{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:30:41Z","timestamp":1766269841484,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T00:00:00Z","timestamp":1551744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The accuracy and rate of convergence are two important performance factors for initial ground alignment of a strapdown inertial navigation system (SINS). For navigation-grade SINS, gyro biases and accelerometer offsets can be modeled as constant values during the alignment period, and they can be calibrated through two-position ground alignment schemes. In many situations for SINS ground alignment, the azimuth of the vehicle remains nearly constant. This quasi-stationary alignment information can be used as an augmented measurement. In this paper, a piecewise combined Kalman filter utilizing relative azimuth constraint (RATP) is proposed to improve the alignment precision and to reduce the time consumption for error convergence. It is presented that a piecewise time-invariant linear system can be combined into a whole extended time-invariant linear system so that a piecewise combined Kalman filter can be designed for state estimation. A two-position ground alignment algorithm for SINS is designed based on the proposed piecewise combined Kalman filter. Numerical simulations and experimental results show its superiority to the conventional algorithms in terms of accuracy and the rate of convergence.<\/jats:p>","DOI":"10.3390\/s19051125","type":"journal-article","created":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T11:19:50Z","timestamp":1551784790000},"page":"1125","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Rapid SINS Two-Position Ground Alignment Scheme Based on Piecewise Combined Kalman Filter and Azimuth Constraint Information"],"prefix":"10.3390","volume":"19","author":[{"given":"Lu","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Intelligence Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenqi","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Intelligence Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maosong","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Intelligence Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,5]]},"reference":[{"key":"ref_1","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 Aerosp. Electron. Syst. Mag."},{"key":"ref_2","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_3","first-page":"78","article-title":"Observability of Strapdown INS Alignment: A Global Perspective","volume":"48","author":"Wu","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/7.135435","article-title":"Error estimation of INS ground alignment through observability analysis","volume":"28","author":"Jiang","year":"1992","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_5","first-page":"1","article-title":"Application of Bilinear Recursive Least Square Algorithm for Initial Alignment of Strapdown Inertial Navigation System","volume":"Volume 1","author":"Malakar","year":"2014","journal-title":"Advanced Computing, Networking and Informatics"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhao, L., Guan, D., Cheng, J., Xu, X., and Fei, Z. (2016). Coarse Alignment of Marine Strapdown INS Based on the Trajectory Fitting of Gravity Movement in the Inertial Space. Sensors, 16.","DOI":"10.3390\/s16101714"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ishibashi, S., Tsukioka, S., Yoshida, H., Hyakudome, T., and Ishikawa, A. (2007, January 18\u201321). Accuracy Improvement of an Inertial Navigation System Brought about by the Rotational Motion. Proceedings of the OCEANS 2007-Europe, Aberdeen, UK.","DOI":"10.1109\/OCEANSE.2007.4302282"},{"key":"ref_8","unstructured":"Tucker, T., and Levinson, E. (2000, January 26\u201328). The AN\/WSN-7B Marine Gyrocompass\/Navigator. Proceedings of the 2000 National Technical Meeting of The Institute of Navigation, Anaheim, CA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"643","DOI":"10.4028\/www.scientific.net\/AMM.313-314.643","article-title":"Single-Axis Rotation Modulation of SINS","volume":"313","author":"Mao","year":"2013","journal-title":"Appl. Mech. Mater."},{"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":"Aerosp. Sci. Technol."},{"key":"ref_11","unstructured":"Barbour, N. (2013, January 19\u201322). Inertial components\u2014Past, present, and future. Proceedings of the AIAA Guidance, Navigation, & Control Conference & Exhibit, Boston, MA, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1166\/jctn.2017.6475","article-title":"Research on Nonlinear Comprehensive Calibration Algorithm for the Single-Axis Rotation Inertial Navigation System Based on Modified Unscented Kalman Filter","volume":"14","author":"Cheng","year":"2017","journal-title":"J. Comput. Theor. Nanosci."},{"key":"ref_13","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":"Aerosp. Sci. Technol."},{"key":"ref_14","first-page":"1596","article-title":"A Fast Initial Alignment Method with Gyro Angular Rate Information","volume":"31","author":"Gao","year":"2010","journal-title":"J. Astronaut."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1016\/j.asr.2015.07.005","article-title":"Fast two-position initial alignment for SINS using velocity plus angular rate measurements","volume":"56","author":"Chang","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"25520","DOI":"10.3390\/s151025520","article-title":"An Improved Inertial Frame Alignment Algorithm Based on Horizontal Alignment Information for Marine SINS","volume":"15","author":"Che","year":"2015","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4368","DOI":"10.3390\/s150204368","article-title":"A Stationary North-Finding Scheme for an Azimuth Rotational IMU Utilizing a Linear State Equality Constraint","volume":"15","author":"Yu","year":"2015","journal-title":"Sensors"},{"key":"ref_19","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_20","doi-asserted-by":"crossref","unstructured":"Xia, X.-W., and Sun, Q. (2018). Initial Alignment Algorithm Based on the DMCS Method in Single-Axis RSINS with Large Azimuth Misalignment Angles for Submarines. Sensors, 7.","DOI":"10.3390\/s18072123"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1016\/j.ijleo.2018.05.119","article-title":"A modified rapid alignment method of SINS based on measurement augmentation","volume":"170","author":"Xu","year":"2018","journal-title":"Optik"},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.1109\/7.259535","article-title":"Multiposition alignment of strapdown inertial navigation system","volume":"29","author":"Lee","year":"1993","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1109\/7.543857","article-title":"Strapdown INS error model for multiposition alignment","volume":"32","author":"Chung","year":"1996","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2181","DOI":"10.1109\/TAES.2015.130674","article-title":"Stochastic Observability-Based Analytic Optimization of SINS Multiposition Alignment","volume":"51","author":"Yu","year":"2015","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_26","unstructured":"Chung, D., Park, C.G., and Lee, J.G. (1996, January 13). Observability analysis of strapdown inertial navigation system using Lyapunov transformation. Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2067","DOI":"10.1007\/s12541-013-0280-y","article-title":"A Two-Stage Initial Alignment Technique for Underwater Vehicles Dropped from a Mother Ship","volume":"14","author":"Cho","year":"2013","journal-title":"Int. J. Precis. Eng. Manuf."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"237","DOI":"10.2514\/3.20299","article-title":"Control theoretic approach to inertial navigation systems","volume":"11","author":"Berman","year":"1988","journal-title":"J. Guid. Control Dyn."},{"key":"ref_29","unstructured":"Rogers, R.M. (2007). Applied Mathematics in Integrated Navigation Systems, American Institute of Aeronautics & Astronautics Inc.. [3rd ed.]."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4364","DOI":"10.1016\/j.ijleo.2013.01.057","article-title":"Rapid transfer alignment of laser SINS using quaternion based angular measurement","volume":"124","author":"Dai","year":"2013","journal-title":"Optik"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Goshen-Meskin, D., and Bar-Itzhack, I.Y. (1990, January 5\u20137). Observability analysis of piece-wise constant systems with application to inertial navigation. Proceedings of the 29th IEEE Conference on Decision and Control, Honolulu, HI, USA.","DOI":"10.1109\/CDC.1990.203702"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/7.165367","article-title":"Observability analysis of piece-wise constant systems. I. Theory","volume":"28","year":"1992","journal-title":"IEEE Trans. Aerosp. Electron. Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/5\/1125\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:36:31Z","timestamp":1760186191000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/5\/1125"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,5]]},"references-count":32,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["s19051125"],"URL":"https:\/\/doi.org\/10.3390\/s19051125","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,3,5]]}}}