Current reconstruction from magnetic field using spherical harmonic expansion to reduce impact of disturbance fields

A current reconstruction method, for determining currents in a set of parallel infinitely long conductors located above the ground from measured magnetic field, is developed. The method is designed to work even if three-dimensional external disturbance fields from external sources are present. The external field is written as an expansion in spherical harmonics. Therefore, the field in the different measurement points is regarded as a linear combination of the expansion coefficients and the currents to be determined. A linear equation system is formed with the currents and the expansion coefficients as the unknowns. The currents are reconstructed by solving the equation system using least squares method and Tikhonov regularization. If the characteristics of the ground below the conductors are known with sufficient precision, the ground effect can also be included into the model. Results of various simulations show that the method works well and noise in the measured magnetic field can be handled.