{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:25:22Z","timestamp":1772252722803,"version":"3.50.1"},"reference-count":65,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2013,6,25]],"date-time":"2013-06-25T00:00:00Z","timestamp":1372118400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Strapdown inertial navigation systems (INS) need an alignment process to determine the initial attitude matrix between the body frame and the navigation frame. The conventional alignment process is to compute the initial attitude matrix using the gravity and Earth rotational rate measurements. However, under mooring conditions, the inertial measurement unit (IMU) employed in a ship\u2019s strapdown INS often suffers from both the intrinsic sensor noise components and the external disturbance components caused by the motions of the sea waves and wind waves, so a rapid and precise alignment of a ship\u2019s strapdown INS without any auxiliary information is hard to achieve. A robust solution is given in this paper to solve this problem. The inertial frame based alignment method is utilized to adapt the mooring condition, most of the periodical low-frequency external disturbance components could be removed by the mathematical integration and averaging characteristic of this method. A novel prefilter named hidden Markov model based Kalman filter (HMM-KF) is proposed to remove the relatively high-frequency error components. Different from the digital filters, the HMM-KF barely cause time-delay problem. The turntable, mooring and sea experiments favorably validate the rapidness and accuracy of the proposed self-alignment method and the good de-noising performance of HMM-KF.<\/jats:p>","DOI":"10.3390\/s130708103","type":"journal-article","created":{"date-parts":[[2013,6,25]],"date-time":"2013-06-25T12:43:50Z","timestamp":1372164230000},"page":"8103-8139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["A Robust Self-Alignment Method for Ship\u2019s Strapdown INS Under Mooring Conditions"],"prefix":"10.3390","volume":"13","author":[{"given":"Feng","family":"Sun","sequence":"first","affiliation":[{"name":"Marine Navigation Research Institute, College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiyu","family":"Lan","sequence":"additional","affiliation":[{"name":"Marine Navigation Research Institute, College of Automation, Harbin Engineering University, Harbin 150001, China"},{"name":"Department of Geomatics Engineering, 2500 University Drive NW, University of Calgary, Calgary, AB T2N 1N4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunyang","family":"Yu","sequence":"additional","affiliation":[{"name":"Marine Navigation Research Institute, College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naser","family":"El-Sheimy","sequence":"additional","affiliation":[{"name":"Department of Geomatics Engineering, 2500 University Drive NW, University of Calgary, Calgary, AB T2N 1N4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangtao","family":"Zhou","sequence":"additional","affiliation":[{"name":"Marine Navigation Research Institute, College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tong","family":"Cao","sequence":"additional","affiliation":[{"name":"Marine Navigation Research Institute, College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hang","family":"Liu","sequence":"additional","affiliation":[{"name":"National Space Science Center, Chinese Academy of Sciences (CAS), Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,6,25]]},"reference":[{"key":"ref_1","unstructured":"Salychev, O.S. (2004). Applied Inertial Navigation: Problems and Solutions, BMSTU Press."},{"key":"ref_2","unstructured":"Farrell, J., and Barth, M. (1999). The Global Positioning System and Inertial Navigation, McGraw-Hill."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Titterton, D., Weston, J., Titterton, D., and Weston, J. (2004). Strapdown Inertial Navigation Technology, Institution of Electrical Engineers.","DOI":"10.1049\/PBRA017E"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"237","DOI":"10.2514\/1.17112","article-title":"A unified mathematical framework for strapdown algorithm design","volume":"29","author":"Savage","year":"2006","journal-title":"J. Guid. Contr. Dyn."