A novel stochastic unscented transform for probabilistic drag modeling and conjunction assessment

Abstract

Space safety and sustainability has recently received formalized recognition in the light of proliferation by large satellite constellations operated by the commercial sector. Enhanced space operations – detection, characterization, and tracking – are critical for safety and sustainability. A large portion of the lethal (non-)trackable debris reside in low Earth orbit (LEO) while the new commercial constellations reside dominantly in the lower LEO (LLEO) regime with significant plans for exploiting very LEO (VLEO) for future missions. With the new LEO population biased toward LLEO and VLEO, operations have become significantly more sensitive to atmospheric drag, modeling of which remains a primary challenge. Under support from the Intelligence Advanced Research Projects Activity (IARPA) Space Debris Identification and Tracking (SINTRA) program and the Office of Space Commerce (OSC), we are developing the next-generation drag modeling framework that accurately characterizes atmospheric density uncertainty due to space weather in a physics- and data-driven approach. This paper introduces one of the elements of the new framework we call stochastic Unscented Transform (SUT), a mathematical formulation designed to capture the joint statistics of probabilistic atmospheric density models and their probabilistic drivers or inputs. We present the mathematical derivation of SUT and its validation with simple numerical examples of linear and non-linear systems and then apply it to the case of drag modeling by incorporating the effects of uncertainty in the solar driver and density models in real-time orbit propagation. Enabled by the generalized nature of the SUT formulation, we also apply it to uncertainty and orbit prediction. This work moves us in the direction of realistic covariance for operations and eventually space safety and sustainability.