Abstract:Nano-machines circulating inside the human body, collecting data on tissue conditions, represent a vital part of next-generation medical diagnostic systems. However, for these devices to operate effectively, they need to relay not only their medical measurements but also their positions. This paper introduces a novel localization method for in-body nano-machines based on the magnetic field, leveraging the advantageous magnetic permeability of all human tissues. The entire proposed localization system is described, starting from 10x10 ${\mu}m^2$ magnetometers to be integrated into the nano-machines, to a set of external wires generating the magnetic field. Mathematical equations for the localization algorithm are also provided, assuming the nano-machines do not execute the computations themselves, but transmit their magnetic field measurements together with medical data outside of the body. The whole system is validated with computer simulations that capture the measurement error of the magnetometers, the error induced by the Earth magnetic field, and a human body model assuming different possible positions of nano-machines. The results show a very high system accuracy with localization errors even below 1 cm.