{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T18:46:35Z","timestamp":1779907595750,"version":"3.53.1"},"reference-count":60,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,8,23]],"date-time":"2017-08-23T00:00:00Z","timestamp":1503446400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>High-precision electrostatic accelerometers have achieved remarkable success in satellite Earth gravity field recovery missions. Ultralow-noise inertial sensors play important roles in space gravitational wave detection missions such as the Laser Interferometer Space Antenna (LISA) mission, and key technologies have been verified in the LISA Pathfinder mission. Meanwhile, at Huazhong University of Science and Technology (HUST, China), a space accelerometer and inertial sensor based on capacitive sensors and the electrostatic control technique have also been studied and developed independently for more than 16 years. In this paper, we review the operational principle, application, and requirements of the electrostatic accelerometer and inertial sensor in different space missions. The development and progress of a space electrostatic accelerometer at HUST, including ground investigation and space verification are presented.<\/jats:p>","DOI":"10.3390\/s17091943","type":"journal-article","created":{"date-parts":[[2017,8,23]],"date-time":"2017-08-23T11:32:27Z","timestamp":1503487947000},"page":"1943","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":67,"title":["Research and Development of Electrostatic Accelerometers for Space Science Missions at HUST"],"prefix":"10.3390","volume":"17","author":[{"given":"Yanzheng","family":"Bai","sequence":"first","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhuxi","family":"Li","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Hu","sequence":"additional","affiliation":[{"name":"Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Liu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shaobo","family":"Qu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dingyin","family":"Tan","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haibo","family":"Tu","sequence":"additional","affiliation":[{"name":"Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuchao","family":"Wu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hang","family":"Yin","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongyin","family":"Li","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zebing","family":"Zhou","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1590","DOI":"10.2514\/3.55086","article-title":"The Drag-Free Satellite","volume":"2","author":"Lange","year":"1964","journal-title":"AIAA J."},{"key":"ref_2","first-page":"14","article-title":"Disturbance compensation system design","volume":"12","author":"DeBra","year":"1973","journal-title":"APL Tech. Dig."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Staff of the Space Department in the Johns Hopkins University, and Staff of the Guidance and Control Laboratory in Stanford University (1974). A satellite freed of all but gravitational forces: \u201cTRIAD I\u201d. J. Spacecr., 11, 637\u2013644.","DOI":"10.2514\/3.62146"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3753","DOI":"10.1029\/JA081i022p03753","article-title":"Exospheric density measurements from the drag-free satellite Triad","volume":"81","author":"Moe","year":"1976","journal-title":"J. Geophys. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1016\/0094-5765(77)90008-X","article-title":"In orbit performance of the Cactus accelerometer (D5B spacecraft)","volume":"4","author":"Beaussier","year":"1977","journal-title":"Acta Astronaut."},{"key":"ref_6","unstructured":"Bouttes, J., and Delattre, M. (1977). The Cactus accelerometer in orbit. Sci. Tech., 17\u201321. (In French)."},{"key":"ref_7","unstructured":"Touboul, P., and Foulon, B. (1996, January 10). ASTRE Accelerometer: Verification tests in Drop Tower Bremen. Proceedings of the Drop Tower Days, Bremen, Germany. ONERA-TAP-96-124."