{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:46:59Z","timestamp":1760230019173,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2022,7,8]],"date-time":"2022-07-08T00:00:00Z","timestamp":1657238400000},"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":["418762222"],"award-info":[{"award-number":["418762222"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To solve the problem of high-precision and fast initial alignment for the Strapdown Inertial Navigation System (SINS) under both dynamic and static conditions, the high-precision attitude measured by the celestial navigation system (CNS) is used as the reference information for the initial alignment. The alignment algorithm is derived in the Earth-centered inertial (ECI) frame. Compared with the alignment algorithm in the navigation frame, it is independent of position parameters and avoids the influence of the approximate error caused by the dynamic deflection angle. In addition, hull deformation is considered in attitude optimal estimation, which can realize initial the alignment of the SINS installed in various parts of the carrier. On this basis, the velocity measurement information is added to the alignment process, which further improves the accuracy and speed of the initial alignment under static conditions. The experimental results show that the algorithms proposed in this paper have better performance in alignment accuracy, speed, and stability. The attitude and velocity matching algorithm in the ECI frame can achieve alignment accuracy better than 0.6\u2032. The attitude matching algorithm in the ECI frame has better robustness and can be used for both dynamic and static conditions, which can achieve alignment accuracy better than 1.3\u2032.<\/jats:p>","DOI":"10.3390\/s22145123","type":"journal-article","created":{"date-parts":[[2022,7,7]],"date-time":"2022-07-07T22:11:47Z","timestamp":1657231907000},"page":"5123","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["One-Step Initial Alignment Algorithm for SINS in the ECI Frame Based on the Inertial Attitude Measurement of the CNS"],"prefix":"10.3390","volume":"22","author":[{"given":"Jun","family":"Tang","sequence":"first","affiliation":[{"name":"The Department of Navigation Engineering, Naval University of Engineering, Wuhan 430033, China"},{"name":"The Department of Navigation, Dalian Naval Academy, Dalian 116018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongwei","family":"Bian","sequence":"additional","affiliation":[{"name":"The Department of Navigation Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heng","family":"Ma","sequence":"additional","affiliation":[{"name":"The Department of Navigation Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rongying","family":"Wang","sequence":"additional","affiliation":[{"name":"The Department of Navigation Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Titterton, D.H., and Weston, J.L. (2004). Strapdown Inertial Navigation Technology: The Institute of Electrical Engineers, American Institute of Aeronautics and Astronautics. [2nd ed.].","DOI":"10.1049\/PBRA017E"},{"key":"ref_2","unstructured":"Groves, P.D. (2008). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House."},{"key":"ref_3","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":"2014","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1017\/S0373463318000437","article-title":"Autonomous in-motion alignment for land vehicle strapdown inertial navigation system without the aid of external sensors","volume":"71","author":"Fu","year":"2018","journal-title":"J. Navig."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4536","DOI":"10.1109\/JSEN.2018.2823359","article-title":"Anti-disturbance initial alignment method based on quadratic integral for airborne distributed POS","volume":"18","author":"Li","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Gao, W., Zhang, Y., and Wang, J. (2015). Research on initial alignment and self-calibration of rotary strapdown inertial navigation systems. Sensors, 15.","DOI":"10.3390\/s150203154"},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1049\/iet-smt.2012.0071","article-title":"Strapdown inertial navigation system alignment based on marginalised unscented Kalman filter","volume":"7","author":"Chang","year":"2013","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1109\/TIM.2014.2359516","article-title":"Backtracking integration for fast attitude determination-based initial alignment","volume":"64","author":"Chang","year":"2014","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1697","DOI":"10.1109\/TAES.2016.130824","article-title":"Optimization-based alignment for strapdown inertial navigation system: Comparison and extension","volume":"52","author":"Chang","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1850","DOI":"10.1109\/TMECH.2017.2698639","article-title":"Indirect Kalman filtering based attitude estimation for low-cost attitude and heading reference systems","volume":"22","author":"Chang","year":"2017","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1109\/TASE.2014.2346581","article-title":"A novel backtracking scheme for attitude determination-based initial alignment","volume":"12","author":"Chang","year":"2014","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"305","DOI":"10.2514\/1.61723","article-title":"Modified unscented quaternion estimator based on quaternion averaging","volume":"37","author":"Chang","year":"2014","journal-title":"J. Guid. Control Dyn."