{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T08:21:26Z","timestamp":1773649286388,"version":"3.50.1"},"reference-count":54,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T00:00:00Z","timestamp":1551744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["PA 1543\/8-2"],"award-info":[{"award-number":["PA 1543\/8-2"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Past temporal gravity field solutions from the Gravity Recovery and Climate Experiment (GRACE), as well as current solutions from GRACE Follow-On, suffer from temporal aliasing errors due to undersampling of the signal to be recovered (e.g., hydrology), which arise in terms of stripes caused by the north\u2013south observation direction. In this paper, we investigate the potential of the proposed mass variation observing system by high\u2013low inter-satellite links (MOBILE) mission. We quantify the impact of instrument errors of the main sensors (inter-satellite link and accelerometer) and high-frequency tidal and non-tidal gravity signals on achievable performance of the temporal gravity field retrieval. The multi-directional observation geometry of the MOBILE concept with a strong dominance of the radial component result in a close-to-isotropic error behavior, and the retrieved gravity field solutions show reduced temporal aliasing errors of at least 30% for non-tidal, as well as tidal, mass variation signals compared to a low\u2013low satellite pair configuration. The quality of the MOBILE range observations enables the application of extended alternative processing methods leading to further reduction of temporal aliasing errors. The results demonstrate that such a mission can help to get an improved understanding of different components of the Earth system.<\/jats:p>","DOI":"10.3390\/rs11050537","type":"journal-article","created":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T11:19:50Z","timestamp":1551784790000},"page":"537","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Gravity Field Recovery Using High-Precision, High\u2013Low Inter-Satellite Links"],"prefix":"10.3390","volume":"11","author":[{"given":"Markus","family":"Hauk","sequence":"first","affiliation":[{"name":"Institute of Astronomical and Physical Geodesy, Technical University of Munich, Arcisstrasse 21, 80333 Munich, Germany"}]},{"given":"Roland","family":"Pail","sequence":"additional","affiliation":[{"name":"Institute of Astronomical and Physical Geodesy, Technical University of Munich, Arcisstrasse 21, 80333 Munich, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"L09607","DOI":"10.1029\/2004GL019920","article-title":"The gravity recovery and climate experiment experiment, mission overview and early results","volume":"31","author":"Tapley","year":"2004","journal-title":"Geophys. Res. Lett."},{"key":"ref_2","unstructured":"Reigber, C., Schwintzer, P., and L\u00fchr, H. (1998, January 7\u201312). The CHAMP geopotential mission, in bollettino di geofisica teoretica ed applicata, 40\/3-4, September\u2013December 1999. Proceedings of the Second Joint Meeting of the International Gravity and the International Geoid Commission, Trieste, Italy."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1883","DOI":"10.1016\/S0273-1177(03)00162-5","article-title":"Earth gravity field model EIGEN-2","volume":"31","author":"Reigber","year":"2003","journal-title":"Adv. Space Res."},{"key":"ref_4","unstructured":"Xu, G. (2003). GPS. Theory, Algorithms and Applications, Springer."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1889","DOI":"10.1016\/S0273-1177(03)00161-3","article-title":"Champ precise orbit determination using GPS data","volume":"31","author":"Visser","year":"2003","journal-title":"Adv. Space Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4289","DOI":"10.1002\/grl.50881","article-title":"Greenland mass variation from time-variable gravity in the absence of GRACE","volume":"40","author":"Baur","year":"2013","journal-title":"Geophys. Res. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1186\/s40623-016-0499-9","article-title":"Gravity field models derived from swarm GPS data","volume":"68","author":"Arnold","year":"2016","journal-title":"Earth Planets Space"},{"key":"ref_8","first-page":"419","article-title":"GOCE: ESA\u2019s first Earth explorer core mission","volume":"Volume 18","author":"Drinkwater","year":"2003","journal-title":"Earth Gravity Field from Space\u2014From Sensors to Earth Science, Space Sciences Series of ISSI"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/s10712-015-9338-y","article-title":"What can be expected from the GRACE-FO laser ranging interferometer for Earth science applications?","volume":"37","author":"Flechtner","year":"2016","journal-title":"Surv. Geophys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1007\/s00190-012-0566-3","article-title":"Intersatelite laser ranging instrument for the GRACE follow-on mission","volume":"86","author":"Sheard","year":"2012","journal-title":"J. Geod."},{"key":"ref_11","first-page":"407","article-title":"Reducing non-tidal aliasing effects by future gravity satellite formations","volume":"Volume 139","author":"Rizos","year":"2014","journal-title":"Earth on the Edge: Science for a Sustainable Planet"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/978-3-642-10634-7_18","article-title":"Designing Earth gravity field missions for the future: A case study","volume":"Volume 135","author":"Mertikas","year":"2010","journal-title":"Gravity, Geoid and Earth Observation, International Association of Geodesy Symposia"},{"key":"ref_13","first-page":"789","article-title":"Space-borne gravimetric satellite constellations and ocean tides: Aliasing effects","volume":"181","author":"Visser","year":"2010","journal-title":"Geophys. J. Int."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wiese, D.N., Nerem, R.S., and Han, S.C. (2011). Expected improvements in determining continental hydrology, ice mass variations, ocean bottom pressure signals, and earthquakes using two pairs of dedicated satellites for temporal gravity recovery. J. Geophys. Res.","DOI":"10.1029\/2011JB008375"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"7343","DOI":"10.1002\/2017JB014250","article-title":"Treatment of temporal aliasing effects in the context of next generation satellite gravimetry missions","volume":"122","author":"Daras","year":"2017","journal-title":"J. Geophys. Res."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Swenson, S., and Wahr, J. (2006). Post-processing removal of correlated errors in GRACE data. Geophys. Res. Lett.","DOI":"10.1029\/2005GL025285"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1007\/s00190-007-0143-3","article-title":"Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models","volume":"81","author":"Kusche","year":"2007","journal-title":"J. Geod."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1111\/j.1365-246X.2009.04355.x","article-title":"Evaluation of GRACE filter tools from a hydrological perspective","volume":"179","author":"Werth","year":"2009","journal-title":"Geophys. J. Int."},{"key":"ref_19","unstructured":"Horvath, A. (2017). Retrieving Geophysical Signals from Current and Future Satellite Gravity Missions. [Ph.D. Thesis, Technische Universit\u00e4t M\u00fcnchen]."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2648","DOI":"10.1002\/2014JB011547","article-title":"Improved methods for observing Earth\u2019s time variable mass distribution with GRACE using spherical cap mascons","volume":"120","author":"Watkins","year":"2015","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_21","unstructured":"Bender, P.L., Wiese, D.N., and Nerem, R.S. (2008, January 23\u201325). A possible dual-GRACE mission with 90 degree and 63 degree inclination orbits. Proceedings of the Third International Symposium on Formation Flying, Missions and Technologies, Noordwijk, The Netherlands."},{"key":"ref_22","unstructured":"Sharifi, M.A., Sneeuw, N., and Keller, W. (September, January 28). Gravity recovery capability of four generic satellite formations. Proceedings of the 1st International Symposium of the International Gravity Field Sevice \u201cGravity Field of the Earth\u201d, Istanbul, Turkey."