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kenyon, S., Pacino, M., and Marti, U. (2012). CHAMP, GRACE, GOCE instruments and beyond. Geodesy for Planet Earth, Springer.","DOI":"10.1007\/978-3-642-20338-1"},{"key":"ref_9","first-page":"1","article-title":"The MESA accelerometer for space application","volume":"14","author":"Lange","year":"1990","journal-title":"NTRS"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1186\/BF03351933","article-title":"Swarm: A constellation to study the Earth\u2019s magnetic field","volume":"58","author":"Hulot","year":"2006","journal-title":"Earth Planets Space"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"S99","DOI":"10.1088\/0264-9381\/20\/10\/312","article-title":"Gravitational sensor for LISA and its technology demonstration mission","volume":"20","author":"Dolesi","year":"2003","journal-title":"Class. Quantum Gravity"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"231101","DOI":"10.1103\/PhysRevLett.116.231101","article-title":"Sub-Femto-g Free Fall for Space-Based Gravitational Wave Observatories: LISA Pathfinder Results","volume":"116","author":"Armano","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.asr.2005.10.040","article-title":"Development status of the differential accelerometer for the MICROSCOPE mission","volume":"39","author":"Hudson","year":"2007","journal-title":"Adv. Space Res."},{"key":"ref_14","first-page":"86","article-title":"Proposal for testing non-Newtonian gravitational force in space","volume":"24","author":"Guan","year":"2007","journal-title":"Jpn. Soc. Microgravity Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"080401","DOI":"10.1088\/0256-307X\/28\/8\/080401","article-title":"Feasibility for testing the equivalence principle with optical readout in space","volume":"28","author":"Gao","year":"2011","journal-title":"Chin. Phys. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"035010","DOI":"10.1088\/0264-9381\/33\/3\/035010","article-title":"TianQin: A space-borne gravitational wave detector","volume":"33","author":"Luo","year":"2016","journal-title":"Class. Quantum Gravity"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s00190-013-0615-6","article-title":"Analytical error analysis for satellite gravity field determination based on two-dimensional Fourier method","volume":"87","author":"Cai","year":"2013","journal-title":"J. Geod."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1016\/S0094-5765(99)00132-0","article-title":"Elctrostatic space accelerometers for present and future missions","volume":"45","author":"Touboul","year":"1999","journal-title":"Acta Astronaut."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3957","DOI":"10.1063\/1.1511798","article-title":"Three-axis superconducting gravity gradiometer for sensitive gravity experiments","volume":"73","author":"Moody","year":"2002","journal-title":"Rev. Sci. Instrum."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"033608","DOI":"10.1103\/PhysRevA.65.033608","article-title":"Sensitive absolute-gravity gradiometry using atom interferometry","volume":"65","author":"McGuirk","year":"2002","journal-title":"Phys. Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"S293","DOI":"10.1088\/0264-9381\/20\/10\/332","article-title":"Flight experience on CHAMP and GRACE with ultra-sensitive accelerometers and return for LISA, Class","volume":"20","author":"Rodrigues","year":"2003","journal-title":"Quantum Gravity"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Flechtner, F., Sneeuw, N., and Schuh, W.D. (2014). Observation of the System Earth from Space CHAMP, GRACE, GOCE and Future Missions, Springer. Geotechnologien Science Report No. 20.","DOI":"10.1007\/978-3-642-32135-1"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.actaastro.2015.06.021","article-title":"A new generation of ultra-sensitive electrostatic accelerometers for GRACE follow-on and towards the next generation gravity missions","volume":"117","author":"Christophe","year":"2015","journal-title":"Acta Astronaut."},{"key":"ref_24","unstructured":"Marque, J.P., Christophe, B., Liorzou, F., and Foulon, B. (2017, July 12). Preliminary in-Orbit Data of the Accelerometers on the ESA GOCE Mission. Available online: https:\/\/iafastro.directory\/iac\/archive\/browse\/IAC-09\/B1\/3\/3526\/."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2269","DOI":"10.1016\/j.asr.2013.01.031","article-title":"Electrostatic gravity gradiometer design for the future mission","volume":"51","author":"Zhu","year":"2013","journal-title":"Adv. Space Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1126\/science.1231507","article-title":"Gravity field of the moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission","volume":"339","author":"Zuber","year":"2013","journal-title":"Science"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1016\/j.asr.2013.04.009","article-title":"Lunar gravity gradiometry and requirement analysis","volume":"52","author":"Cai","year":"2013","journal-title":"Adv. Space Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.12942\/lrr-2013-7","article-title":"Testing general relativity with low-frequency, space-based gravitational-wave detectors","volume":"16","author":"Gair","year":"2013","journal-title":"Living Rev. Relativ."