A Novel Stochastic Unscented Transform for Robust State Estimation Enabling Enhanced Space Domain Awareness

\noindent The challenge of detecting and tracking lethal non-trackable (LNT) objects is crucial for mitigating collision risk and maintaining space safety. These objects are often too small to be tracked effectively using conventional methods, making them a threat to operational satellites or other resident space objects (RSOs). Efforts like IARPA's SINTRA program contribute to addressing the growing challenges and risks of LNTs. Specifically, it is important to maintain both continuous custody and a realistic covariance, providing a more comprehensive understanding of the dynamic nature of space systems, as covariance information is crucial for robust decision-making. This paper presents an application of the new stochastic unscented transform (SUT)\cite{SUT_DER} that incorporates additional statistics of probabilistic models in orbit propagation and determination. Because of its generic nature, this framework supports a myriad of applications in various fields. The new stochastic unscented approach is particularly advantageous in complex environments where traditional deterministic models are insufficient and where modeling using Monte Carlo techniques are inefficient. The derivation and validation of the new SUT algorithm has been previously performed for accurate capture of joint statistics of probabilistic inputs driving stochastic density models for drag modeling in low Earth orbit (LEO). In this work, the SUT is extended by using a generalized method to incorporate such probabilistic models for space object tracking and space domain awareness. Specifically, the SUT has been embedded within the CAR-MHF (Constrained Admissible Region-Multi Hypothesis Filter) algorithm to enhance its ability to model atmospheric density for LEO drag force modeling. This enables more accurate modeling of the dynamics and, thus, allows one to reduce process noise for unmodeled force perturbations. The SUT's ability to handle stochastic dynamics provides a more realistic representation of the space environment, enabling CAR-MHF to make more informed multiple hypothesis decisions based on probabilistic predictions.