Predicting TLE Covariance Using Transformer-Based Time Series Forecasting

This paper introduces the notion of using a transformer-inspired time series forecasting model, more specifically IBM’s Tiny Time Mixer (TTM), to predict the covariance of Two-Line Elements (TLEs). The pre-trained compact univariate model is finetuned on a dataset of historical TLEs. Using the well established technique of pairwise differencing, a fixed-interval time series of TLE covariances is generated. This series is merged with exogenous variables extracted from the TLEs themselves, such as the classical orbital elements. The multi-level modeling capabilities of the TTM allow it to capture inter-channel correlations, crucial to capture the complex interactions inherent in the prediction of TLE covariances. The TTM model is set up with generalizability in mind, training it on a dataset of satellites, completely distinct from the test set. This approach ensures that the model can generalize well to unseen satellites, making it applicable to a wide range of objects in Earth orbit. The performance of the model is demonstrated by assessing its ability to predict the covariance of TLEs for a distinct set of satellites. Across the different orbital regimes, the model demonstrates variable precision across the covariance components, with the tangential positional component remaining the most difficult to predict.