Current dipole estimation based on the measurement of higher spatial differentials

This paper proposes a method to estimate the number, positions, and moments of current dipoles in a 3-D bounded domain. As observable quantities, we take higher spatial differentials of the magnetic field and electric potential measured via gradiometers and surface integrals, which leads to algebraic equations that can be solved using a method proposed last year: projection onto the Riemann sphere. The numerical simulations showed that the algorithm stably estimated the dipole parameters under a noisy condition.