{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T07:49:56Z","timestamp":1769154596280,"version":"3.49.0"},"reference-count":24,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,18]],"date-time":"2018-04-18T00:00:00Z","timestamp":1524009600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2017YFC0601603"],"award-info":[{"award-number":["2017YFC0601603"]}]},{"name":"HUST Key Innovation Team Foundation for Interdisciplinary Promotion","award":["2016JCTD102"],"award-info":[{"award-number":["2016JCTD102"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A method for automatic compensation of misalignment angles during matching the scale factors of two pairs of the accelerometers in developing the rotating accelerometer gravity gradient instrument (GGI) is proposed and demonstrated in this paper. The purpose of automatic scale factor matching of the four accelerometers in GGI is to suppress the common mode acceleration of the moving-based platforms. However, taking the full model equation of the accelerometer into consideration, the other two orthogonal axes which is the pendulous axis and the output axis, will also sense the common mode acceleration and reduce the suppression performance. The coefficients from the two axes to the output are \u03b4O and \u03b4P respectively, called the misalignment angles. The angle \u03b4O, coupling with the acceleration along the pendulous axis perpendicular to the rotational plane, will not be modulated by the rotation and gives little contribution to the scale factors matching. On the other hand, because of coupling with the acceleration along the centripetal direction in the rotating plane, the angle \u03b4P would produce a component with 90 degrees phase delay relative to the scale factor component. Hence, the \u03b4P component coincides exactly with the sensitive direction of the orthogonal accelerometers. To improve the common mode acceleration rejection, the misalignment angle \u03b4P is compensated by injecting a trimming current, which is proportional to the output of an orthogonal accelerometer, into the torque coil of the accelerometer during the scale factor matching. The experimental results show that the common linear acceleration suppression achieved three orders after the scale factors balance and five orders after the misalignment angles compensation, which is almost down to the noise level of the used accelerometers of 1~2 \u00d7 10\u22127 g\/\u221aHz (1 g \u2248 9.8 m\/s2).<\/jats:p>","DOI":"10.3390\/s18041247","type":"journal-article","created":{"date-parts":[[2018,4,19]],"date-time":"2018-04-19T10:12:01Z","timestamp":1524132721000},"page":"1247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Study on Misalignment Angle Compensation during Scale Factor Matching for Two Pairs of Accelerometers in a Gravity Gradient Instrument"],"prefix":"10.3390","volume":"18","author":[{"given":"Xiangqing","family":"Huang","sequence":"first","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement &amp; Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"TianQin Research Center for Gravitational Physics and School of Physics and Astronomy, Sun Yat-sen University (Zhuhai Campus), Zhuhai 519082, China"}]},{"given":"Zhongguang","family":"Deng","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement &amp; Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Yafei","family":"Xie","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement &amp; Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Ji","family":"Fan","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement &amp; Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"Institute of Geophysics, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Chenyuan","family":"Hu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement &amp; Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1014-9784","authenticated-orcid":false,"given":"Liangcheng","family":"Tu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement &amp; Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"TianQin Research Center for Gravitational Physics and School of Physics and Astronomy, Sun Yat-sen University (Zhuhai Campus), Zhuhai 519082, China"},{"name":"Institute of Geophysics, Huazhong University of Science and Technology, Wuhan 430074, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,18]]},"reference":[{"key":"ref_1","unstructured":"Lane, R.J.L. (2010, August 23). Airborne Gravity 2010\u2014Abstracts from the ASEG-PESA Airborne Gravity 2010 Workshop: Published Jointly by Geoscience Australia and the Geological Survey of New South Wales. Available online: https:\/\/d28rz98at9flks.cloudfront.net\/70673\/Rec2010_023.pdf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1190\/1.1437806","article-title":"Gravity instruments; past, present, future","volume":"17","author":"Chapin","year":"1998","journal-title":"Lead. Edge"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1111\/j.1365-2478.2008.00764.x","article-title":"Gravity gradiometer systems-advances and challenges","volume":"57","author":"DiFrancesco","year":"2009","journal-title":"Geophys. Prospect."