{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T22:15:35Z","timestamp":1778710535840,"version":"3.51.4"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2017,7,25]],"date-time":"2017-07-25T00:00:00Z","timestamp":1500940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As a typical navigation system, the strapdown inertial navigation system (SINS) is crucial for autonomous underwater vehicles (AUVs) since the SINS accuracy determines the performance of AUVs. Initial alignment is one of the key technologies in SINS, and initial alignment time and initial alignment accuracy affect the performance of SINS directly. As actual systems are nonlinear, the nonlinear filter is widely used to improve the accuracy of the initial alignment. Due to its higher precision and lower computational load, the cubature Kalman filter (CKF) has done well in state estimation. However, the noise characteristics need to be known exactly as prior knowledge, which is difficult or even impossible to achieve. Thus, the adaptive filter should be introduced in the initial alignment algorithm to suppress the uncertainty effect caused by the unknown system noise. Therefore, taking the nonlinearity and uncertainty into account, a novel initial alignment algorithm for AUVs is proposed in this manuscript, based on CKF and the adaptive variance components estimation (VCE) filter (VCKF). Additionally, the simulation and experiment results show that not only the accuracy, but also the convergence speed can be improved with this proposed method. The validity and superiority of this novel adaptive initial alignment algorithm based on VCKF are verified.<\/jats:p>","DOI":"10.3390\/sym9080129","type":"journal-article","created":{"date-parts":[[2017,7,25]],"date-time":"2017-07-25T10:04:36Z","timestamp":1500977076000},"page":"129","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["An Adaptive Initial Alignment Algorithm Based on Variance Component Estimation for a Strapdown Inertial Navigation System for AUV"],"prefix":"10.3390","volume":"9","author":[{"given":"Qianhui","family":"Dong","sequence":"first","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4510-982X","authenticated-orcid":false,"given":"Yibing","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qian","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ya","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/JOE.2013.2278891","article-title":"AUV navigation and localization: A review","volume":"39","author":"Paull","year":"2014","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"34","DOI":"10.5772\/56346","article-title":"The path planning of AUV based on DS information fusion map building and bio-inspired neural network in unknown dynamic environment","volume":"11","author":"Zhu","year":"2014","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5772\/62076","article-title":"A multi-model EKF integrated navigation algorithm for deep water AUV","volume":"13","author":"Li","year":"2016","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1109\/TIM.2014.2355652","article-title":"Initial Alignment by Attitude Estimation for Strapdown Inertial Navigation Systems","volume":"64","author":"Chang","year":"2015","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"27930","DOI":"10.3390\/s151127930","article-title":"A New Analytic Alignment Method for a SINS","volume":"15","author":"Tan","year":"2015","journal-title":"Sensors"},{"key":"ref_7","unstructured":"Dorveaux, E., Boudot, T., Hillion, M., and Petit, N. (July, January 29). Combining inertial measurements and distributed magnetometry for motion estimation. Proceedings of the American Control Conference (ACC), San Francisco, CA, USA."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Gao, W., Deng, L., Yu, F., Zhang, Y., and Sun, Q. (2016, January 11\u201314). A novel initial alignment algorithm based on the interacting multiple model and the Huber methods. Proceedings of the 2016 IEEE\/ION Position, Location and Navigation Symposium (PLANS), Savannah, GA, USA.","DOI":"10.1109\/PLANS.2016.7479787"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1017\/S0373463310000214","article-title":"A Novel Initial Alignment Scheme for Low-Cost INS Aided by GPS for Land Vehicle Applications","volume":"63","author":"Han","year":"2010","journal-title":"J. Navig."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1016\/j.asr.2014.02.026","article-title":"A two-position SINS initial alignment method based on gyro information","volume":"53","author":"Xiong","year":"2014","journal-title":"Adv. Space Res."