Removal of extraneous magnetic measurement components from magnetic anomaly detection (MAD) tends to increase its accuracy. Conventional removal accounts for anomalous magnetism manifested by the MAD vehicle (typically, unmanned), but assumes that the magnetic field applied to the MAD vehicle is the earth's magnetic field, i.e., is non-anomalous and known. In contrast, the present invention accounts not only for anomalous magnetism manifested by the MAD vehicle, but also for anomalous magnetism manifested in the MAD vehicle's vicinity, such as by a manned control vehicle. The present invention's mathematical characterization of vehicular “self-noise” due to induced and permanent magnetization is more refined, especially insofar as treating the vehicle's ambient magnetic field as an unknown (empirical) quantity, rather than a known (non-empirical) quantity. A typical inventive system for vehicular magnetic self-noise-reduced magnetic anomaly detection includes magnetic and other sensors, and a computer implementing the inventive mathematical characterization in processing the signals.