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1190\/1.1437431","article-title":"Gravity gradiometry resurfaces","volume":"16","author":"Bell","year":"1997","journal-title":"Lead. Edge"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1190\/tle32080908.1","article-title":"Performance of airborne gravity gradiometers","volume":"32","author":"Dransfield","year":"2013","journal-title":"Lead. Edge"},{"key":"ref_6","unstructured":"Lane, R.J.L. (2004, August 15). Airborne Gravity 2004\u2014Abstracts from the ASEG-PESA Airborne Gravity 2004 Workshop: Geoscience Australia Record 2004\/18. Available online: https:\/\/d28rz98at9flks.cloudfront.net\/61129\/Rec2004_018.pdf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"B213","DOI":"10.1190\/geo2014-0104.1","article-title":"3D full tensor gradiometry and Falcon Systems data analysis for iron ore exploration: Bau Mine, Quadrilatero Ferrifero, Minas Gerais, Brazil","volume":"79","author":"Braga","year":"2014","journal-title":"Geophysics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"16833","DOI":"10.3390\/s150716833","article-title":"Performance evaluation and requirements assessment for gravity gradient referenced navigation","volume":"15","author":"Lee","year":"2015","journal-title":"Sensors"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1071\/EG01247","article-title":"FALCON gravity gradiometer technology","volume":"32","author":"Lee","year":"2001","journal-title":"Exp. Geophys."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Metzger, E.H. (1977, January 8\u201310). Recent Gravity Gradiometer Developments. Proceedings of the Guidance and Control Conference, Hollywood, FL, USA.","DOI":"10.2514\/6.1977-1081"},{"key":"ref_11","first-page":"323","article-title":"Development experience of gravity gradiometer system","volume":"82","author":"Metzger","year":"1982","journal-title":"IEEE PLANS"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s10712-005-3826-4","article-title":"Airborne gradiometry error analysis","volume":"27","author":"Jekeli","year":"2006","journal-title":"Surv. Geophys."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Difrancesco, D. (2007, January 15\u201318). Advances and Challenges in the Development and Deployment of Gravity Gradiometer Systems. Proceedings of the EGM 2007 International Workshop, Capri, Italy.","DOI":"10.3997\/2214-4609-pdb.166.C_OP_02"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Moody, M.V. (2011). A superconducting gravity gradiometer for measurements from a moving vehicle. Rev. Sci. Instrum., 82.","DOI":"10.1063\/1.3632114"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1103\/PhysRevLett.81.971","article-title":"Measurement of the Earth\u2019s gravity gradient with an atom interferometer-based gravity gradiometer","volume":"81","author":"Snadden","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1063\/1.4944709","article-title":"A seesaw-lever force-balancing suspension design for space and terrestrial gravity-gradient sensing","volume":"119","author":"Liu","year":"2016","journal-title":"J. Appl. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wei, H.W., Wu, M.P., and Cao, J.L. (2017). New matching method for accelerometers in gravity gradiometer. Sensors, 17.","DOI":"10.3390\/s17081710"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"095108","DOI":"10.1063\/1.4895647","article-title":"Implementation of the scale factor balance on two pairs of quartz-flexure capacitive accelerometers by trimming bias voltage","volume":"85","author":"Tu","year":"2014","journal-title":"Rev. Sci. Instrum."},{"key":"ref_19","unstructured":"IEEE Aerospace and Electronic Systems Society (2009). IEEE recommended practice for precision centrifuge testing of linear accelerometers. IEEE Std, 836, 33\u201334."},{"key":"ref_20","unstructured":"O\u2019keefe, G.J., Lee, J.B., Turner, R.J., Adams, G.J., and Goodwin, G.C. (1999). Gravity Gradiometer. (5922951), U.S. Patent."},{"key":"ref_21","unstructured":"Brett, J., and Brewster, J. (2010). Accelerometer and Rate Sensor Pakage for Gravity Gradiometer Instruments. (7788975 B2), U.S. Patent."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Huang, X.Q., Deng, Z.G., Xie, Y.F., Li, Z., Fan, J., and Tu, L.C. (2017). A new scale factor adjustment method for magnetic force feedback accelerometer. Sensors, 17.","DOI":"10.3390\/s17112471"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"125003","DOI":"10.1063\/1.4903969","article-title":"Testing accelerometer rectification error caused by multidimensional composite inputs with double turntable centrifuge","volume":"85","author":"Guan","year":"2014","journal-title":"Rev. Sci. Instrum."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Yan, S.T., Xie, Y.F., Zhang, M.Q., Deng, Z.G., and Tu, L.C. (2017). A subnano-g electrostatic force-rebalanced flexure accelerometer for gravity gradient instruments. Sensors, 17.","DOI":"10.3390\/s17112669"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1247\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:01:11Z","timestamp":1760194871000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1247"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,18]]},"references-count":24,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["s18041247"],"URL":"https:\/\/doi.org\/10.3390\/s18041247","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,18]]}}}