{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T03:21:48Z","timestamp":1771039308695,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,18]],"date-time":"2018-03-18T00:00:00Z","timestamp":1521331200000},"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":["No. 2016YFC0303002"],"award-info":[{"award-number":["No. 2016YFC0303002"]}]},{"name":"the Key Laboratory of Aeronautical Geophysics and Remote Sensing Geology, china","award":["No. 2016YPL06"],"award-info":[{"award-number":["No. 2016YPL06"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Horizontal gravity disturbances are an important factor that affects the accuracy of inertial navigation systems in long-duration ship navigation. In this paper, from the perspective of the coordinate system and vector calculation, the effects of horizontal gravity disturbance on the initial alignment and navigation calculation are simultaneously analyzed. Horizontal gravity disturbances cause the navigation coordinate frame built in initial alignment to not be consistent with the navigation coordinate frame in which the navigation calculation is implemented. The mismatching of coordinate frame violates the vector calculation law, which will have an adverse effect on the precision of the inertial navigation system. To address this issue, two compensation methods suitable for two different navigation coordinate frames are proposed, one of the methods implements the compensation in velocity calculation, and the other does the compensation in attitude calculation. Finally, simulations and ship navigation experiments confirm the effectiveness of the proposed methods.<\/jats:p>","DOI":"10.3390\/s18030906","type":"journal-article","created":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T06:57:11Z","timestamp":1521529031000},"page":"906","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Compensation of Horizontal Gravity Disturbances for High Precision Inertial Navigation"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8989-8931","authenticated-orcid":false,"given":"Junbo","family":"Tie","sequence":"first","affiliation":[{"name":"National University of Defense Technology, Deya Road No. 109, Kaifu District, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juliang","family":"Cao","sequence":"additional","affiliation":[{"name":"National University of Defense Technology, Deya Road No. 109, Kaifu District, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meiping","family":"Wu","sequence":"additional","affiliation":[{"name":"National University of Defense Technology, Deya Road No. 109, Kaifu District, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junxiang","family":"Lian","sequence":"additional","affiliation":[{"name":"National University of Defense Technology, Deya Road No. 109, Kaifu District, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaokun","family":"Cai","sequence":"additional","affiliation":[{"name":"National University of Defense Technology, Deya Road No. 109, Kaifu District, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Wang","sequence":"additional","affiliation":[{"name":"National University of Defense Technology, Deya Road No. 109, Kaifu District, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1017\/S0373463305003395","article-title":"Gravity requirements for compensation of ultra-precise inertial navigation","volume":"58","author":"Kwon","year":"2005","journal-title":"J. Navig."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"419","DOI":"10.2514\/3.20127","article-title":"Gravity-induced errors in airborne inertial navigation","volume":"9","author":"Harriman","year":"1986","journal-title":"J. Guid. Control Dyn."},{"key":"ref_3","unstructured":"Hofmann-Wellenhof, B., and Moritz, H. (2009). Physical Geodesy, Springer."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"095103","DOI":"10.1088\/0957-0233\/27\/9\/095103","article-title":"Application of the spherical harmonic gravity model in high precision inertial navigation systems","volume":"27","author":"Wang","year":"2016","journal-title":"Meas. Sci. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"125007","DOI":"10.1088\/0957-0233\/27\/12\/125007","article-title":"An improved gravity compensation method for high-precision free-INS based on MEC\u2013BP\u2013adaboost","volume":"27","author":"Zhou","year":"2016","journal-title":"Meas. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"978","DOI":"10.2514\/3.29743","article-title":"Effect of deflections of the vertical on the performance of a terrestrial inertial navigation system","volume":"6","author":"Gelb","year":"1969","journal-title":"J. Spacecr. Rocket."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3660","DOI":"10.1029\/JB077i020p03660","article-title":"Self-consistent statistical models for the gravity anomaly, vertical deflections, and undulation of the geoid","volume":"77","author":"Jordan","year":"1972","journal-title":"J. Geophys. