Sriram Narayanan, West Virginia University; Daniele Sicoli, West Virginia University; Hang Woon Lee, West Virginia University; Piyush Mehta, West Virginia University
https://doi.org/10.64861/XQDN7455
Keywords: Thermospheric density, reduced-order modeling, data assimilation, Kalman filtering, space weather, orbit determination, Koopman Operator, space situational awareness, drag modeling, low-Earth orbit
Abstract:
Accurate specification of thermospheric mass density remains a persistent challenge for high-fidelity orbit determination and prediction. Physics-based general circulation and whole-atmosphere models provide the most complete representation of upper-atmospheric processes, but their computational cost limits operational and real-time use, while empirical models are efficient yet struggle to capture nonlinear, transient responses outside nominal conditions. Reduced-order modeling combined with data assimilation balances physical structure, computational tractability, and responsiveness to observations. Its skill, however, depends as much on where observations are collected as on how they are assimilated; this work addresses both.
The first thrust is an adaptive reduced-order data assimilation framework that uses sequential in situ measurements to update a low-dimensional dynamical state derived from a full physics model through data-driven techniques. Rather than treating observations solely as corrections to a fixed background model, the framework allows measurement information to influence the evolution of the reduced-order state itself, so the assimilated solution reflects both the structural constraints of the underlying model and dynamical behaviors revealed by observations. Two classes of reduced-order models are considered within a unified Kalman filtering architecture: a sparse identification of nonlinear dynamics with control (SINDYc) formulation, enabling state-dependent responses to space-weather drivers, and a linear dynamic mode decomposition with control (DMDc) baseline providing a transparent reference.
The framework is evaluated using in situ density measurements from multiple low-Earth-orbit missions spanning a range of altitudes, local times, and geomagnetic conditions. Single- and multi-satellite experiments assess the consistency of information propagation across orbital regimes. The nonlinear formulation demonstrates improved adaptability during periods of elevated geomagnetic forcing, when extrapolation beyond the nominal training envelope is required, while the linear baseline provides a stable reference under quiescent conditions.
The second thrust addresses the complementary question of observing-system design: from which orbits, and from how many platforms, should density be observed to maximize the information delivered to the estimator? Candidate orbits are scored by how much uncertainty they remove from the reduced-order state, and constellation size and composition are selected jointly, so that information is traded explicitly against platform count rather than fixed in advance. A diagnostic of the underlying observability limit identifies which reduced-order structures can be constrained at all from a given set of candidates, and a spatial balance term distributes observations across latitude, local solar time, and altitude.
Because candidates can be restricted to objects already on orbit and routinely tracked, the loop is closed end-to-end with real data: densities inferred from the orbital decay of the selected objects are assimilated and scored against an independent high-accuracy reference spanning a broad altitude range. Reliance only on two-line-element–derived orbit data indicates that neither thrust requires specialized measurement infrastructure. The assimilated states further constitute observation-informed datasets for periodically retraining the reduced-order models, establishing a feedback loop in which routine assimilation refines the underlying dynamical representation. Together, these results link where observations are placed to how much they improve operationally relevant density specification.
Date of Conference: September 15-18, 2026
Track: Atmospherics/Space Weather