A method for estimating a precise position of a user device from signals from a low earth orbit (LEO) satellite includes receiving at least one carrier signal at a user device, each carrier signal being transmitted a distinct LEO satellite. The user device processes the carrier signals to obtain a first carrier phase information. The user device recalls an inertial position fix derived at an inertial reference unit. The user device derives a position of the user device based on the inertial position fix and the first carrier phase information.