Hybrid Gaussian mixture model and unscented transformation algorithm for uncertainty propagation within the PUZZLE software

Nowadays, the constant increase of space debris represents a great concern for all space operators and agencies. With a higher amount of space junk, the collision risk for active missions inevitably grows. For this reason, building up accurate models for space debris is useful to support the reconstruction of past fragmentation events, but also to foster the prediction of possible future breakups. However, the available data about space debris distribution are not always accurate and the models may lead to incorrect previsions. The work proposed in this paper has two main objectives: firstly, the development of a hybrid method for the non-linear propagation of the uncertainty associated with the state of orbital fragments, then, the inclusion of such model within the PUZZLE software, a routine developed at Politecnico di Milano (initially under a contract with Italian Space Agency) for the detection and characterisation of a past fragmentation event. The first goal is achieved by combining the Gaussian Mixture Model (GMM) and the Unscented Transformation (UT) methods for propagating the uncertainty associated with a non-linear system over time. To accomplish the second goal, a simplified version of the hybrid algorithm is introduced within the PUZZLE software to enrich the data set given as input with additional Two Line Elements (TLEs) for each object, taking into account the specified value of uncertainty. Numerical results and graphical representations will show the capability of the updated software for studying breakup events.