The present paper deals with the problem of characterization of oscillating magnetic dipole (OMD) signals and the development of a suitable magnetic anomaly detection (MAD) algorithm for it. The resulting outcomes of investigating the above mentioned problem are: (1) a development of a complete model of the noise and the signal based on a non-linear gravity pendulum model. This model was compared and verified against real world magnetic signals, as well as simulated ones. (2) A detection algorithm that utilizes this model by whitening the noise and seeking for periodical features in the signal. The developed algorithm has high noise immunity with high detection probabilities even at as low SNR as -10 dB. Compared to benchmark detectors, our detection scheme offers performance improved by 5-10 dB. Moreover, when testing the detector against real world signals, the SNR difference in respect to the performance predicted by the simulations was less than 2.5 dB.