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"19","DOI":"10.2514\/2.4228","article-title":"Strapdown inertial navigation integration algorithm design part 1: Attitude algorithms","volume":"21","author":"Savage","year":"1998","journal-title":"J. Guid. Contr. Dyn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"287","DOI":"10.2514\/3.21382","article-title":"Study of strapdown navigation attitude algorithms","volume":"18","author":"Musoff","year":"1995","journal-title":"J. Guid. Contr. Dyn."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.ast.2010.06.007","article-title":"Improved self-alignment scheme for SINS using augmented measurement","volume":"15","author":"Acharya","year":"2011","journal-title":"Aeros. Sci. Tech."},{"key":"ref_8","unstructured":"Nebot, E., and Durrant-Whyte, H. (1997, January 23\u201325). Initial Calibration and Alignment of an Inertial Navigation. Toowoomba, Queensland, Australia."},{"key":"ref_9","unstructured":"Schimelevich, L., and Naor, R. (1996, January 22\u201326). New Approach to Coarse Alignment. Atlanta, GA, USA."},{"key":"ref_10","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":"Aeros. Sci. Tech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/TAES.2012.6129622","article-title":"Observability of Strapdown INS Alignment: A Global Perspective","volume":"48","author":"Wu","year":"2012","journal-title":"IEEE Trans. Aeros. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1016\/j.measurement.2011.01.010","article-title":"Initial orientation of inertial navigation system realized through nonlinear modeling and filtering","volume":"44","author":"Ali","year":"2011","journal-title":"Measurement"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/j.measurement.2008.10.002","article-title":"A consistent and robust Kalman filter design for in-motion alignment of inertial navigation system","volume":"42","author":"Ali","year":"2009","journal-title":"Measurement"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sun, F., Sun, W., and Wu, L. (2010, January 4\u20136). Coarse Alignment based on IMU Rotational Motion for Surface Ship. Indian Well, CA, USA.","DOI":"10.1109\/PLANS.2010.5507297"},{"key":"ref_15","first-page":"1","article-title":"A Ground Fine Alignment of Strapdown INS under a Vibrating Base","volume":"1","author":"Li","year":"2013","journal-title":"J. Navigation"},{"key":"ref_16","first-page":"929","article-title":"Research on coarse alignment of rotary SINS on a swing base","volume":"4","author":"Sun","year":"2010","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1016\/j.measurement.2010.08.008","article-title":"Mooring alignment for marine SINS using the digital filter","volume":"43","author":"Sun","year":"2010","journal-title":"Measurement"},{"key":"ref_18","unstructured":"Sun, F., Sun, Q., Ben, Y., and Zhang, Y. (2012, January 23\u201326). A New Method of Initial Alignment and Self-Calibration based on Dual-Axis Rotating Strapdown Inertial Navigation System. Myrtle Beach, SC, USA."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhao, G., Gao, W., Zhang, X., and Ben, Y. (2010, January 20\u201323). Application for Autonomous Underwater Vehicle Initial Alignment with Divided Difference Filter. Harbin, China.","DOI":"10.1109\/ICINFA.2010.5512290"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2887","DOI":"10.1109\/TAES.2011.6034671","article-title":"Rapid Fine Strapdown INS Alignment Method under Marine Mooring Condition","volume":"47","author":"Gao","year":"2011","journal-title":"IEEE Tran. Aero. Elec. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/MAES.2004.1365016","article-title":"Wavelet de-noising for IMU alignment","volume":"19","author":"Nassar","year":"2004","journal-title":"IEEE Aeros. Electron. Syst. Mag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1017\/S0373463304003005","article-title":"Wavelet analysis for improving INS and INS\/DGPS navigation accuracy","volume":"58","author":"Nassar","year":"2005","journal-title":"J. Navigation"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"513","DOI":"10.3969\/j.issn.1004-4132.2011.03.022","article-title":"Novel approach to GPS\/SINS integration for IMU alignment","volume":"22","author":"Sun","year":"2011","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_24","first-page":"1032","article-title":"INS\/GPS integrated navigation filter algorithm based on cubature Kalman filter","volume":"27","author":"Sun","year":"2012","journal-title":"Control Decis."