{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T14:32:43Z","timestamp":1774276363746,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,12]],"date-time":"2018-05-12T00:00:00Z","timestamp":1526083200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61603208"],"award-info":[{"award-number":["61603208"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Transverse navigation has been proposed to help inertial navigation systems (INSs) fill the gap of polar navigation ability. However, as the transverse system does not have the ability of navigate globally, a complicated switch between the transverse and the traditional algorithms is necessary when the system moves across the polar circles. To maintain the inner continuity and consistency of the core algorithm, a hybrid transverse polar navigation is proposed in this research based on a combination of Earth-fixed-frame mechanization and transverse-frame outputs. Furthermore, a thorough analysis of kinematic error characteristics, proper damping technology and corresponding long-term contributions of main error sources is conducted for the high-precision INSs. According to the analytical expressions of the long-term navigation errors in polar areas, the 24-h period symmetrical oscillation with a slowly divergent amplitude dominates the transverse horizontal position errors, and the first-order drift dominates the transverse azimuth error, which results from the     g 0     gyro drift coefficients that occur in corresponding directions. Simulations are conducted to validate the theoretical analysis and the deduced analytical expressions. The results show that the proposed hybrid transverse navigation can ensure the same accuracy and oscillation characteristics in polar areas as the traditional algorithm in low and mid latitude regions.<\/jats:p>","DOI":"10.3390\/s18051538","type":"journal-article","created":{"date-parts":[[2018,5,14]],"date-time":"2018-05-14T02:57:20Z","timestamp":1526266640000},"page":"1538","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Hybrid Transverse Polar Navigation for High-Precision and Long-Term INSs"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3484-022X","authenticated-orcid":false,"given":"Ruonan","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiuping","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8425-6764","authenticated-orcid":false,"given":"Fengtian","family":"Han","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peida","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haixia","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Precision Instrument, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1016\/j.marpol.2009.10.009","article-title":"The implications of Arctic sea ice decline on shipping","volume":"34","author":"Ho","year":"2010","journal-title":"Mar. Policy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.retrec.2011.11.003","article-title":"The melting Arctic and its impact on China\u2019s maritime transport","volume":"35","author":"Hong","year":"2012","journal-title":"Res. Transp. Econ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1002\/j.2161-4296.1955.tb00183.x","article-title":"Polar airline navigation","volume":"4","author":"Pedersen","year":"1955","journal-title":"Navigation"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1017\/S0373463300016623","article-title":"Navigation in polar regions","volume":"10","author":"Anderson","year":"1957","journal-title":"J. Navig."},{"key":"ref_5","unstructured":"Greenaway, K.R., and Gates, M.D. (2009). Polar Air Navigation: A Record, Art Bookbindery."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1016\/j.jastp.2010.03.014","article-title":"GPS phase scintillation observed over a high-latitude Antarctic station during solar minimum","volume":"72","author":"Ngwira","year":"2010","journal-title":"J. Atmos. Sol.-Terr. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1277","DOI":"10.1002\/2014RS005418","article-title":"Observed high-latitude GNSS disturbances during a less-than-minor geomagnetic storm","volume":"49","author":"Andalsvik","year":"2014","journal-title":"Radio Sci."},{"key":"ref_8","unstructured":"Britting, K.R. (1971). Inertial Vavigation Systems Analysis, Wiley-Interscience."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1017\/S0373463300022335","article-title":"Polar navigation\u2014A New transverse Mercator technique","volume":"24","author":"Dyer","year":"1971","journal-title":"J. Navig."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1002\/j.2161-4296.1972.tb01686.x","article-title":"An all-Earth inertial navigation scheme","volume":"19","author":"Ignagni","year":"1972","journal-title":"Navigation"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"436","DOI":"10.2307\/209975","article-title":"Grid navigation","volume":"34","author":"Herrick","year":"1944","journal-title":"Geogr. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1017\/S0373463300031519","article-title":"Transverse navigation: An alternative to the grid system","volume":"2","author":"Fox","year":"1949","journal-title":"J. Navig."