{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T13:47:28Z","timestamp":1762004848957,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,1,29]],"date-time":"2017-01-29T00:00:00Z","timestamp":1485648000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61473085","51175082","51375088"],"award-info":[{"award-number":["61473085","51175082","51375088"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a self-alignment method for strapdown inertial navigation systems based on the q-method is studied. In addition, an improved method based on integrating gravitational apparent motion to form apparent velocity is designed, which can reduce the random noises of the observation vectors. For further analysis, a novel self-alignment method using a Kalman filter based on adaptive filter technology is proposed, which transforms the self-alignment procedure into an attitude estimation using the observation vectors. In the proposed method, a linear psuedo-measurement equation is adopted by employing the transfer method between the quaternion and the observation vectors. Analysis and simulation indicate that the accuracy of the self-alignment is improved. Meanwhile, to improve the convergence rate of the proposed method, a new method based on parameter recognition and a reconstruction algorithm for apparent gravitation is devised, which can reduce the influence of the random noises of the observation vectors. Simulations and turntable tests are carried out, and the results indicate that the proposed method can acquire sound alignment results with lower standard variances, and can obtain higher alignment accuracy and a faster convergence rate.<\/jats:p>","DOI":"10.3390\/s17020264","type":"journal-article","created":{"date-parts":[[2017,1,30]],"date-time":"2017-01-30T11:36:30Z","timestamp":1485776190000},"page":"264","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["A Kalman Filter for SINS Self-Alignment Based on Vector Observation"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8312-3350","authenticated-orcid":false,"given":"Xiang","family":"Xu","sequence":"first","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Nanjing 210096, China"},{"name":"Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5165-0981","authenticated-orcid":false,"given":"Xiaosu","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Nanjing 210096, China"},{"name":"Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Nanjing 210096, China"},{"name":"Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yao","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Nanjing 210096, China"},{"name":"Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinwu","family":"Tong","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Nanjing 210096, China"},{"name":"Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Titterton, D.H., and Weston, J.L. (2004). Strapdown Inertial Navigation Technology, IET, Lavenham Press Ltd.. [2nd ed.].","DOI":"10.1049\/PBRA017E"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Petritoli, E., and Leccese, F. (2015, January 4\u20135). Improvement of Altitude Precision in Indoor and Urban Canyon Navigation for Small Flying VehiclesIn. Proceedings of the 2015 IEEE Metrology for Aerospace (MetroAeroSpace), Benevento, Italy.","DOI":"10.1109\/MetroAeroSpace.2015.7180626"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Petritoli, E., Giagnacovo, T., and Leccese, F. (2014, January 29\u201330). Lightweight GNSS\/IRS Integrated Navigation System for UAV Vehicles. Proceedings of the 2014 IEEE Metrology for Aerospace (MetroAeroSpace), Benevento, Italy.","DOI":"10.1109\/MetroAeroSpace.2014.6865894"},{"key":"ref_4","unstructured":"Rogers, R.M. (2003). Applied Mathematics in Integrated Navigation Systems, AIAA. [2nd ed.]."},{"key":"ref_5","first-page":"1","article-title":"A Method for SINS Alignment with Large Initial Misalignment Angles Based on Kalman Filter with Parameters Resetting","volume":"2014","author":"Liu","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1017\/S0373463314000575","article-title":"Kalman Filter Design for Initial Precision Alignment of a Strapdown Inertial Navigation System on a Rocking Base","volume":"68","author":"Li","year":"2015","journal-title":"J. Navig."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1109\/TIM.2010.2084710","article-title":"Study on innovation adaptive EKF for in-flight alignment of airborne POS","volume":"60","author":"Jiancheng","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_8","first-page":"95","article-title":"Study on SINS alignment algorithm with inertial frame for swaying bases","volume":"29","author":"Lian","year":"2007","journal-title":"J. Natl. Univ. Def. Technol."},{"key":"ref_9","first-page":"634","article-title":"New initial alignment algorithm for SINS on moving base","volume":"3","author":"Yan","year":"2009","journal-title":"Syst. Eng. Electron."