Stellar Positioning System (Part II): Improving Accuracy During Implementation

Abstract

This paper discusses the implementation of a Stellar Positioning System as well as techniques for error mitigation in experimentation and data post‐processing. The hardware used during the development and testing of the Stellar Positioning System is described. Star‐centroiding, star‐identification, attitude estimation, and the local gravity vector were used by the Stellar Positioning System to determine latitude and longitude. Image processing, attitude filtering, and focal length estimation are presented as techniques to further improve the capabilities of the system. The resulting prototype was tested in three different locations and the results demonstrate accuracy of the Stellar Positioning System to be within 50 meters for short time intervals.

High Accurate Mathematical Tools to Estimate the Gravity Direction Using Two Non-Orthogonal Inclinometers

“…The static Stellar Positioning System [ 15 , 16 , 17 ] introduces a framework for estimating the geographical position of a vehicle on the surface of a planetary body using a pair of inclinometers along with an atomic clock and a night-sky camera to observe celestial directions (e.g., stars, visible planets). This system, which can be used in GPS-denied scenarios or in locations where the GPS signal is not available (i.e., on Moon or Mars), assumes that a reliably accurate estimate of the local gravity direction is available, which in turn would require a geoid correction.…”

“…Inclinometers are also used in more complex systems, such as in problems of estimating the position and orientation of a calibrated camera observing a set of n 3D points, known as Perspective- n -Point (PnP) problems [ 14 ], and in “Stellar Positioning Systems” [ 15 , 16 , 17 ], where the gravity direction along with celestial references can be used to estimate the geographical position in scenarios where real-time GPS information is unavailable (e.g., on Mars). Such systems can also be used on Earth as a backup system during instances of GPS jamming or spoofing.…”

A Return to the Sextant—Maritime Navigation Using Celestial Bodies and the Horizon

“…On the ground, star trackers have been both evaluated and tested on Earth in previous work of the authors [ 29 , 30 , 31 ]. Both have demonstrated arc-second precision.…”

“…The object is slightly elevated above the surface at a height δ. Using this approximation, alongside the approximate gravity vector in a geocentric model, where g = cos λ cos φ, sin λ cos φ, sin φ T , (30) the position of the user in terms of latitude and longitude may be known from only the horizon measurements and a known pointing attitude. Recalling that first the body measurements of the horizon need to be transformed to the planetary frame, the final model expression is…”

Navigation Requirements Development and Performance Assessment of a Martian Ascent Vehicle

“…A prior study funded by NASA/MSFC called the Stellar Positioning System (SPS) [23,24], looked to use the relationship described in Fig. 11 to relate the attitude of the spacecraft acquired by a star tracker to the position by way of inclinometers to determine the spacecraft's orientation in the local reference frame.…”