Covariance and Uncertainty Realism in Space Surveillance and Tracking

Characterizing uncertainty in estimating the state of a resident space object is one of the fundamentals of many space surveillance tasks.

Air Force Space Command, Peterson, Colorado

The characterization of uncertainty in the estimate of the state of a resident space object is fundamental to many space surveillance tasks including data association, uncorrelated track (UCT) resolution, catalog maintenance, sensor tasking and scheduling, as well as space situational awareness (SSA) missions such as conjunction assessments and maneuver detection. Generally, uncertainties are classified as either aleatoric, epistemic, or a mixture of both. Aleatoric uncertainty is the natural randomness or physical variability present in the system or its environment and is thus statistical in nature. In contrast, epistemic uncertainty is uncertainty that is due to limited data or knowledge.

With respect to some terms, covariance realism means that the uncertainty in the state of an object can be represented as a Gaussian random variable and that the estimated mean and covariance of said Gaussian are the true mean and true covariance, respectively. Since the underlying dynamical processes are not always linear nor Gaussian, one may generalize covariance realism to uncertainty realism described by a potentially non-Gaussian probability density function. Uncertainty realism requires that all cumulants (beyond a state and covariance) be properly characterized. The relationship between covariance realism and uncertainty realism is that the former is a necessary but not a sufficient condition for achieving the latter. The two definitions coincide if the process is Gaussian.