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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 5145419, 17 pages
Research Article

Influence of the Choice of Lunar Gravity Model on Orbit Determination for Lunar Orbiters

Lunar Exploration Operation Team, Korea Aerospace Research Institute, Daejeon 34133, Republic of Korea

Correspondence should be addressed to Young-Rok Kim

Received 8 September 2017; Revised 15 December 2017; Accepted 26 December 2017; Published 1 February 2018

Academic Editor: Viktor Avrutin

Copyright © 2018 Young-Rok Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We examine the influence of the lunar gravity model on the orbit determination (OD) of a lunar orbiter operating in a 100 km high, lunar polar orbit. Doppler and sequential range measurements by three Deep Space Network antennas and one Korea Deep Space Antenna were used. For measurement simulation and OD analysis, STK11 and ODTK6 were utilized. GLGM2, LP100K, LP150Q, GRAIL420A, and GRAIL660B were used for investigation of lunar gravity model selection effect. OD results were assessed by position and velocity uncertainties with error covariance and an external orbit comparison using simulated true orbit. The effect of the lunar gravity models on the long-term OD, degree and order level, measurement-acquisition condition, and lunar altitude was investigated. For efficiency verification, computational times for the five lunar gravity models were compared. Results showed that significant improvements to OD accuracy are observed by applying a GRAIL-based model; however, applying a full order and degree gravity modeling is not always the best strategy, owing to the computational burden. Consequently, we consider that OD using GRAIL660B with 70 × 70 degree and order is the most efficient strategy for mission preanalysis. This study provides useful guideline for KPLO OD analysis during nominal mission operation.