{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:28:15Z","timestamp":1772252895192,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,4,27]],"date-time":"2015-04-27T00:00:00Z","timestamp":1430092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Nature Science Foundation of China","award":["61473085"],"award-info":[{"award-number":["61473085"]}]},{"name":"the National Nature Science Foundation of China","award":["51175082"],"award-info":[{"award-number":["51175082"]}]},{"name":"the National Nature Science Foundation of China","award":["51375088"],"award-info":[{"award-number":["51375088"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Initial alignment is always a key topic and difficult to achieve in an inertial navigation system (INS). In this paper a novel self-initial alignment algorithm is proposed using gravitational apparent motion vectors at three different moments and vector-operation. Simulation and analysis showed that this method easily suffers from the random noise contained in accelerometer measurements which are used to construct apparent motion directly. Aiming to resolve this problem, an online sensor data denoising method based on a Kalman filter is proposed and a novel reconstruction method for apparent motion is designed to avoid the collinearity among vectors participating in the alignment solution. Simulation, turntable tests and vehicle tests indicate that the proposed alignment algorithm can fulfill initial alignment of strapdown INS (SINS) under both static and swinging conditions. The accuracy can either reach or approach the theoretical values determined by sensor precision under static or swinging conditions.<\/jats:p>","DOI":"10.3390\/s150509827","type":"journal-article","created":{"date-parts":[[2015,4,27]],"date-time":"2015-04-27T12:16:51Z","timestamp":1430137011000},"page":"9827-9853","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A Self-Alignment Algorithm for SINS Based on Gravitational Apparent Motion and Sensor Data Denoising"],"prefix":"10.3390","volume":"15","author":[{"given":"Yiting","family":"Liu","sequence":"first","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology,  Ministry of Education, School of Instrument Science and Engineering, Southeast University,  Nanjing 210096, China,"}]},{"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,  Ministry of Education, School of Instrument Science and Engineering, Southeast University,  Nanjing 210096, China,"}]},{"given":"Xixiang","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology,  Ministry of Education, School of Instrument Science and Engineering, Southeast University,  Nanjing 210096, China,"}]},{"given":"Yiqing","family":"Yao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology,  Ministry of Education, School of Instrument Science and Engineering, Southeast University,  Nanjing 210096, China,"}]},{"given":"Liang","family":"Wu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology,  Ministry of Education, School of Instrument Science and Engineering, Southeast University,  Nanjing 210096, China,"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1074-8202","authenticated-orcid":false,"given":"Jin","family":"Sun","sequence":"additional","affiliation":[{"name":"Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology,  Ministry of Education, School of Instrument Science and Engineering, Southeast University,  Nanjing 210096, China,"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,27]]},"reference":[{"key":"ref_1","unstructured":"Lian, J.X. (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_2","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1017\/S0373463398007802","article-title":"The development of the gyrocompass-inventors as navigators","volume":"51","author":"Broelmann","year":"1998","journal-title":"J. Navig."},{"key":"ref_3","unstructured":"Salychev, O.S. (2004). Applied Inertial Navigation: Problems and Solutions, BMTU Press."},{"key":"ref_4","first-page":"140","article-title":"INS in-motion alignment for land-vehicle aided by odometer","volume":"20","author":"Xiao","year":"2012","journal-title":"J. Chin. Inert. Technol."},{"key":"ref_5","unstructured":"Levinson, E., and Willcocks, M. (1994, January 11\u201315). The next generation marine inertial navigation is here now. Proceedings of the IEEE Position Location and Navigation Symposium, Las Vegas, NV, USA."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Gu, D., El-Sheimy, N., and Hassan, T. (2008, January 5\u20138). Coarse alignment for marine SINS using gravity in the inertial frame as a reference. Proceedings of the Position, Location and Navigation Symposium, Monterey, CA, USA.","DOI":"10.1109\/PLANS.2008.4570038"},{"key":"ref_7","unstructured":"Gaiffe, T., Cottreau, Y., and Faussot, N. (2000, January 23\u201326). Highly compact fiber optic gyrocompass for applications at depths up to 3000 m. Proceedings of the 2000 International Symposium on Underwater Technology (2000. UT 00.), Tokyo, Japan."},{"key":"ref_8","unstructured":"Gaiffe, T. (2002, January 10). From R&D brassboards to navigation grade FOG-based INS: The experience of Photonetics\/Ixsea. Proceedings of the Optical Fiber Sensors Conference Technical Digest, Portland, OR, USA."