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4259","DOI":"10.1029\/JB074i017p04259","article-title":"Statistical models for the vertical deflection from Gravity Anomaly Models","volume":"74","author":"Shaw","year":"1969","journal-title":"J. Geophys. Res."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Welker, T.C., Pachter, M., and Huffman, R. (2013, January 17\u201319). Gravity gradiometer integrated inertial navigation. Proceedings of the 2013 European Control Conference (ECC), Zurich, Switzerland.","DOI":"10.23919\/ECC.2013.6669109"},{"key":"ref_10","unstructured":"Richeson, J.A. (2008). Gravity Gradiometer Aided Inertial Navigation within non-GNSS Environments. [PhD Thesis, University of Maryland]."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"704","DOI":"10.2514\/1.15368","article-title":"Precision free-inertial navigation with gravity compensation by an onboard gradiometer","volume":"29","author":"Jekeli","year":"2006","journal-title":"J. Guid. Control Dyn."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"B04406","DOI":"10.1029\/2011JB008916","article-title":"The development and evaluation of the earth gravitational model 2008 (EGM2008)","volume":"117","author":"Pavlis","year":"2012","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Pavlis, N.K., Holmes, S.A., Kenyon, S.C., and Factor, J.K. (2008, January 13\u201318). An earth gravitational model to degree 2160: EGM2008. Proceedings of the European Geosciences Union General Assembly, Vienna, Austria.","DOI":"10.1190\/1.3063757"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wu, R., Wu, Q., Han, F., Liu, T., Hu, P., and Li, H. (2016). Gravity compensation using EGM2008 for high-precision long-term inertial navigation systems. Sensors, 16.","DOI":"10.3390\/s16122177"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhou, X., Yang, G., Cai, Q., and Wang, J. (2016). A novel gravity compensation method for high precision free-INS based on \u201cextreme learning machine\u201d. Sensors, 16.","DOI":"10.3390\/s16122019"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wang, J., Yang, G., Li, J., and Zhou, X. (2016). An online gravity modeling method applied for high precision free-INS. Sensors, 16.","DOI":"10.3390\/s16101541"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Titterton, D., and Weston, J.L. (2004). Strapdown Inertial Navigation Technology, Institution of Engineering and Technology.","DOI":"10.1049\/PBRA017E"},{"key":"ref_18","unstructured":"Britting, K.R. (2010). Inertial Navigation Systems Analysis, Artech House."},{"key":"ref_19","unstructured":"(2017, May 01). Egm2008 Website. Available online: http:\/\/earth-info.nga.mil\/GandG\/wgs84\/gravitymod\/egm2008."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1017\/S0373463312000318","article-title":"A fast SINS initial alignment scheme for underwater vehicle applications","volume":"66","author":"Li","year":"2013","journal-title":"J. Navig."},{"key":"ref_21","unstructured":"Groves, P. (2013). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Emerald Group Publishing Limited. [2nd ed.]."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.2514\/3.61479","article-title":"The effects of vertical deflections on aircraft inertial navigation systems","volume":"14","author":"Bernstein","year":"1976","journal-title":"AIAA J."},{"key":"ref_23","unstructured":"Hanson, P.O. (December, January 29). Correction for deflections of the vertical at the runup site. Proceedings of the 1988 Record Navigation into the 21st Century, Position Location and Navigation Symposium (IEEE PLANS \u201988), Orlando, FL, USA."},{"key":"ref_24","unstructured":"Wang, H., Xiao, X., Deng, Z.-H., and Fu, M.-Y. (2014, January 18\u201320). The influence of gravity disturbance on high-precision long-time ins and its compensation method. Proceedings of the 2014 Fourth International Conference on Instrumentation and Measurement, Computer, Communication and Control, Harbin, China."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Simon, D. (2006). The discrete-time kalman filter. Optimal State Estimation, John Wiley & Sons, Inc.","DOI":"10.1002\/0470045345"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Grewal, M.S., Weill, L.R., and Andrews, A.P. (2006). Inertial navigation systems. Global Positioning Systems, Inertial Navigation, and Integration, John Wiley & Sons, Inc.","DOI":"10.1002\/0470099720"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/3\/906\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:57:34Z","timestamp":1760194654000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/3\/906"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,18]]},"references-count":26,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,3]]}},"alternative-id":["s18030906"],"URL":"https:\/\/doi.org\/10.3390\/s18030906","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,18]]}}}