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Sun, F., and Zhang, H. (2011, January 7\u201310). Application of a New Adaptive Kalman Filitering Algorithm in Initial Alignment of INS. Beijing, China.","DOI":"10.1109\/ICMA.2011.5986346"},{"key":"ref_26","first-page":"630","article-title":"Fine alignment by rotation in strapdown inertial navigation systems","volume":"3","author":"Sun","year":"2010","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"9424","DOI":"10.3390\/s101009424","article-title":"An integration of GPS with INS sensors for precise long-baseline kinematic positioning","volume":"10","author":"Lee","year":"2010","journal-title":"Sensors"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"9252","DOI":"10.3390\/s101009252","article-title":"Intelligent sensor positioning and orientation through constructive neural network-embedded INS\/GPS integration algorithms","volume":"10","author":"Chiang","year":"2010","journal-title":"Sensors"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1930","DOI":"10.1109\/TIM.2011.2113131","article-title":"Coarse alignment of a ship's strapdown inertial attitude reference system using velocity loci","volume":"60","author":"Silson","year":"2011","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1046","DOI":"10.3390\/s130101046","article-title":"A novel scheme for DVL aided SINS In-motion alignment using UKF techniques","volume":"13","author":"Li","year":"2013","journal-title":"Sensors"},{"key":"ref_31","first-page":"1","article-title":"A fast SINS initial alignment scheme for underwater vehicle applications","volume":"1","author":"Li","year":"2012","journal-title":"J. Navigation"},{"key":"ref_32","unstructured":"El-Hawary, F. (2002). The Ocean Engineering Handbook, CRC Press."},{"key":"ref_33","first-page":"437","article-title":"Research on SINS Alignment Algorithm Based on FIR Filters","volume":"16","author":"Lian","year":"2007","journal-title":"J. Beijing Inst. Technol."},{"key":"ref_34","unstructured":"Lian, J. (2007). Research on a New Moving-base Alignment Approach and Error Depression of Strapdown Inertial Navigation System. [Ph.D. Thesis, National University of Defense Technology]."},{"key":"ref_35","unstructured":"Zhao, G. (2011). Calibration and Offshore Alignment of Marine Strapdown Inertial Navigation System Based on Fiber Optic Gyro. [Ph.D. Thesis, College of Automation, Harbin Engineering University]."},{"key":"ref_36","first-page":"10","article-title":"Kalman filter fine alignment in inertial frame based on multistage FIR digital filter","volume":"18","author":"Zhao","year":"2010","journal-title":"Chin. J. Inert. Technol."},{"key":"ref_37","unstructured":"Zhang, X. (2009). Research of Alignment Base on Ship FOG Strap-down Inertial System. [Ph.D. Thesis, College of Automation, Harbin Engineering University]."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1016\/j.measurement.2012.08.015","article-title":"A novel algorithm for marine strapdown gyrocompass based on digital filter","volume":"46","author":"Li","year":"2012","journal-title":"Measurement"},{"key":"ref_39","first-page":"1870","article-title":"Research on mooring alignment with digital filter","volume":"25","author":"Sun","year":"2010","journal-title":"Control Decis."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1016\/j.jfranklin.2009.09.003","article-title":"New techniques for initial alignment of strapdown inertial navigation system","volume":"346","author":"Xie","year":"2009","journal-title":"J. Frankl. Inst."},{"key":"ref_41","first-page":"2520","article-title":"Prefiltering for initial alignment of ring laser gyroscope SINS on rocking base","volume":"17","author":"Xie","year":"2009","journal-title":"Opt. Precis. Eng."},{"key":"ref_42","unstructured":"Gaiffe, T., Cottreau, Y., Faussot, N., Hardy, G., Simonpietri, P., and Arditty, H. (2000, January 23\u201326). Highly Compact Fiber Optic Gyrocompass for Applications at Depths up to 3000 Meters. Tokyo, Japan."},{"key":"ref_43","unstructured":"Napolitano, F., Gaiffe, T., Cottreau, Y., and Loret, T. (2002, January 27\u201329). PHINS \u2013 The First High Performances Inertial Navigation System based on Fibre Optic Gyroscopes. St. Petersburg, Russia."},{"key":"ref_44","first-page":"1486","article-title":"SINS Anti-Rocking Disturbance Initial Alignment Based on Frequency Domain Isolation Operator","volume":"7","author":"Yan","year":"2011","journal-title":"J. Astronaut."},{"key":"ref_45","unstructured":"Yan, G. (2008). On SINS in-movement inertial alignment and some other problems. [Ph.D. Thesis, Department of Electrical Engineering, Northwest Polytechnical University]."