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1016\/j.asr.2011.05.027","article-title":"Estimating low resolution gravity fields at short time intervals to reduce temporal aliasing errors","volume":"48","author":"Wiese","year":"2011","journal-title":"Adv. Space Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1093\/gji\/ggy145","article-title":"Treatment of ocean tide aliasing in the context of a next generation gravity field mission","volume":"214","author":"Hauk","year":"2018","journal-title":"Geophys. J. Int."},{"key":"ref_25","unstructured":"Pail, R., Bamber, J., Biancale, R., Bingham, R., Braitenberg, C., Cazenave, A., Eicker, A., Flechtner, F., Gruber, T., and G\u00fcntner, A. (2018, January 4\u201313). Mass variation observing system by high low inter-satellite links (MOBILE)\u2014A mission proposal for ESA Earth Explorer 10. Proceedings of the 20th EGU General Assembly, EGU2018, Vienna, Austria."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2032","DOI":"10.1016\/j.asr.2017.01.028","article-title":"Gravity field recovery in the framework of a Geodesy and Time Reference in Space (GETRIS)","volume":"59","author":"Hauk","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_27","first-page":"235","article-title":"Discovery of the magnetosphere","volume":"Vol. 7","author":"Gillmor","year":"1997","journal-title":"History of Geophysics"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1175\/BAMS-D-12-00227.1","article-title":"The Earthcare satellite: The next step forward in global measurements of clouds, aerosols, precipitation and radiation","volume":"96","author":"Illingworth","year":"2015","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"ref_29","first-page":"38","article-title":"Lageos\u2014A geodynamics tool in the making","volume":"25","author":"Spencer","year":"1977","journal-title":"J. Geol. Educ."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1016\/j.asr.2011.06.016","article-title":"Optical response of nanosatellite BLITS measured by the Graz 2 kHz SLR system","volume":"48","author":"Kucharski","year":"2011","journal-title":"Adv. Space Res."},{"key":"ref_31","unstructured":"Sch\u00e4fer, W., Flechtner, F., Nothnagel, A., Bauch, A., and Hugentobler, U. (2013). Geodetic Time Reference in Space (GETRIS), ESA Study AO\/1-6311\/2010\/F\/WE Final Report GETRIS-TIM-FR-0001."},{"key":"ref_32","unstructured":"Iran Pour, S., Reubelt, T., Sneeuw, N., Daras, I., Murb\u00f6ck, M., Gruber, T., Pail, R., Weigelt, M., van Dam, T., and Visser, P. (2015). Assessment of Satellite Constellations for Monitoring the Variations in Earth Gravity Field\u2014SC4MGV, ESA\u2014ESTEC Contract No. AO\/1-7317\/12\/NL\/AF, Final Report."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s00190-014-0764-2","article-title":"Gravity field processing with enhanced numerical precision for LL-SST missions","volume":"89","author":"Daras","year":"2015","journal-title":"J. Geod."},{"key":"ref_34","unstructured":"Daras, I. (2016). Gravity Field Processing Towards Future LL-SST Satellite Missions. [Ph.D. Thesis, Technische Universit\u00e4t M\u00fcnchen]."},{"key":"ref_35","unstructured":"Yi, W. (2012). The Earth\u2019s Gravitational Field from GOCE. [Ph.D. Thesis, Centre of Geodetic Earth System Research]."},{"key":"ref_36","unstructured":"Shampine, L.F., and Gordon, M.K. (1975). Computer Solution of Ordinary Differential Equations: The Initial Value Problem, W.H. Freeman."},{"key":"ref_37","unstructured":"Champion, K.S.W., Smith, P.A., and Smith-Rose, R.L. (1969). Outline of a general orbit determination method. Space Research IX, Proceedings of the Open Meetings of Working Groups (OMWG) on Physical Sciences of the 11th Plenary Meeting of the Committee on Space Research (COSPAR), Tokyo, Japan, North Holland Publ. Company. Mitteilungen aus dem Institut f\u00fcr Astronomische und Physikalische Geod\u00e4sie, Nr. 51."},{"key":"ref_38","unstructured":"Mayer-G\u00fcrr, T. (2006). Gravitationsfeldbestimmung aus der Analyse Kurzer Bahnb\u00f6gen am Beispiel der Satellitenmissionen CHAMP und GRACE. [Ph.D. Thesis, Rheinische Friedrich-Wilhelms-Universit\u00e4t zu Bonn]."},{"key":"ref_39","unstructured":"Mayer-G\u00fcrr, T., J\u00e4ggi, A., Meyer, U., Yoomin, J., Susnik, A., Weigelt, M., van Dam, T., Flechtner, F., Gruber, C., and G\u00fcnter, A. (2016, January 17\u201322). European gravity service for improved emergency management\u2014Status and project highlights. Proceedings of the EGU General Assembly, EGU 2016, Vienna, Austria."