【助成 39 - 27】

非太陽周回小天体ミッションにおける天体暦エラーの影響の定量化と軽減
代表研究者
研究者 九州大学 大学院工学研究院 助教

陳 泓儒〔研究の概要〕Many small celestial bodies (i.e., comets, asteroids, and small planetary moons) preserve pristine relics of theearly solar system. Small-body missions Hayabusa-1, -2, Rosetta, and Osiris-REx have returned notablesamples and data. The confirmed MMX (JAXA) and HERA-Juventas (ESA) missions will explore Martianmoons (i.e., Phobos and Deimos) and the binary asteroid Dimorphos, respectively, which are small bodies
orbiting a primary body. In such missions, not only the complex gravity of the primary body, but also theposition of the secondary relative to the primary, the ephemeris, perturbs the orbiting operations as well as
the science return. The ephemeris error had not been experienced in previous missions. However, it cangreatly perturb the GNC and geodesy in the near-term non-heliocentric small body missions. The impact ofephemeris error had not been identified nor tackled before, which was addressed in this project.

〔研究経過および成果〕

as the overall uncertainties are too large, and theP r o b l e m s t a t e me n t

estimation problem has too many local optima.

Previous work generally constraints the number ofApproach 1: Consider ephemeris time shift inestimated variables or set the a-priori uncertainties

e s t i ma t i o n

to 5%, and only assumes a few hundred meters of

The ephemeris error can by approximated by theephemeris error. The error of estimated C22 goes toerror in the transvers direction and represented by a30%, libation amplitude cannot be estimated, errors ofmean anomaly or time shift Δet. As the fly tracking

orbits are 200 m and 5 cm/s large, libration amplitude

information barely exhibits signature of the ephemeris

cannot be observed, as ephemeris error goes from 0error, it is still tricky to recover this single variable.

to just a few hundreds of meters. The realistic

The applicant treated Δet as a “consider parameter”

ephemeris error can be a few kilometers. Thisin estimation. That means, it is not estimated, but its

accuracy of degree-2 gravity terms and librationnoise on the estimation of other parameters isamplitude is useful in reflecting the internal structure

considered (Pub. [1]). As a result, even under anof the target. Ephemeris error has at least threeephemeris error of 2 km, orbit determination error

influencing position components. It is tricky tobecomes 10 times smaller, and the libration amplitudeidentify all variables, namely, spacecraft’s six orbit(θ) identification of geodetic parameters of thestates, geodetic parameters, and the ephemeris error,

target is significantly improved. The degree-2 terms

54can be estimated to an accuracy of 0.5%, and librationsuch a non-convex problem. While there are theamplitude 8%. which is excellent for distinguishing thesigma points, which are 2 times the number ofinterior families (Fig.1).

estimated variables, to propagate, the propagations
can be performed in parallel. Therefore, the parallel
propagator comes to play a role (Fig.2). The
estimation takes into account almost all variables (30of them) and reasonable a-priori uncertainties, andstill return good estimation performance. The OD
accuracy reaches 20 m and 0.4 cm/s in just one day

Fig. 1 Errors of gravity coefficients(Fig.2), much more advanced than the presumed

estimated in the three situations

performance of MMX, namely 86 m and 0.5 cm/s inApproach

2:Pa r a l l e l

h i g h- f i d e l i t y

one week. Thus, this mission manner is promising toor bi t

p r o p a g a t o r - b a s e d e s t i ma t i o n

support quick and autonomous navigation in theThe applicant developed the full dynamics orbit

highly perturbed small-body environment.

propagator that can take dynamical variables, such as〔発表論文〕

ephemerides and non-spherical gravity fields of

１． Chen, H.; Rambaux, N.; Lainey, V.; Hestroffer,celestial bodies. The tool is coded in C to enjoy fast

D. Mothership-Cubesat Radioscience for Phobos

integration and can be called by Matab (using theGeodesy and Autonomous Navigation. Remote

C-MEX interface) to enjoy fast and handy matrix

Sens. 2022, 14, 1619.

operations. In the problem of interest with many

２． Chen, H., Rambaux, N., Lainey, V., andvariables to estimate, many local minima exist and canHestroffer,

D.,

cause

Radiosciencefor

thelinearization-basedestimation(e.g.,“Mothership-CubeSat
PhobosGeodesyandextended Kalman filter) to fail. The estimation based

Autonomous Navigation”, in 44th COSPAR

on the more accurate modeling unscented transform

Scientific Assembly. Held 16-24 July, 2022, vol.

(e.g., unscented Kalman filter) works much better for

44, p. 228.

Fig. 2 Parallel high-fidelity
propagator-based estimation result.

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