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


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.

Meeting Name

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


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)

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International Standard Serial Number (ISSN)


Document Type

Article - Conference proceedings

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Publication Date

01 Jan 2014

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