four solutions, two of which are reflections through the origin of the bearing and scaled moment vectors of the other two. In the present paper, we describe an algorithm for mapping the time rate of change of the gradient tensor measured by a sensor of known velocity into the dipole bearing vector and the dipole moment vecot scaled by the inverse fifth power of the range. An extensive computer exercise with random position and moment vector geometries consistently produces at least one and at most four distinct solutions, with an equal number of additional solutions related to these by reflection of the bearing vector through the origin, for a total of at least two and at most eight solutions. In the same exercise, the solution common to this algorithm and the gradient equation iversion algorithm is consistently unique, and the two different moment vector scalings allow the range to be determined, resulting in a unique solution for dipole position and moment vectors. A general proof of uniqueness is not yet available.