An algorithm for the automatic resolution of the position, orientation and dipole moment of a magnetic dipole antenna buried in rock
Date
2008-05-05T07:29:42Z
Authors
Lishman, Ryan M
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Abstract
Abstract
In this paper, an algorithm for accurately finding the position, orientation and dipole moment of
a transmitting dipole antenna buried in rock is presented. The algorithm is based on simplified
radiation equations that are shown to be valid within a region of space in the extreme near field
surrounding the antenna called termed quasi-static region. Within this region, medium dependent
propagation effects are negligible, allowing accurate, medium independent resolution of position,
orientation and dipole moment.
The magnetic field magnitude and direction values observed at a number of arbitrarily located points
in space are used by the algorithm to generate a system of nonlinear equations. This system of
equations is solved using a simultaneous multi-variable Newton-Raphson solver with line searches
and backtracking providing a measure of global convergence. An additional method, based on an
iterated random search, further improves the global convergence capability of the algorithm.
If the dipole moment of the transmitting antenna is known, measurements from two observer points
are sufficient to resolve the position and orientation of the dipole. If the dipole moment is unknown,
three observer points are required to solve for the unknown position, orientation and dipole moment.
The algorithm is able to find an exact solution using exact theoretical measurements, and a minimised
least squares solution where measurements are subject to noise.
The theory relating to the algorithm is discussed including distance-frequency relations for the quasistatic
region of a number of common rock types. Probabilistic modelling, simulation and test results
of the algorithm are also included.
Description
Keywords
magnetic dipole antenna