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Schumaker, B.L. (2003). Disturbance reduction requirements for LISA. Class. Quantum Gravity, 20.","DOI":"10.1088\/0264-9381\/20\/10\/327"},{"key":"ref_30","unstructured":"(2017, July 12). LISA: A Cornerstone Mission for the Observation of Gravitational Waves. Available online: http:\/\/elmer.tapir.caltech.edu\/ph237\/week17\/sts_1.05.pdf."},{"key":"ref_31","unstructured":"Amaro-Seoane, P., Audley, H., Babak, S., Baker, J., Barausse, E., Bender, P., Berti, E., Binetruy, P., Born, M., and Bortoluzzi, D. (2017, July 12). Laser Interferometer Space antenna. Available online: https:\/\/arxiv.org\/abs\/1702.00786."},{"key":"ref_32","unstructured":"McNamara, P., and Racca, G. (2017, July 12). Introduction to LISA Pathfinder. Available online: https:\/\/www.google.com.hk\/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahUKEwiczZXEnOfVAhWLV7wKHcxMCEwQFggtMAE&url=http%3A%2F%2Fsci.esa.int%2Fscience-e%2Fwww%2Fobject%2Fdoc.cfm%3Ffobjectid%3D45820&usg=AFQjCNH7IlxX5vASqNSjYRHaGNwu2nGW8A."},{"key":"ref_33","first-page":"151001","article-title":"Achieving geodetic motion for LISA test masses: Ground testing results","volume":"91","author":"Carbone","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"S537","DOI":"10.1088\/0264-9381\/22\/10\/055","article-title":"Torsion pendulum for the performance test of the inertial sensor for ASTROD-I","volume":"22","author":"Zhou","year":"2005","journal-title":"Class. Quantum Gravity"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Schlamminger, S., Hagedorn, C.A., Famulare, M.G., Pollack, S.E., and Gundlach, J.H. (2006, January 19\u201323). High sensitivity torsion balance tests for LISA proof mass modeling. Proceedings of the 6th International LISA Symposium, Greenbelt, MD, USA.","DOI":"10.1063\/1.2405035"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"205016","DOI":"10.1088\/0264-9381\/27\/20\/205016","article-title":"Performance measurements of an inertial sensor with a two-stage controlled torsion pendulum","volume":"27","author":"Tu","year":"2010","journal-title":"Class Quantum. Gravity"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"140601","DOI":"10.1103\/PhysRevLett.103.140601","article-title":"Increased Brownian force noise from molecular impacts in a constrained volume","volume":"103","author":"Cavalleri","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"181101","DOI":"10.1103\/PhysRevLett.108.181101","article-title":"Interaction between stray electrostatic fields and a charged free-falling TM","volume":"108","author":"Antonucci","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1757","DOI":"10.1088\/0264-9381\/19\/7\/372","article-title":"Torsion pendulum facility for ground testing of gravitational sensors for LISA","volume":"19","author":"Hueller","year":"2002","journal-title":"Class. Quantum Gravity"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"071101","DOI":"10.1103\/PhysRevLett.101.071101","article-title":"Temporal extent of surface potentials between closely spaced metal","volume":"101","author":"Pollack","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1016\/S0273-1177(99)00982-5","article-title":"The gravity probe B relativity mission","volume":"25","author":"Buchman","year":"2000","journal-title":"Adv. Space Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1142\/S0218271808012619","article-title":"ASTROD and ASTROD I\u2014Overview and progress","volume":"17","author":"Ni","year":"2008","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"S125","DOI":"10.1088\/0264-9381\/23\/8\/S17","article-title":"The Japanese space gravitational wave antenna: DECIGO","volume":"23","author":"Kavamura","year":"2006","journal-title":"Class. Quantum Gravity"},{"key":"ref_44","unstructured":"Blaser, J.P., Bye, M., Cavallo, G., Damour, T., Everitt, C.W.F., Hedin, A., Hellings, R.W., Jafry, Y., Laurance, R., and Lee, R. (2017, July 12). STEP report on the Phase A Study, Available online: https:\/\/ntrs.nasa.gov\/search.jsp?R=19950019764."},{"key":"ref_45","unstructured":"Will, C.M. (2017, July 12). The Confrontation between General Relativity and Experiment. Available online: https:\/\/link.springer.com\/article\/10.12942\/lrr-2006-3."