Initial Relative Orbit Determination Using Multiple Los Measurements and Gaussian Mixture Models

Author

Keith A. Legrand
Kyle J. DeMars, Missouri University of Science and TechnologyFollow
Henry J. Pernicka, Missouri University of Science and TechnologyFollow

Abstract

The unobservability of space-based angles-only orbit determination can be mitigated by the inclusion of angle measurements from a second optical sensor fixed at a known baseline on the observing spacecraft. Previous approaches to the problem have used these stereoscopic angles to triangulate the position of a second satellite at a given time step. However, due to the nonlinearity of stereo triangulation, zero-mean Gaussian noise of these measurements cannot be assumed. This work investigates a modified approach in which the uncertainty of both angle measurements is used to bound a region for all possible positions of the second satellite. A Gaussian mixture that represents uniform uncertainty across the bounded region for the position of the second object is constructed at two initial time steps. Linkage of the Gaussian mixtures is performed using a new second-order relative Lambert solver in order to formulate a full state probability density function that can be further refined through processing subsequent measurement data in a Bayesian framework.

Recommended Citation

K. A. Legrand et al., "Initial Relative Orbit Determination Using Multiple Los Measurements and Gaussian Mixture Models," Proceedings of the 24th AAS/AIAA Space Flight Mechanics Meeting (2014, Santa Fe, NM), vol. 152, pp. 1343 - 1359, Univelt Inc., Jan 2014.

Meeting Name

24th AAS/AIAA Space Flight Mechanics Meeting (2014: Jan. 26-30, Santa Fe, NM)

Department(s)

Mechanical and Aerospace Engineering

Keywords and Phrases

Angle measurement; Data handling; Gaussian distribution; Orbits; Probability density function; Space flight; Stereo image processing; Tracking (position); Uncertainty analysis; Bayesian frameworks; Gaussian Mixture Model; Gaussian mixtures; LOS measurement; Measurement data; Orbit determination; Stereo triangulation; Unobservability; Gaussian noise (electronic)

International Standard Book Number (ISBN)

978-0877036111

International Standard Serial Number (ISSN)

0065-3438

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2014 Univelt Inc., All rights reserved.

Publication Date

01 Jan 2014