},{"key":"ref_46","first-page":"618","article-title":"Initial in-movement alignment and position determination based on inertial reference frame","volume":"33","author":"Yan","year":"2011","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_47","first-page":"681","article-title":"A clever way of SINS coarse alignment despite rocking ship","volume":"23","author":"Qin","year":"2005","journal-title":"J. Northwest. Polytech. Univ."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Sun, F., Cao, T., Xu, B., Ben, Y., and Wang, Y. (2009, January 9\u201312). Initial Alignment for Strapdown Inertial Navigation System Based on Inertial Frame. Changchun, China.","DOI":"10.1109\/ICMA.2009.5246606"},{"key":"ref_49","first-page":"2410","article-title":"Accuracy analysis of coarse alignment based on gravity in inertial frame","volume":"11","author":"Sun","year":"2011","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_50","first-page":"96","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_51","unstructured":"Elliott, R.J., Aggoun, L., and Moore, J.B. (1995). Hidden Markov Models: Estimation and Control, Springer-Verlag."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1109\/78.668544","article-title":"Wavelet-based statistical signal processing using hidden Markov models","volume":"46","author":"Crouse","year":"1998","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1080\/00401706.1991.10484833","article-title":"Hidden Markov models for speech recognition","volume":"33","author":"Juang","year":"1991","journal-title":"Technometrics"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"9163","DOI":"10.3390\/s101009163","article-title":"A zero velocity detection algorithm using inertial sensors for pedestrian navigation systems","volume":"10","author":"Park","year":"2010","journal-title":"Sensors"},{"key":"ref_55","unstructured":"Cao, T. (2012). On-line Alignment and calibration technique of fiber optic gyroscope SINS. [Ph.D. Thesis, College of Automation, Harbin Engineering University]."},{"key":"ref_56","unstructured":"Brown, R.G., and Hwang, P.Y.C. (1997). Introduction to Random Signals and Applied Kalman Filtering, John Wiley & Sons."},{"key":"ref_57","unstructured":"Antoniou, A. (2006). Digital Signal Processing, McGraw-Hill."},{"key":"ref_58","unstructured":"IXSEA Inc. Available online: http:\/\/www.ixsea.com\/en\/defense\/1.3\/phins.html."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"86","DOI":"10.12720\/joace.1.2.86-90","article-title":"Wavelet-Based Method for Fog Signal Denoising","volume":"1","author":"Zu","year":"2013","journal-title":"J. Automat. Control Eng."},{"key":"ref_60","first-page":"774","article-title":"Research on real-time de-noising of FOG based on second generation wavelet transform","volume":"4","author":"Gao","year":"2012","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_61","first-page":"34","article-title":"Application of digital filter in inertial measurement unit","volume":"11","author":"Li","year":"2003","journal-title":"Chin. J. Inert. Technol."},{"key":"ref_62","first-page":"839","article-title":"Research on measurement method of warship instantaneous line motion under condition of dynamic motion","volume":"25","author":"Sun","year":"2013","journal-title":"J. Syst. Simul."},{"key":"ref_63","unstructured":"Cao, B. (2011). The Measurement Technology of Ship's Instantaneous Line Motion under Multi Dynamic Environment. [Master's Degree Project, College of Automation, Harbin Engineering University]."},{"key":"ref_64","unstructured":"Gong, J. (2010). Research on Strap-down Inertial Navigation System of Ship's Instantaneous Line Motion Parameters. [Master's Degree Project, College of Automation, Harbin Engineering University]."},{"key":"ref_65","unstructured":"Liu, X. (2009). Study on the Measuring of the Instantaneous Movements of the Ships Based on SINS. [Master's Degree Project, College of Automation, Harbin Engineering University]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/7\/8103\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:47:32Z","timestamp":1760219252000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/7\/8103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,25]]},"references-count":65,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2013,7]]}},"alternative-id":["s130708103"],"URL":"https:\/\/doi.org\/10.3390\/s130708103","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6,25]]}}}