},{"key":"ref_40","unstructured":"Mayer-G\u00fcrr, T., Rieser, D., H\u00f6ck, E., Brockmann, J.M., Schuh, W.D., Krasbutter, I., Kusche, J., Maier, S., Krauss, S., and Hausleitner, W. (2012, January 9\u201312). The new combined satellite only model GOCO03s. Proceedings of the IAG Symposium Gravity, Geoid and Height Systems, Venice, Italy."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1007\/s00190-014-0787-8","article-title":"The updated ESA Earth system model for future gravity mission simulation studies","volume":"89","author":"Dobslaw","year":"2015","journal-title":"J. Geod."},{"key":"ref_42","unstructured":"Savcenko, R., and Bosch, W. (2012). EOT11a-Empirical Ocean Tide Model from Multi-Mission Satellite Altimetry, Deutsches Geod\u00e4tisches Forschungsinstitut. DGFI Report No. 89."},{"key":"ref_43","unstructured":"Ray, R. (1999). A Global Ocean Tide Model from Topex\/Poseidon Altimetry: Got99.2, Goddard Space Flight Center. NASA Technical Memorandum 209478."},{"key":"ref_44","unstructured":"Siemes, C. (2008). Digital Filtering Algorithms for Decorrelation within Large Least Square Problems. [Ph.D. Thesis, University of Bonn]."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1007\/s00190-011-0467-x","article-title":"First GOCE gravity field models derived by three different approaches","volume":"85","author":"Pail","year":"2011","journal-title":"J. Geod."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2667","DOI":"10.1029\/1998JB900036","article-title":"Seasonal variations in low degree zonal harmonics of the Earth\u2019s gravity field from satellite laser ranging observation","volume":"104","author":"Cheng","year":"1999","journal-title":"J. Geophys. Res."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1111\/j.1365-246X.2010.04669.x","article-title":"Propagation of atmospheric model errors to gravity potential harmonics-impact on GRACE de-aliasing","volume":"182","author":"Zenner","year":"2010","journal-title":"Geophys. J. Int."},{"key":"ref_48","first-page":"B04403","article-title":"Time-variable aliasing effects of ocean tides, atmosphere, and continental water mass on monthly mean GRACE gravity field","volume":"109","author":"Han","year":"2004","journal-title":"J. Geophys. Res."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"L06619","DOI":"10.1029\/2003GL019285","article-title":"Impact of short period, non-tidal, temporal mass variability on GRACE gravity estimates","volume":"31","author":"Thompson","year":"2004","journal-title":"Geophys. Res. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1178","DOI":"10.1029\/2001GL014005","article-title":"Correcting GRACE gravity fields for ocean tide effects","volume":"29","author":"Knudsen","year":"2002","journal-title":"Geophys. Res. Lett."},{"key":"ref_51","first-page":"B03405","article-title":"Gravity recovery and climate experiment (GRACE) alias error from ocean tides","volume":"113","author":"Seo","year":"2008","journal-title":"J. Geophys. Res."},{"key":"ref_52","unstructured":"Flechtner, F. (2007). AOD1b Product Description Document for Product Releases 01 to 04, GeoForschungszentrum Potsdam. GRACE 327-750."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"L18401","DOI":"10.1029\/2009GL039401","article-title":"Dwindling groundwater resources in northern India, from satellite gravity observations","volume":"36","author":"Tiwari","year":"2009","journal-title":"Geophys. Res. Lett."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"8130","DOI":"10.1002\/2014GL061052","article-title":"Regional acceleration in ice mass loss from Greenland and Antarctica using GRACE time-variable gravity data","volume":"41","author":"Velicogna","year":"2014","journal-title":"Geophys. Res. Lett."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/5\/537\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:36:31Z","timestamp":1760186191000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/5\/537"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,5]]},"references-count":54,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["rs11050537"],"URL":"https:\/\/doi.org\/10.3390\/rs11050537","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,5]]}}}