Abstract: A method for detecting tunnels within an area comprising in one embodiment the steps of providing horizontal tensor gravity gradients for the area, calculating a plurality of gravity gradient vector field pairs from the horizontal tensor gravity gradients, each gravity gradient vector field pair including one gravity gradient vector field and a respective orthogonal gravity gradient vector field, detecting dipolar points and polar source points in each of the one and respective orthogonal gravity gradient vector fields for each gravity gradient vector field pair, identifying the polar source points that are present in one but not in both of the one gravity gradient vector field and the respective orthogonal gravity gradient vector field for each gravity gradient vector field pair to identify endpoints, and distinguishing the endpoints resulting from surface features from the endpoints resulting from tunnels. The polar source points form the endpoints of the tunnels.

Abstract: A method for detecting tunnels within an area comprising in one embodiment the steps of providing horizontal tensor gravity gradients for the area, calculating a plurality of gravity gradient vector field pairs from the horizontal tensor gravity gradients, each gravity gradient vector field pair including one gravity gradient vector field and a respective orthogonal gravity gradient vector field, detecting dipolar points and polar source points in each of the one and respective orthogonal gravity gradient vector fields for each gravity gradient vector field pair, identifying the polar source points that are present in one but not in both of the one gravity gradient vector field and the respective orthogonal gravity gradient vector field for each gravity gradient vector field pair to identify endpoints, and distinguishing the endpoints resulting from surface features from the endpoints resulting from tunnels. The polar source points form the endpoints of the tunnels.

Abstract: A method of navigation includes receiving a magnetic field signal from a magnetic field transducer, the magnetic field signal proportional to sensed magnetic fields associated with magnetic field sources, in a processor, processing the magnetic field signal to determine magnetic field axes of rotation corresponding to rotations of the sensed magnetic fields, and using the magnetic field axes of rotation to render a position of the magnetic field transducer.