Alejandro Cano, GMV; Sergio Fernández, GMV; Alejandro Pastor, GMV; Diego Escobar, GMV;
Keywords: Covariance realism, consider analysis, covariance determination, uncertainty quantification
Abstract:
The provision of most of the Space Situational Awareness (SSA) and Space Traffic Management (STM) services relies on the orbit uncertainty characterization for catalogued resident space objects (RSOs). These services comprise conjunction analysis, sensor tasking and scheduling, catalogue build-up and maintenance or maneuver and anomaly analysis, among others. The achievement of uncertainty realism is of the utmost relevance and becomes the central issue regarding the provision of reliable products, critical to the operability and accessibility of the current space environment. As a matter of fact, uncertainty misrepresentation (either in orientation or dimension) can lead to differences of more than an order of magnitude in the computation of the probability of collision between two RSOs.
Under the assumption that the state of an RSO can be represented by Gaussian random variables, uncertainty realism becomes covariance realism, and the required statistical moments to represent the Probability Density Function (PDF) of the orbital state are reduced to the mean and variance. This is the usual approach in operational applications, such as catalogues of RSOs, where the uncertainty is characterized with a covariance matrix. This work falls within the challenging uncertainty quantification field, whose goal is to properly determine and characterize the sources of errors and uncertainties. In Space Surveillance and Tracking (SST), one of the main sources of uncertainty are the errors in the dynamical model involved in orbit determination processes, which are not captured by the so-called noise-only covariance, as it only includes the measurement uncertainty contribution. Scaling techniques are sometimes used to increase the PDF volume in some operational environments, in the same way as a safety margin. However, this approach does not enable physical interpretation and may lead to an undesirable increase in false alarms due to the lack of covariance realism.
The aim of this work is to present a methodology to improve the covariance realism of orbit determination processes through the classical theory of consider parameters in batch least-squares estimation. The consider parameters are included in the underlying dynamical models, such as atmospheric force, solar radiation pressure force or sensor time bias, providing the means to account for different uncertainty sources while maintaining an unbiased estimation. However, the main drawback of the consider analysis is the choice of realistic variances of these consider parameters. In order to solve this issue the following method is used. Under Gaussian assumption, the orbital differences between predicted and estimated states projected into the covariance space, i.e. Mahalanobis distance, shall follow a Chi-square distribution. Thus, a methodology is proposed here to estimate the variance of the consider parameters by means of a minimization process of the difference between the observed Mahalanobis distance distribution and the expected one (e.g. Chi-square).
This work focuses on the application of the proposed methodology in Geostationary Orbits (GEO), concretely in two of the most relevant sources of dynamical models uncertainty in this orbital regime: the Solar Radiation Pressure (SRP) and the sensor time bias. The impact of model errors on orbit determination and propagation is assessed via simulated Monte Carlo analysis. Along this process, Gaussianity tests and PDF agreement metrics are used to understand the impact of the analyzed uncertainty sources and the effect of the consider parameters in the covariance determination process. For this purpose, physically meaningful covariance realism metrics are derived (e.g. containment tests), aiming to determine the suitability of the consider covariance as opposed to the noise-only covariance. All simulations are performed in progressively more realistic scenarios, aiming for the operational applicability of the proposed covariance determination methodology. The effect on the final covariance from the consider parameter variances and or different OD scenarios is also assessed, tracing the effect of each parameter in the covariance realism improvement.
Date of Conference: September 14-17, 2021
Track: Astrodynamics