Accelerometer Measurements for Orbit and Gravity Recovery: Challenges and Benefits for the BepiColombo Mission

Abstract

The European Space Agency's BepiColombo mission continues its pioneering voyage to Mercury, the innermost planet of the Solar System. Among the advanced instruments onboard the Mercury Planetary Orbiter (MPO) is the Italian Spring Accelerometer (ISA), whose scientific objectives are closely linked to the Mercury Orbiter Radio-Science Experiment (MORE). Together, these instruments aim to provide high-precision data on the spacecraft's orbit, as well as Mercury's gravity field and internal structure. This simulation study investigates how the modeling and parametrization of accelerometer measurements influence orbit and gravity field recovery and explores strategies to overcome the challenges associated with the co-estimation of all parameters. We assess the integrated retrieval accuracy of the spacecraft orbit, gravity field, and accelerometer parameters under different noise levels and varying observation geometries during the mission. The MPO orbit is propagated, and Doppler and accelerometer measurements are simulated based on available noise models. Our results indicate that postponing the estimation of accelerometer biases until a preliminary gravity field is established helps prevent gravity field mismodelings from being absorbed into the accelerometer parameters. The daily estimation of bias was found to be essential. Using one year of Doppler tracking data and applying Kaula regularization, we demonstrate the potential to recover Mercury's gravity field up to degree and order 40. Low-degree coefficients improve under more optimistic noise conditions. Errors in cross-track bias estimation rise sharply when the beta-Earth angle falls below 45°, corresponding to the degraded Doppler observability. Orbit determination achieved centimetre-level radial accuracy and metre-level along- and cross-track accuracy, with increased cross-track errors during low-observability periods.

Figures (6)

• Figure S1: Artistic visualization of the spacecraft around Mercury; orbit determination is done using the two-way radio tracking signal. Image generated using OpenAI's ChatGPT (DALL·E), June 2025.
• Figure S2: Simulation of the ISA accelerometer noise in frequency (top) and time (bottom) domains.
• Figure S3: Difference and error degree amplitude using one year of MPO's 2-way Doppler observations. The blue curve shows the recovered gravity field with biased accelerometer data; further recovery of the gravity field during the nominal mission, by co-estimating accelerometer biases when assuming a realistic (red) or optimistic (green) accelerometer noise model. Differences are mainly visible at low degrees, where the green curve matches formal uncertainties. A Kaula regularization constraint was applied from d/o 40 upwards, using a standard deviation of $\sigma_n = 10^{-4} / n^2$ for each degree $n$.
• Figure S4: Daily RMS error of the radial (top), along-track (middle), and cross-track (bottom) accelerometer biases as a function of the $\beta$-Earth angle (see Section \ref{['sec:modelingDop']}). $3\sigma$ bins are plotted on top of the scatter values to highlight the dependency on the $\beta$-Earth angle. The left column corresponds to the realistic scenario, while the right column corresponds to the optimistic scenario.
• Figure S5: Position and velocity errors for the first $120$ days of the mission. Orbits are propagated from our final converged solution using one year of Doppler observations, when assuming an optimistic (green) or a more realistic (red) scenario for the accelerometer noise. Considerably larger errors in the cross-track direction are observed between days $30$ and $70$, corresponding to periods when the $\beta$-Earth angle (as defined in Section \ref{['sec:modelingDop']}) consistently remains below $45^\circ$ (gray area).