Distributed Quantum Magnetic Sensing for Infrastructure-free Geo-localization

Abstract: Modern navigation systems rely heavily on Global Navigation Satellite Systems (GNSS), whose weak spaceborne signals are vulnerable to jamming, spoofing, and line-of-sight blockage. As an alternative, the Earth's magnetic field entails location information and is found critical to many animals' cognitive and navigation behavior. However, the practical use of the Earth's magnetic field for geo-localization hinges on an ultra-sensitive magnetometer. This work investigates how quantum magnetic sensing can be used for this purpose. We theoretically derive the Cramér-Rao lower bound (CRLB) for the estimation error of quantum sensing when using a nitrogen-vacancy (NV) center and prove the quantum advantage over classical magnetometers. Moreover, we employ a practical distributed quantum sensing protocol to saturate CRLB. Based on the estimated magnetic field and the earth's magnetic field map, we formulate geo-localization as a map-matching problem and introduce a coarse-to-fine Mahalanobis distance search in both gradient space (local field derivatives) and corner space (raw field samples). We simulate the proposed quantum sensing-based geo-localization framework over four cities in the United States and Canada. The results report that in high-gradient regions, gradient-space Mahalanobis search achieves sub-kilometer median localization error; while in magnetically smoother areas, corner-space search provides better accuracy and a $4-8\times$ reduction in runtime.