},{"key":"ref_10","first-page":"320","article-title":"Improved Kalman filter for SINS coarse alignment based on parameter identification","volume":"24","author":"Xu","year":"2016","journal-title":"J. Chin. Inert. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.measurement.2014.06.004","article-title":"An initial alignment method for strapdown gyrocompass based on gravitational apparent motion in inertial frame","volume":"55","author":"Liu","year":"2014","journal-title":"Measurement"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"9827","DOI":"10.3390\/s150509827","article-title":"A Self-Alignment Algorithm for SINS Based on Gravitational Apparent Motion and Sensor Data Denoising","volume":"15","author":"Liu","year":"2015","journal-title":"Sensors"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1930","DOI":"10.1109\/TIM.2011.2113131","article-title":"Coarse Alignment of a Ship\u2019s Strapdown Inertial Attitude Reference System Using Velocity Loci","volume":"60","author":"Silson","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"15006","DOI":"10.3390\/s150715006","article-title":"Optimal Parameter Design of Coarse Alignment for Fiber Optic Gyro Inertial Navigation System","volume":"15","author":"Lu","year":"2015","journal-title":"Sensors"},{"key":"ref_15","first-page":"724","article-title":"Alignment algorithm based on quaternion estimator for SINS on rocking base","volume":"22","author":"Gao","year":"2014","journal-title":"J. Chin. Inert. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"643","DOI":"10.2514\/1.40423","article-title":"Filter quest or request","volume":"32","author":"Shuster","year":"2009","journal-title":"J. Guid. Control Dyn."},{"key":"ref_17","unstructured":"Markley, F.L., and Mortari, D. (1999, January 16\u201319). How to estimate attitude from vector observations. Proceedings of the AAS\/AIAA Astrodynamics Specialist Conference, Girdwood, AK, USA."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ast.2010.05.004","article-title":"Optimization-based alignment for inertial navigation systems: Theory and algorithm","volume":"15","author":"Wu","year":"2011","journal-title":"Aerosp Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2916","DOI":"10.1109\/TIM.2012.2202989","article-title":"Quaternion-optimization-based in-flight alignment approach for airborne POS","volume":"61","author":"Taizhong","year":"2012","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4581","DOI":"10.1016\/j.ijleo.2013.01.069","article-title":"Optimization-based INS in-motion alignment approach for underwater vehicles","volume":"124","author":"Li","year":"2013","journal-title":"Optik-Int. J. Light Electron Opt."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1006","DOI":"10.1109\/TAES.2013.6494395","article-title":"Velocity\/Position integration formula part I: Application to in-flight coarse alignment","volume":"49","author":"Wu","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1109\/TAES.2006.1603413","article-title":"Novel quaternion Kalman filter","volume":"42","author":"Choukroun","year":"2006","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Panuska, V. (1979, January 12\u201314). A New form of the Extended Kalman Filter for Parameter Estimation in Linear Systems. Proceedings of the 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, Fort Lauderdale, FL, USA.","DOI":"10.1109\/CDC.1979.270083"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1109\/TAC.1980.1102269","article-title":"A new form of the extended Kalman filter for parameter estimation in linear systems with correlated noise","volume":"25","author":"Panuska","year":"1980","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_25","unstructured":"Keat, J. (1977). Analysis of Least-Squares Attitude Determination Routine DOAOP, Computer Sciences Corporation. Technical Report CSC\/TM-77\/6034."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"70","DOI":"10.2514\/3.19717","article-title":"Three-axis attitude determination from vector observations","volume":"4","author":"Shuster","year":"1981","journal-title":"J. Guid. Control Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Bar-Itzhack, I.Y., Deutschmann, J., and Markley, F.L. (1991). Quaternion normalization in additive EKF for spacecraft attitude determination. AIAA Pap., 908.","DOI":"10.2514\/6.1991-2706"},{"key":"ref_28","first-page":"568","article-title":"System calibration techniques for inertial measurement units","volume":"17","author":"Liu","year":"2009","journal-title":"J. Chin. Inert. Technol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/2\/264\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:27:13Z","timestamp":1760207233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/2\/264"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,29]]},"references-count":28,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,2]]}},"alternative-id":["s17020264"],"URL":"https:\/\/doi.org\/10.3390\/s17020264","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,1,29]]}}}