Multiple-Order Magnetic Gradient Tensors for Localization of a Magnetic Dipole

This letter gives expressions for the second-order and third-order gradient tensors produced by a magnetic dipole. We describe a method for extracting second-order and third-order gradient tensor components from a uniaxial magnetic field sensor mounted on a spinning disk that undergoes orbital motion about multiple axes. Experiments for localization of a magnetic dipole, which has many applications, based on second-order and third-order gradient tensors verify the proposed method and demonstrate the advantages of multiple-order gradient tensors.