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1017\/S0373463315000715","article-title":"Transverse navigation under the ellipsoidal Earth model and its performance in both polar and non-polar areas","volume":"69","author":"Yao","year":"2015","journal-title":"J. Navig."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"7791","DOI":"10.1109\/TVT.2015.2497713","article-title":"Bin Transversal strapdown INS based on reference ellipsoid for vehicle in the polar region","volume":"65","author":"Li","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","first-page":"18","article-title":"Indirect grid inertial navigation mechanization for transpolar aircraft","volume":"22","author":"Zhou","year":"2014","journal-title":"J. Chin. Inert. Technol."},{"key":"ref_16","first-page":"29","article-title":"Indirect transverse inertial navigation algorithm in polar region","volume":"23","author":"Yao","year":"2015","journal-title":"J. Chin. Inert. Technol."},{"key":"ref_17","unstructured":"Salychev, O.S. (2004). Applied Inertial Navigation Problems and Solutions, BMSTU press."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.ast.2018.02.029","article-title":"Improved polar inertial navigation algorithm based on pseudo INS mechanization","volume":"77","author":"Liu","year":"2018","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Gao, Y., Liu, M., Li, G.C., and Guang, X.X. (2017). Initial alignment for SINS based on pseudo-Earth frame in polar regions. Sensors, 17.","DOI":"10.3390\/s17061416"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Cheng, J.H., Wang, T., Wang, L., and Wang, Z.M. (2017). A new polar transfer alignment algorithm with the aid of a star sensor and based on an adaptive unscented Kalman filter. Sensors, 17.","DOI":"10.3390\/s17102417"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"095101","DOI":"10.1088\/1361-6501\/aa781a","article-title":"Modified compensation algorithm of lever-arm effect and flexural deformation for polar shipborne transfer alignment based on improved adaptive Kalman filter","volume":"28","author":"Wang","year":"2017","journal-title":"Meas. Sci. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1599","DOI":"10.3390\/s17071599","article-title":"Polar grid navigation algorithm for unmanned underwater vehicles","volume":"17","author":"Yan","year":"2017","journal-title":"Sensors"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Li, Q., Ben, Y.Y., Sun, F., and Huo, L. (2014, January 5\u20138). Transversal strapdown INS and damping technology for marine in polar region. Proceedings of the IEEE\/ION Position, Location and Navigation Symposium\u2014PLANS 2014, Monterey, CA, USA.","DOI":"10.1109\/PLANS.2014.6851511"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Huang, W.Q., Fang, T., Luo, L., Zhao, L., and Che, F.Z. (2017). A damping grid strapdown inertial navigation system based on a Kalman filter for ships in polar regions. Sensors, 17.","DOI":"10.3390\/s17071551"},{"key":"ref_25","unstructured":"Gao, Z.Y. (2012). Inertial Navigation System Technology, Tsinghua University Press. (In Chinese)."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Grewal, M.S., Weill, L.R., and Andrews, A.P. (2007). Global Positioning Systems, Inertial Navigation, and Integration, John Wiley & Sons.","DOI":"10.1002\/0470099720"},{"key":"ref_27","unstructured":"Hofmann-Wellenhof, B., and Moritz, H. (2006). Physical Geodesy, Springer Science & Business Media."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1109\/TAES.1971.310404","article-title":"Error analysis of space-stable inertial navigation systems","volume":"4","author":"Nash","year":"1971","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Blankinship, K.G. (2008, January 5\u20138). A general theory for inertial navigator error modeling. Proceedings of the 2008 IEEE\/ION Position, Location and Navigation Symposium, Monterey, CA, USA.","DOI":"10.1109\/PLANS.2008.4570002"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"648","DOI":"10.2514\/3.20887","article-title":"Unified approach to inertial navigation system error modeling","volume":"15","year":"1992","journal-title":"J. Guid. Control Dyn."},{"key":"ref_31","first-page":"240","article-title":"Identification of the gyro drift error model by using a two-axis servo turntable","volume":"13","author":"Gao","year":"1989","journal-title":"Z. Flugwiss. Weltraumforsch."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"223","DOI":"10.4173\/mic.2004.4.2","article-title":"DVL velocity aiding in the HUGIN 1000 integrated inertial navigation system","volume":"25","author":"Jalving","year":"2004","journal-title":"Model. Identif. Control"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s10291-014-0399-z","article-title":"Shipborne heading determination and error compensation based on a dynamic baseline","volume":"19","author":"Hu","year":"2015","journal-title":"GPS Solut."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/5\/1538\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:04:02Z","timestamp":1760195042000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/5\/1538"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,12]]},"references-count":33,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,5]]}},"alternative-id":["s18051538"],"URL":"https:\/\/doi.org\/10.3390\/s18051538","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,12]]}}}