Estimating Geodetic Parameters from the Cassini-Titan Orbit Determination Problem: A Systematic Simulation Study

[Introduction] The existing literature on Titan geodetic parameter estimation from Cassini Doppler data provides an ambiguous view on Titan’s interior and evolution. Recently, three different analyses of this kind have delivered three different (and in parts conflicting) sets of constraints on models of Titan’s interior [1,2,3]. Such parameter estimation analyses involve numerous choices that are rarely documented in full, making it hard to understand, let alone reproduce, published results. Additionally, the analyses are performed using different proprietary software packages. With the present work, we aim to offer a more transparent and accessible analysis of the Cassini-Titan inversion problem and to elucidate the factors underlying differences between previous analyses.

[Method] Using the open-source high-fidelity parameter estimation software Tudat [4], we conduct a systematic simulation study of the inversion problem, in preparation of a full inversion of the Doppler data. As such, this analysis will not present another parameter estimate, but instead studies in a controlled environment the mechanisms that govern the inversion problem. Specifically, we study choices of data selection and weighting, the prior information that is supplied to the filter, and various dynamic models and assess their effect on key geodetic parameters such as the tidal Love number Re(k2) and the static gravity field.

[Results] While many of these aspects significantly affect the formal uncertainty and even the stability with which geodetic parameters are recovered from the inversion, we focus our findings on the treatment of the Titan state estimation. We find that the formal uncertainties of Re(k2), the degree 2 gravity field parameters and even Titan’s gravitational parameter are strongly dependent on how the Titan state is constrained a-priori. We show that choosing prior constraints from a fully independent (astrometry-based) Titan ephemeris solution [5] and applying them in their full form (i.e. including correlations between state parameters) results in more realistic quantification of formal uncertainties and improves the overall stability of the solution. This will also provide important insight towards the fitting of a single consistent Titan orbit across all Cassini flyby arcs. In addition, the lessons learned through our analysis will inform the best practices for the inversion of JUICE’s and Europa Clipper’s multi-flyby and orbit data sets in the Jovian system [6].

We thank V. Lainey for helpful discussions and for providing the covariance matrices of the 2018 JPL/IMCCE Titan ephemeris solution.

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