Abstract: An apparatus and method for determining the coordinates of a body, where the coordinates express the body's inertial or kinematic properties, including, for example, its trajectory. The apparatus and method employ atom interferometers provided in a body frame X of the body whose inertial or kinematic properties are to be studied. During operation, interfering entities used by the atom interferometers are released into a known frame X?, such as an inertial frame or the Earth frame Xe, that is decoupled from the body frame X and an optical pulse sequence is applied to the interfering entities to affect the quantum-mechanical matter-wave phases of the interfering entities as a function of the coordinates. Under these conditions, the coordinates of the body are determined from the phases of the atom interferometers and analytic expressions for the trajectories of the interfering entities under the simultaneous action of the gravity gradient, Coriolis and centrifugal forces.

Abstract: There is provided a method for phase extraction between coupled atom interferometers using ellipse-specific fitting. The method includes fitting an ellipse to data representing a first gravimeter measurement and a second gravimeter measurement, and determining a phase shift between the first gravimeter measurement and the second gravimeter measurement based on a spread of the data around the ellipse.