A Quadrature Approach To Detection, Localization And Estimation Of Magnetic Dipoles

We describe a matched filter algorithm for detecting, locating and characterizing magnetic dipoles. The matched filter operates on an array of vector magnetic field measurements at an arbitrary set of orientations and points in space. For a given dipole location, the algorithm finds a best-fit magnetic dipole moment by projecting the N-dimensional vector representing the magnetic measurements onto the three-dimensional subspace spanned by the calculated data vectors for all possible magnetic moments at that location. It then varies the dipole location to find a best global match between the calculated and measured data. This approach, which is analogous to quadrature decomposition of a signal into sine and cosine components of a given frequency, removes the need to search exhaustively through all possible magnetic moments at each trial location. The algorithm provides optimal detection of a magnetic dipole in a background of white Gaussian noise, and unbiased estimation of the location and vector moment of an isolated dipole within the spatial sampling resolution defined by the user. An application to UXO is demonstrated using a moving magnetic tensor gradiometer to detect and localize inert artillery shells. The extension of the algorithm to active EM systems is explored in theory and computer simulations.