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hu, Z., and Su, Y. (2016, January 11\u201313). Initial alignment of the MEMS inertial measurement system assisted by magnetometers. Proceedings of the 2016 31st Youth Academic Annual Conference of Chinese Association of Automation (YAC), Wuhan, China.","DOI":"10.1109\/YAC.2016.7804903"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.3390\/s140101511","article-title":"A Strapdown Interial Navigation System\/Beidou\/Doppler Velocity Log Integrated Navigation Algorithm Based on a Cubature Kalman Filter","volume":"14","author":"Gao","year":"2014","journal-title":"Sensors"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"157","DOI":"10.2514\/1.G000496","article-title":"Fractional-Order Tension Control Law for Deployment of Space Tether System","volume":"37","author":"Sun","year":"2014","journal-title":"J. Guid. Control Dyn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1279","DOI":"10.1109\/TVT.2015.2397004","article-title":"Integrated Indoor Navigation System for Ground Vehicles With Automatic 3-D Alignment and Position Initialization","volume":"64","author":"Atia","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","unstructured":"Han, H., Xu, T., and Wang, J. (2016). Tightly Coupled Integration of GPS Ambiguity Fixed Precise Point Positioning and MEMS-INS through a Troposphere-Constrained Adaptive Kalman Filter. Sensors, 16.","DOI":"10.3390\/s16071057"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1109\/TAC.1968.1098986","article-title":"Suboptimal state estimation for continuous-time nonlinear systems from discrete noisy measurements","volume":"13","author":"Athans","year":"1968","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_18","unstructured":"Haykin, S. (2002). Chapter 7: The Unscented Kalman Filter, John Wiley & Sons, Inc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.2514\/1.G001046","article-title":"Fractional-Order Dynamics and Control of Rigid-Flexible Coupling Space Structures","volume":"38","author":"Sun","year":"2015","journal-title":"J. Guid. Control Dyn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1109\/TAC.2009.2019800","article-title":"Cubature Kalman Filters","volume":"54","author":"Arasaratnam","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4977","DOI":"10.1109\/TSP.2010.2056923","article-title":"Cubature Kalman Filtering for Continuous-Discrete Systems: Theory and Simulations","volume":"58","author":"Arasaratnam","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"43","DOI":"10.5081\/jgps.8.1.43","article-title":"Simplified Algorithms of Variance Component Estimation for Static and Kinematic GPS Single Point Positioning","volume":"8","author":"Wang","year":"2009","journal-title":"J. Glob. Position. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1049\/iet-smt.2016.0133","article-title":"Robust H-infinity CKF\/KF hybrid filtering method for SINS alignment","volume":"10","author":"Zhang","year":"2016","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Narasimhappa, M., Rangababu, P., Sabat, S.L., and Nayak, J. (2012, January 7\u20139). A modified Sage-Husa adaptive Kalman filter for denoising Fiber Optic Gyroscope signal. Proceedings of the 2012 Annual IEEE India Conference (INDICON), Kochi, India.","DOI":"10.1109\/INDCON.2012.6420813"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.measurement.2013.11.022","article-title":"The adaptive Kalman filter based on fuzzy logic for inertial motion capture system","volume":"49","author":"Jin","year":"2014","journal-title":"Measurement"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3367","DOI":"10.1109\/JSEN.2014.2384492","article-title":"Huber\u2019s M-estimation-based process uncertainty robust filter for integrated INS\/GPS","volume":"15","author":"Chang","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Wang, R., Xiong, Z., Liu, J.Y., Li, R., and Peng, H. (2012, January 23\u201326). SINS\/GPS\/CNS information fusion system based on improved Huber filter with classified adaptive factors for high-speed UAVs. Proceedings of the 2012 IEEE\/ION Position, Location and Navigation Symposium (PLANS), Myrtle Beach, SC, USA.","DOI":"10.1109\/PLANS.2012.6236913"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/671589","article-title":"A SLAM Algorithm Based on Adaptive Cubature Kalman Filter","volume":"2014","author":"Yu","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_29","unstructured":"(2017, July 18). Available online: http:\/\/www.ixblue.com\/products\/phins\/."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/8\/129\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:52Z","timestamp":1760208232000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/8\/129"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,25]]},"references-count":29,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2017,8]]}},"alternative-id":["sym9080129"],"URL":"https:\/\/doi.org\/10.3390\/sym9080129","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,25]]}}}