Covariance determination for improving uncertainty realism in orbit determination and propagation Articles uri icon

publication date

  • October 2023

start page

  • 2759

end page

  • 2777


  • 7


  • 72

International Standard Serial Number (ISSN)

  • 0273-1177

Electronic International Standard Serial Number (EISSN)

  • 1879-1948


  • The reliability of the uncertainty characterization, also known as uncertainty realism, is of the uttermost importance for Space Situational Awareness (SSA) services. Among the many sources of uncertainty in the space environment, the most relevant one is the inherent uncertainty of the dynamic models, which is generally not considered in the batch least-squares Orbit Determination (OD) processes in operational scenarios. A classical approach to account for these sources of uncertainty is the theory of consider parameters. In this approach, a set of uncertain parameters are included in the underlying dynamical model, in such a way that the model uncertainty is represented by the variances of these parameters. However, realistic variances of these consider parameters are not known a priori. This work introduces a methodology to infer the variance of consider parameters based on the observed distribution of the Mahalanobis distance of the orbital differences between predicted and estimated orbits, which theoretically should follow a chi-square distribution under Gaussian assumptions. Empirical Distribution Function statistics such as the Cramer-von-Mises and the Kolmogorov–Smirnov distances are used to determine optimum consider parameter variances. The methodology is presented in this paper and validated in a series of simulated scenarios emulating the complexity of operational applications.


  • Computer Science
  • Electronics
  • Industrial Engineering
  • Telecommunications


  • uncertainty realism; covariance realism; space situational awareness; covariance determination; mahalanobis distance; chi-square distribution; cramer-von-mises; kolmogorov-smirnov