A gravitational radiation positioning system, comprising a plurality of gravitational radiation transmitters and a gravitational radiation receiver, each of the plurality of transmitters and the receiver comprising:
- a first cylindrical superconducting cavity having a first length, a first diameter, and an entrance aperture for receiving electromagnetic radiation;
- a second cylindrical superconducting cavity having a second length, a second diameter, and a first aperture for gravitational radiation, the second cavity being coaxial with and adjacent the first cavity;
- a third cylindrical superconducting cavity having a third length, a third diameter, and a second exit aperture for gravitational radiation, the third cavity being coaxial with and adjacent the second cavity;
- a superconducting movable membrane positioned between the first cavity and the second cavity and configured to provide parametric amplification of electromagnetic fields in the second cavity;
- and
- a superconducting iris positioned between the second cavity and the third cavity, the iris having an aperture,
- wherein the first and the second apertures are configured to pass gravitational radiation, and
- wherein the receiver is configured to calculate a position of the receiver from time information encoded in gravitational radiation received by the receiver from the plurality of transmitters.