Coupled and decoupled strategies for spacecraft's and natural bodies' state estimation - Application to the JUICE mission

 

Abstract

When generating ephemerides from planetary missions' tracking data, the natural bodies' dynamics are typically estimated separately from the spacecraft's state. A different approach, in which the spacecraft orbit determination and natural bodies' state determination are performed concurrently, allows to fully account for the coupling of the spacecraft's and natural bodies' dynamics.

Using JUICE data, we will compare the concurrent spacecraft's and natural satellite's state estimation with the per-flyby estimation of the natural satellite's state followed by a simulated ephemeris determination. The strong coupling between the three inner Galilean moons' dynamics due to Laplace resonances, combined with an unbalanced data set for these moons, makes the JUICE mission a very special test case which is particularly well-adapted to compare the two estimation strategies.

 

1. Introduction

In ephemerides generation, the spacecraft's and natural bodies' dynamics are typically not solved concurrently. When determining the natural bodies' ephemerides from a series of flybys, the state of the central body and the state of the spacecraft with respect to this natural body are first solved for each flyby. The natural bodies' dynamics are then reconstructed in a subsequent step, combining all per-flyby single data points and using them as inputs in a second estimation (e.g. Lainey et al., 2020). However, obtaining a dynamically consistent solution reconciling the natural bodies' states estimated at the different flybys is not always achievable (e.g. Titan's ephemeris from Cassini's flybys, Durante et al., 2019).

When using both range and Doppler measurements collected during an orbital phase, the spacecraft orbit determination and ephemeris generation are also conducted in two separate, consecutive steps. The spacecraft's state with respect to the central body is usually first determined using Doppler data. Range measurements can then be translated from spacecraft-centred to body-centred and used to solve for the natural body's dynamics. This is generally a practical approach, as the frequencies of interest are so distinct (Dirkx et al, 2019).

However, such estimation approaches do not fully account for the coupling between the spacecraft's and natural bodies' dynamics, thus hindering the achievement of a consistent solution. An alternative strategy therefore consists in concurrently estimating both the spacecraft's and natural bodies' states, the former being solved for in a multi-arc manner while the latter is determined in a single arc. Such a coupled method reduces the risk of a signal in the spacecraft's dynamics being wrongly captured in the natural body's estimated state.

The detailed mathematical description of this coupled state estimation, while already used in many other studies (e.g. Dirkx et al, 2019 ; Lari et al., 2019), is not provided in literature and is thus explicitly laid out in Section 2. 

 

2. Coupled estimation

To estimate both the spacecraft's and natural bodies' states, the state transition matrix is required. We note 

the full state at time t (for clarity, dimensions are added as superscripts when needed). It combines the states of n natural bodies y_S(t) and the arc-wise spacecraft's state y_M,i(t), with t∈[ti,t_i+1]  (t_i being the starting time of arc i). The initial states vector to be estimated is defined as

and contains the natural bodies' initial single-arc states and N spacecraft states y_M,i(t_i), defined at the start of each arc i (N multi-arcs in total). The state transition matrix Φ is then given by

where Φ_SS and Φ_MM,i designate the single-arc and multi-arc state transition matrices, respectively. The matrix Φ_MS,i describes the influence of the natural bodies' initial states on the spacecraft's dynamics. On the contrary, the natural bodies' trajectory is assumed to be independent of the spacecraft's. Both Φ and the sensitivity matrix S, necessary to also solve for dynamical parameters q, are propagated and used to perform the estimation.

 

JUICE mission test case

The improvement in the ephemerides solution achieved by a concurrent estimation rather than decoupled techniques remains to be quantified. The Galilean moons' ephemerides generation from the JUICE data represents a perfect test case for a comparative analysis.

The Laplace resonances between the three innermost Galilean moons indeed induce a very strong coupling between their dynamics. It thus strengthens the need for a consistent concurrent estimation approach when reconstructing their ephemerides. This effect is further enhanced by the unique orbital design of the JUICE mission, which consists in a series of flybys, unevenly distributed between Europa, Ganymede and Callisto, before a long orbital phase around Ganymede. This results in an unbalanced data set, making the highly coupled dynamics of the Galilean moons even more challenging to solve for. 

We will perform the concurrent state estimation for these satellites, focusing primarily on the flyby phase. We will also check whether a dynamically consistent solution can be achieved when conducting the ephemerides generation separately from the spacecraft orbit determination. If achievable, this solution will be compared with the coupled strategy's one. 

We will also assess the impact of a fully coupled approach on the estimation of dynamical parameters, investigating tidal dissipation rates in particular, as tidal dissipation processes are key to understanding the long-term evolution of the Jovian system.

 

Future plans

The coupled estimation framework presented here will eventually be applied to develop and disseminate an open-source Python estimation simulator for the JUICE mission, with flexible data planning and acquisition scenarios (using Tudat(Py) software: Python interface, C++ back-end).

Another future step is to investigate the possible synergy between JUICE and other Jovian system missions: Europa Clipper and possibly IVO. The data sets of these three missions are indeed expected to complement each other, as they separately focus on the three Galilean moons in resonance. The possibility for the Europa Clipper and JUICE spacecraft to be in the Jovian system simultaneously also represents a unique opportunity to perform concurrent in-system measurements. The contribution of such observations to the estimation solution will be quantified.

This multi-mission analysis will be achieved by expanding the current coupled estimation framework and developing a global inversion tool to concurrently perform the orbit determination of multiple spacecraft while generating ephemerides for several natural bodies. This extended estimation software, applicable to any tracking scenarios, will also be disseminated open-source with a Python interface.