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhang, G., Hu, B., Chang, L., and Xue, B.Y. (2018, January 10\u201312). Nonlinear Initial Alignment based on Quaternion Error Model. Proceedings of the 2018 IEEE CSAA Guidance, Navigation and Control Conference (CGNCC), Xiamen, China.","DOI":"10.1109\/GNCC42960.2018.9019158"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1109\/JSEN.2021.3108497","article-title":"Strapdown Inertial Navigation System Initial Alignment Based on Group of Double Direct Spatial Isometries","volume":"22","author":"Chang","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1109\/TVT.2020.3048730","article-title":"A new Kalman filter-based in-motion initial alignment method for DVL-aided low-cost SINS","volume":"70","author":"Luo","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1109\/TMECH.2016.2616412","article-title":"Initial alignment for a Doppler velocity log-aided strapdown inertial navigation system with limited information","volume":"22","author":"Chang","year":"2016","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1109\/JSEN.2016.2633428","article-title":"In-motion initial alignment for odometer-aided strapdown inertial navigation system based on attitude estimation","volume":"17","author":"Chang","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"102119","DOI":"10.1109\/ACCESS.2020.2998719","article-title":"An improved real-time transfer alignment algorithm based on adaptive noise estimation for distributed POS","volume":"8","author":"Wang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1659","DOI":"10.1109\/TMECH.2020.2982199","article-title":"Robust initial alignment for SINS\/DVL based on reconstructed observation vectors","volume":"25","author":"Xu","year":"2020","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1109\/TMECH.2018.2835486","article-title":"A new fast in-motion coarse alignment method for GPS-aided low-cost SINS","volume":"23","author":"Huang","year":"2018","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_24","first-page":"62","article-title":"Study of CNS\/INS Integrated Navigation System Based on Speed Damping Technology","volume":"10","author":"Lu","year":"2012","journal-title":"Opt. Optoelectron. Technol."},{"key":"ref_25","unstructured":"Qi, Z. (2015). Research on the Key Technology of Warship SINS\/CNS\/DVL Integrated Navigation System. [Ph.D. Thesis, Dept. Automation. Eng. Harbin Engineering Univ.]."},{"key":"ref_26","first-page":"321","article-title":"Application of SINS\/CNS\/DNS integrated navigation in ship navigation system","volume":"6","author":"Li","year":"2014","journal-title":"J. Nanjing Univ. Inf. Sci. Technol. (Nat. Sci. Ed.)"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1038\/s41598-021-04732-4","article-title":"Adaptive transfer alignment method based on the observability analysis for airborne pod strapdown inertial navigation system","volume":"12","author":"Chen","year":"2022","journal-title":"Sci. Rep."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S037346331900050X","article-title":"The Effectiveness of Acceleration Matching According to the Sensor Performance in Shipboard Rapid Transfer Alignment","volume":"73","author":"Ju","year":"2020","journal-title":"J. Navig."},{"key":"ref_29","first-page":"012088","article-title":"Design of a fast transfer alignment matching algorithm","volume":"Volume 1654","author":"Geng","year":"2020","journal-title":"Journal of Physics: Conference Series"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.oceaneng.2015.07.062","article-title":"Performance Enhancement of INS\/CNS Integration Navigation System Based on Particle Swarm Optimization Back Propagation Neural Network","volume":"108","author":"Wang","year":"2015","journal-title":"Ocean Eng."},{"key":"ref_31","first-page":"128","article-title":"The federated filtering algorithm based on INS\/GPS\/CNS","volume":"40","author":"Du","year":"2018","journal-title":"Ship Sci. Technol."},{"key":"ref_32","first-page":"137","article-title":"Star Sensor Technology Applications and Future Trends in the Field of Unmanned Combat","volume":"37","author":"He","year":"2016","journal-title":"J. Ordnance Equip. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1550147718810695","DOI":"10.1177\/1550147718810695","article-title":"A model-free hull deformation measurement method with time delay compensation","volume":"14","author":"He","year":"2018","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_34","first-page":"34","article-title":"A hull deformation measurement method based on fiber optic gyro angular rate matching in complex sea conditions","volume":"236","author":"Li","year":"2022","journal-title":"Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.ijleo.2018.11.023","article-title":"Research on hull deformation measurement for large azimuth misalignment angle based on attitude quaternion","volume":"182","author":"He","year":"2019","journal-title":"Optik"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/14\/5123\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:44:13Z","timestamp":1760139853000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/14\/5123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,8]]},"references-count":35,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["s22145123"],"URL":"https:\/\/doi.org\/10.3390\/s22145123","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,7,8]]}}}