Matthew McQuinn, Miguel Morales, Casey McGrath, Alyssa Alvarez, Katelyn Glasby, T. Joseph W. Lazio, Kiyoshi Masui, Lyujia Pan, Jonathan Pober, Huangyu Xiao

We investigate the feasibility and scientific potential of the Cosmic Positioning System (CPS), a space mission concept enabling purely geometric distance measurements to sources at hundreds of megaparsecs by directly detecting electromagnetic wavefront curvature. CPS consists of a constellation of radio antennas distributed across the outer Solar System, operating on baselines of tens of astronomical units. By precisely timing the arrival of repeating fast radio bursts (FRBs), CPS infers source distances via trilateration -- analogous to global navigation satellite systems such as GPS but on cosmological scales. We show that CPS distance measurements could result in sub-percent constraints on the Hubble constant with even a handful of detections, whereas we predict that 10-100 FRB sources are likely visible. We evaluate dominant sources of uncertainty -- wavefront timing precision, interstellar refractive delays, spacecraft positional knowledge, and onboard clock stability -- finding these controllable at required levels using near-term technologies. Our nominal design employs five spacecraft with 8 m deployable antennas, 3-6 GHz receivers with sub-30 K system temperatures, and space-qualified atomic clocks similar to those on GPS satellites, supported by a ground network for ranging calibration and FRB alerts. Beyond cosmic expansion, CPS may enable frontier measurements in astrophysics and fundamental physics, including constraints on small-scale dark matter structure, microhertz gravitational waves (bridging pulsar timing arrays and LISA), and the outer Solar System mass distribution. The most significant viability issue concerns FRB properties at several-GHz frequencies; we recommend observational campaigns to characterize repeating FRBs in this band.