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2487","DOI":"10.1088\/0264-9381\/18\/13\/311","article-title":"The MICROSCOPE space mission","volume":"18","author":"Touboul","year":"2001","journal-title":"Class. Quantum Gravity"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"012028","DOI":"10.1088\/1742-6596\/840\/1\/012028","article-title":"MICROSCOPE: Five months after launch","volume":"840","author":"Touboul","year":"2017","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s11467-009-0019-5","article-title":"Capacitive position measurement for high-precision space inertial sensor","volume":"4","author":"Bai","year":"2009","journal-title":"Front. Phys. China"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"055001","DOI":"10.1063\/1.4873334","article-title":"Resonant frequency detection and adjustment method for a capacitive transducer with differential transformer bridge","volume":"85","author":"Hu","year":"2014","journal-title":"Rev. Sci. Instrum."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"095002","DOI":"10.1063\/1.4749845","article-title":"High resolution space quartz-flexure accelerometer based on capacitive sensing and electrostatic control technology","volume":"83","author":"Tian","year":"2012","journal-title":"Rev. Sci. Instrum."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"125004","DOI":"10.1063\/1.4833398","article-title":"Design and validation of a high-voltage levitation circuit for electrostatic accelerometers","volume":"84","author":"Li","year":"2013","journal-title":"Rev. Sci. Instrum."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"195016","DOI":"10.1088\/0264-9381\/32\/19\/195016","article-title":"A low-frequency vibration insensitive pendulum bench based on translation-tilt compensation in measuring the performances of inertial sensors","volume":"32","author":"Liu","year":"2015","journal-title":"Class. Quantum Gravity"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"055010","DOI":"10.1088\/0264-9381\/29\/5\/055010","article-title":"Measurement of the effect of a thin discharging wire for an electrostatic inertial sensor with a high-quality-factor pendulum","volume":"29","author":"Liu","year":"2012","journal-title":"Class. Quantum Gravity"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"175018","DOI":"10.1088\/0264-9381\/32\/17\/175018","article-title":"Improving the measurement sensitivity of angular deflection of a torsion pendulum by an electrostatic spring","volume":"32","author":"Bai","year":"2015","journal-title":"Class. Quantum Gravity"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"175012","DOI":"10.1088\/0264-9381\/27\/17\/175012","article-title":"Seismic noise limit for ground-based performance measurements of an inertial sensor using a torsion balance","volume":"27","author":"Zhou","year":"2010","journal-title":"Class. Quantum Gravity"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"090401","DOI":"10.1088\/0256-307X\/32\/9\/090401","article-title":"Seismic noise suppression for ground-based investigation of an inertial sensor by suspending the electrode cage","volume":"32","author":"Tan","year":"2015","journal-title":"Chin. Phys. Lett."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"122001","DOI":"10.1103\/PhysRevD.90.122001","article-title":"Measurements of temporal and spatial variation of surface potential using a torsion pendulum and a scanning conducting probe","volume":"90","author":"Yin","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"114502","DOI":"10.1063\/1.4966248","article-title":"Self-calibration method of the bias of a space electrostatic accelerometer","volume":"87","author":"Qu","year":"2016","journal-title":"Rev. Sci. Instrum."},{"key":"ref_59","first-page":"897","article-title":"Least squares estimation of in-orbit mass center position of the electrostatic accelerometer","volume":"60","author":"Li","year":"2017","journal-title":"Chin. J. Geophys."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Li, H.Y., Bai, Y.Z., Hu, M., Luo, Y.X., and Zhou, Z.B. (2017). A novel controller design for the next generation space electrostatic accelerometer based on disturbance observation and rejection. Sensors, 17.","DOI":"10.3390\/s17010021"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/9\/1943\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:06Z","timestamp":1760208186000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/9\/1943"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,23]]},"references-count":60,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["s17091943"],"URL":"https:\/\/doi.org\/10.3390\/s17091943","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,23]]}}}