On physics-constrained magnetic anomaly detection

Magnetic anomaly detection involves exploiting the earth field local anomaly created by the presence of ferromagnetic objects to detect them. In this work, we revisit the classical detection scheme, taking better account of the physics that creates the anomaly. It is well known that the signal measured by the sensor of a moving object along a rectilinear trajectory decomposes on a basis, where the coefficients depend on the unknown magnetic moment of the object. In the case where the measured signal is the squared induction modulus, we show that by constraining the basis coefficients to live in the semi-algebraic subspace which stems from their relationships to the moment components (i.e., the physics of the problem), we significantly improve detection performance. Even more, the performance is very close to the optimal detector one, based on the full knowledge of the parameters.