},{"key":"ref_9","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_10","unstructured":"Savage, P.G. (2000). Strapdown Analytics, Strapdown Associates, Inc."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Silson, P.M.G. (2010, January 2\u20135). A novel inertial coarse alignment method. Proceedings of the AIAA Guidance, Navigation and Control Conference, Tornado, ON, Canada.","DOI":"10.2514\/6.2010-8330"},{"key":"ref_12","first-page":"2409","article-title":"Accuracy analysis of coarse alignment based on gravity in inertial frame","volume":"32","author":"Sun","year":"2011","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_13","first-page":"586","article-title":"Error analysis of indirect analytic alignment algorithm","volume":"35","author":"Wu","year":"2013","journal-title":"Syst. Eng. Electron."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"8103","DOI":"10.3390\/s130708103","article-title":"A robust self-alignment method for ship\u2019s strapdown INS under mooring conditions","volume":"13","author":"Sun","year":"2013","journal-title":"Sensors"},{"key":"ref_15","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_16","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. Navig."},{"key":"ref_17","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":"Syst. Eng. Electron."},{"key":"ref_18","first-page":"2322","article-title":"SINS initial alignment of swaying base under geographic latitude uncertainty","volume":"33","author":"Wang","year":"2012","journal-title":"Acta Aeronaut. Astronaut. Sin."},{"key":"ref_19","first-page":"1486","article-title":"SINS anti-rocking disturbance initial alignment based on frequency domain isolation operator","volume":"32","author":"Yan","year":"2011","journal-title":"J. Astronaut."},{"key":"ref_20","first-page":"437","article-title":"Research on SINS alignment algorithm based on FIR filter","volume":"16","author":"Lian","year":"2007","journal-title":"Beijing Inst. Technol. (Engl. Ed.)"},{"key":"ref_21","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":"2013","journal-title":"Measurement"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.measurement.2014.11.010","article-title":"A novel self-alignment method for SINS based on three vectors of gravitational apparent motion in inertial frame","volume":"62","author":"Liu","year":"2015","journal-title":"Measurement"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1017\/S0373463314000198","article-title":"An improved Optimal Method for Initial Alignment","volume":"67","author":"Li","year":"2014","journal-title":"J. Navig."},{"key":"ref_24","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":"Lv","year":"2009","journal-title":"J. Frankl. Inst."},{"key":"ref_25","first-page":"2520","article-title":"Prefiltering for initial alignment for ring laser gyroscope SINS on rocking base","volume":"17","author":"Lv","year":"2009","journal-title":"Opt. Precis. Eng."},{"key":"ref_26","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_27","unstructured":"Zarchan, P., and Musoff, H. (2005). Fundamentals of Kalman Filtering: A Practical Approach, American Institute of Astronautics and Aeronautics, AIAA."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/B978-0-12-012720-7.50012-7","article-title":"Inertial navigation system error-model consideration in Kalman filtering application","volume":"20","author":"Huddle","year":"1983","journal-title":"Control Dyn. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.dsp.2010.09.001","article-title":"Optimization approach to adapt Kalman filters for the real-time application of accelerometer and gyroscope signal\u2019 filtering","volume":"21","author":"Cezary","year":"2011","journal-title":"Digit. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1016\/j.ijleo.2013.07.161","article-title":"An innovation based random weighting estimation mechanism for denoising fiber optic gyro drift signal","volume":"125","author":"Mundla","year":"2014","journal-title":"Optik"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1813","DOI":"10.1016\/j.dsp.2013.04.010","article-title":"Design and implementation of a realtime co-processor for denoising Fiber Optic Gyroscope signal","volume":"23","author":"Rangababu","year":"2013","journal-title":"Digit. Signal Process."},{"key":"ref_32","first-page":"568","article-title":"System calibration techniques for inertial measurement units","volume":"17","author":"Liu","year":"2009","journal-title":"J. Chin. Inert. Technol."},{"key":"ref_33","unstructured":"IXBLUE Inc. (2008). PHINS, IXBLUE Inc."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/5\/9827\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:45:25Z","timestamp":1760215525000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/5\/9827"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,27]]},"references-count":33,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,5]]}},"alternative-id":["s150509827"],"URL":"https:\/\/doi.org\/10.3390\/s150509827","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,27]]}}}