Ensemble Kalman filtering for spatio-temporal parameter estimation in Hall effect thrusters using correlated uncertainties

Hall effect thrusters (HETs), a type of plasma-based propulsion device, exhibit complex multiscale dynamics spanning from nanoseconds to milliseconds and from Debye lengths to device dimensions, involving electron transport, ionization, and plasma oscillations. Modeling such multiscale phenomena requires approximations that introduce uncertain parameters. Data assimilation (DA) addresses this challenge by combining simplified physics-based models with experimental measurements to systematically estimate these parameters. Previous work demonstrated extended Kalman filter (EKF) to be successful in parameter estimation based on 1D partial differential equations using spatially correlated noise models. However, EKF requires model linearization, motivating exploration of the derivative-free ensemble Kalman filter (EnKF) for state and parameter estimation in HET spatiotemporal dynamics. This study investigates EnKF performance on a 1D predator-prey model that captures breathing mode oscillations, a low-frequency instability where neutral depletion and subsequent refilling create periodic fluctuations in plasma density and discharge current. We introduce spatially and temporally correlated noise representing modeling uncertainties in electron transport and ionization processes. By comparing EnKF and EKF implementations, we examine how ensemble methods handle correlated uncertainty sources versus linearization-based approaches. Results will guide development of robust DA frameworks for HET optimization and control.