Statistical Impact Prediction of Decaying Objects

Abstract

This paper describes a method for statistically predicting the impact time and location of an orbital object under 200 km altitude. It also investigates the influence of the chief parameter uncertainties on the statistical dispersion. Unlike the main methods used nowadays, which derive drag parameters from historical state data, a shape model is used to acquire aerodynamic coefficients in the various flow regimes. As a test object, the Delta-K rocket stage is chosen, due to the high data availability for validating the tool. Using a Monte Carlo sequence, multiple six-degrees-of-freedom simulations are executed, in which the initial state and the density output of the atmosphere model are varied within their uncertainty windows. By kernel density estimation, the resulting data are used to derive a probability density function of the impact time and infer a ground track expressing impact probability. In a comparative study with the Tracking and Impact Predictions published by the United States Space Surveillance Network, the method’s performance is tested. In this comparison, a decrease in impact window size is observed, while maintaining the reliability. Moreover, by a variance-based sensitivity analysis, the uncertainty in the density model is identified as the prime contributor to footprint dispersion and it is shown that knowledge of the rotational state can be critical in decreasing impact windows.