Half Cauchy-Modified Exponential Uncertainty Quantification for Tethered Satellites Using the Kalmag Geomagnetic Field Model

In this paper, we seek the impact of non‑Gaussian heavy-tailed uncertainty in the dynamics of an inextensible tethered satellite due to Earth’s oblateness (J2) and geomagnetic influences. The residual geomagnetic field error is modeled using the Half Cauchy‑modified Exponential (HCME) distribution. It correlates positive heavy‑tailed noise. Realistic mean magnetic fields and their uncertainties are given by the high-resolution Kalmag model. Using Monte Carlo framework, we propagate the stochastic torque through the nonlinear equations of motion taking 10,000 realizations. We derive the stochastic differential equation governing the tether angle, providing complete mathematical characterization of the HCME noise and perform rigorous statistical inferences- maximum likelihood estimation of noise parameters, bootstrap confidence intervals for excedance probabilities and Kolmogorov‑Smirnov test comparing output distributions. Results show that the HCME model leads to a significant higher probability of extreme tether tension events as compared to Gaussian model with the same variance. Specifically, the probability of exceeding 5 N increases from 1.2% (Gaussian) to 8.3% (HCME), a nearly seven‑fold rise. We provide R code for generating HCME random variates through the Lambert W function and for visualizing the heavy‑tailed noise distribution. The methodology is compatible with Kalmag geomagnetic field model and provides a pathway for data‑driven uncertainty quantification in space tether mission.