Local positioning system as a classic alternative to atomic navigation

TL;DR

This paper introduces a local positioning system that uses particle trajectories and sensor measurements to determine a platform's position and orientation relative to Earth, offering an alternative to traditional atomic navigation methods.

Contribution

It presents a novel LPS approach that avoids solving navigation equations by utilizing particle trajectories and sensor data, including a new iterative method for orientation restoration without gyroscopes.

Findings

Navigation error can be reduced to about 10 meters per hour.

Derived exact expressions for particle trajectories considering gravity-gradient, Coriolis, and centrifugal forces.

Simulation results validate the effectiveness of the proposed LPS method.

Abstract

A local positional system (LPS) is proposed, in which particles are launched at given velocities, and a sensor system measures the trajectory of particles in the platform frame. These measurements allow us to restore the position and orientation of the platform in the frame of the rotating Earth, without solving navigation equations. If there are also velocimeters installed on the platform, then one can restore the velocity and angular rate of the platform rotation in respect to the Earth. Instead of navigational equations, it is necessary to obtain the classical trajectory of a particle in the field of a rotating gravity source. Taking into account the gravity-gradient, Coriolis, and centrifugal forces, the exact expression for this trajectory is derived, which can be widely used in atomic interferometry. A new iterative method for restoring the orientation of the platform without using gyroscopes is proposed. The simulation allowed us to determine the conditions under which the LPS-navigation error per hour is about 10m.