Modelization of underwater magnetic objects according a dipolar or an ellipsoidal hypothesis

The detection or the localization problem of submerged or surface magnetic objects moving along a straight line parallel to an axis of a Euclidian reference is the subject of several studies aimed at building systems in which information is then computed with more or less complex algorithms. Complexity is a function of the number of parameters to be estimated (source speed, magnetization, distances,…). The author shows that a solution to reduce the complexity of the algorithm is based on the knowledge of a vectorial space of the dipolar or ellipsoidal magnetic signals. The author shows that each component of the magnetic field is a linear combination of three functions that are the Anderson ones if a dipolar model is considered or the Pretet-Quinquis-GESMA functions if an ellipsoidal hypothesis is considered. The magnetic sensor is placed in an ellipsoid around the target. Finally, the author shows that when the ellipsoid is sufficiently distant (so it is like a dipole), the Pretet-Quinquis-GESMA functions are similar to the Anderson functions