Constant, Charles; Mutschler, Shaylah M; Bhattarai, Santosh; Pilinski, Marcin; (2025) Bring the Noise: Three Rules for Improving Thermospheric Density Retrieval from LEO POD Data. In: Proceedings of the 2025 AMOS Conference. Maui Economic Development Board: Wailea, HI, USA. (In press).

Text POD_Assimilation___AMOS_2025-14.pdf - Accepted Version Access restricted to UCL open access staff Download (3MB)

Abstract

Thermospheric drag represents one of the largest sources of operational uncertainty for Low Earth Orbit (LEO) operations today. This uncertainty translates into degraded operational products and ultimately a worse characterisation of the future risk of collision between space objects. This problem is particularly acute during geomagnetic storms, where density at a given altitude may rise by up to an order of magnitude in a matter of hours. Accurate, timely knowledge of current and future thermospheric density in LEO is increasingly critical for the Space Situational Awareness (SSA) and satellite operations communities as the space object population continues to grow. Available methods of providing density estimates fall short of the community’s needs on several counts (e.g. accuracy, latency, and licensing restrictions). As a result, interest has grown in leveraging Precise Orbit Determination (POD) data streams generated by the growing number of LEO spacecraft to enable a step change in the quality and quantity of data available to drive the next generation of assimilative thermospheric density models. One frequently used type of method for using satellite tracking data to invert for thermospheric density along orbital trajectories is called the Energy Dissipation Rate (EDR) method. This approach relies on converting state vectors to orbital energy and translating the fluctuations in energy into estimates of thermospheric density. We quantify how four factors influence the performance of density retrievals using the EDR method on POD data: POD noise level, drag acceleration the satellites are exposed to, time interval over which the estimation is carried (“fit-span”), and the number of spacecraft used simultaneously to generate observations. We simulate the orbits of satellites along Starlink–like trajectories over the month of April 2023, using HASDM as the density model. To improve on the commonly used white-noise representation for POD noise, we propose and implement a higher-fidelity POD noise model that incorporates anisotropy, autocorrelation, and geometric dilution of precision (GDOP) modulation, reflecting more realistic performance bounds. We test this model at three noise levels, informed by values reported in the literature. We then modify the semi-major axis of the orbits to sample ten drag different levels, vary the fit-span over which the density is inverted from one to five orbits, and measure the effect of averaging simultaneous observations from up to 18 equally spaced co-orbital satellites. Three clear rules of thumb emerge: / 1. Fit-span: Doubling the observation window roughly halves the RMS percentage error. / 2. Satellite-count rule: For satellites distributed along a single orbital track, adding satellites to the average reduces error following an inverse power law: ∼ N −0.6 for unassimilated retrievals and ∼ N −0.25 for averages of individually assimilated estimates. / 3. Drag rule: Density retrieval performance follows a logistic-like response to drag: for weak signals (< 2 × 10−8 ms−2 ) improvements are negligible; in a transition band (2×10−8–2×10−7 ms−2 ) each ∼ 3× increase in drag yields ∼ 50% error reduction; beyond 10−6 ms−2 returns diminish. This pattern is consistent across all three noise levels studied. / When the number of contributing satellites is sufficiently large or the POD data sufficiently low-noise, a simple mean of unassimilated retrievals can match or exceed the average of individually assimilated estimates. Because this result arises from a per-satellite assimilation scheme, it should be interpreted as a lower bound on assimilative performance; more advanced multi-satellite frameworks are expected to perform better. Assimilation remains essential for providing four-dimensional density estimates. Overall, the results provide a first sampling of the density-retrieval error space and a compact analytical approximation of how errors scale with POD noise, drag regime, fit-span, and satellite count. These results aim to support the development of the next generation of assimilative thermospheric density models.

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