A Statistical Comparison Between Gibbs and Herrick-Gibbs Orbit Determination Methods
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The detection, tracking, identification, and characterization (DTIC) of resident space objects (RSOs) is an important aspect of space situational awareness (SSA). Monitoring the space environment can prevent collisions and eliminate hazards for spacecraft, as well as help enforce norms in the on-orbit regime. Consequently, there is a strong need for accurate RSO state estimates. For radar measurements of RSOs, these estimates are initiated by algorithms such as Gibbs and Herrick-Gibbs. Both methods use a track containing three sets of position vector (i.e., range + bearings) observations to analytically compute the objects' velocity at the time of the second observation. Presently, there is no clear distinction on when to switch between these two methods. In this paper, we present a statistical comparison between Gibbs and Herrick-Gibbs, taking into account measurement errors. We implement two separate approaches to investigate this problem. The first approach is via Monte Carlo. We add Gaussian white noise at several iterations and evaluate Gibbs and Herrick-Gibbs performances over track length. The second approach is an analytic probability density function approach used to characterize the uncertainty of the Herrick-Gibbs state estimate. We observe that the overall trend of the performance of the methods is consistent with what is expected. However, the results also show that Herrick-Gibbs can remain the more accurate method for much larger track lengths than is suggested in the literature. This is shown by both numerical and analytic statistical error analysis.
Kaushik, Arvind Shankar (2016). A Statistical Comparison Between Gibbs and Herrick-Gibbs Orbit Determination Methods. Master's thesis, Texas A & M University. Available electronically from