{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T16:21:42Z","timestamp":1784996502765,"version":"3.55.0"},"reference-count":24,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:00:00Z","timestamp":1671580800000},"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>We address the angular misalignment calibration problem, which arises when a multi-antenna GNSS serves as a source of aiding information for inertial sensors in an integrated navigation system. Antennas usually occupy some outside structure of the moving carrier object, whilst an inertial measurement unit typically remains inside. Especially when using low- or mid-grade MEMS gyroscopes and accelerometers, it is either impossible or impractical to physically align IMU-sensitive axes and GNSS antenna baselines within some 1\u20133 degrees due to the micromechanical nature of the inertial sensors: they are just too small to have any physical reference features to align to. However, in some applications, it is desirable to line up all sensors within a fraction-of-a-degree level of accuracy. One may imagine solving this problem via the long-term averaging of sensor signals in different positions to ensure observability and then using angle differences for analytical compensation. We suggest faster calibration in special rotations using sensor fusion. Apart from quicker convergence, this method also accounts for run-to-run inertial sensor bias instability. In addition, it allows further on-the-fly finer calibration in the background when the navigation system performs its regular operation, and carrier objects may undergo gradual deformations of its structure over the years.<\/jats:p>","DOI":"10.3390\/s23010077","type":"journal-article","created":{"date-parts":[[2022,12,22]],"date-time":"2022-12-22T02:59:06Z","timestamp":1671677946000},"page":"77","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Angular Misalignment Calibration for Dual-Antenna GNSS\/IMU Navigation Sensor"],"prefix":"10.3390","volume":"23","author":[{"given":"Alexander","family":"Kozlov","sequence":"first","affiliation":[{"name":"Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991 Moscow, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3408-4516","authenticated-orcid":false,"given":"Fedor","family":"Kapralov","sequence":"additional","affiliation":[{"name":"Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991 Moscow, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,21]]},"reference":[{"key":"ref_1","unstructured":"Savage, P. (2007). Strapdown Analytics, Strapdown Associates, Inc.. [2nd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1109\/JMEMS.2013.2282936","article-title":"What is MEMS Gyrocompassing? Comparative Analysis of Maytagging and Carouseling","volume":"22","author":"Prikhodko","year":"2013","journal-title":"J. Microelectromech. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Kragh, M., Christiansen, P., Laursen, M., Larsen, M., Steen, K., Green, O., Karstoft, H., and J\u00f8rgensen, R. (2017). FieldSAFE: Dataset for Obstacle Detection in Agriculture. Sensors, 17.","DOI":"10.3390\/s17112579"},{"key":"ref_4","first-page":"64","article-title":"Performance of GPS and Low-cost INS Integration in Marine Surveying","volume":"5","author":"Hide","year":"2004","journal-title":"Int. Hydrogr. Rev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"03007","DOI":"10.1051\/e3sconf\/20199503007","article-title":"A Short-baseline Dual-antenna BDS\/MIMU Integrated Navigation System","volume":"95","author":"Cai","year":"2019","journal-title":"E3S Web Conf."},{"key":"ref_6","unstructured":"Henkel, P., and G\u00fcnther, C. (2013, January 16\u201320). Attitude Determination with low-cost GPS\/INS. Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, USA."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Li, W., Fan, P., Cui, X., Zhao, S., Ma, T., and Lu, M. (2018). A Low-Cost INS-Integratable GNSS Ultra-Short Baseline Attitude Determination System. Sensors, 18.","DOI":"10.3390\/s18072114"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3449","DOI":"10.1109\/JSEN.2019.2891783","article-title":"Dual-Antenna GNSS Integrated With MEMS for Reliable and Continuous Attitude Determination in Challenged Environments","volume":"19","author":"Zhu","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Leick, A., Rapoport, L., and Tatarnikov, D. (2015). GPS Satellite Surveying, John Wiley & Sons, Inc.. [4th ed.].","DOI":"10.1002\/9781119018612"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Vasilyuk, N., Vorobiev, M., and Tokarev, D. (2019, January 10\u201311). Attitude determination with the aid of a triple-antenna GNSS receiver without integer ambiguity resolutions integrated with a low-cost inertial measurement unit. Proceedings of the 2019 DGON Inertial Sensors and Systems (ISS), Braunschweig, Germany.","DOI":"10.1109\/ISS46986.2019.8943610"},{"key":"ref_11","unstructured":"Madgwick, S. (2014). AHRS Algorithms and Calibration Solutions to Facilitate New Applications Using Low-Cost MEMS. [Ph.D. Thesis, University of Bristol]."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1109\/TAES.1971.310252","article-title":"A New Mathematical Formulation for Strapdown Inertial Navigation","volume":"AES-7","author":"Bortz","year":"1971","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Kozlov, A., Sazonov, I., and Vavilova, N. (2014, January 25\u201326). IMU Calibration on a Low Grade Turntable: Embedded Estimation of the Instrument Displacement from the Axis of Rotation. Proceedings of the 2014 International Symposium on Inertial Sensors and Systems (ISISS), Laguna Beach, CA, USA.","DOI":"10.1109\/ISISS.2014.6782525"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"35","DOI":"10.3103\/S0027133012020021","article-title":"A \u201ctelescopic\u201d system in the calibration problem for strapdown inertial navigation systems","volume":"67","author":"Derevyankin","year":"2012","journal-title":"Mosc. Univ. Mech. Bull."},{"key":"ref_15","unstructured":"Skog, I., and H\u00e4ndel, P. (2006, January 17\u201322). Calibration of a MEMS inertial measurement unit. Proceedings of the XVII IMEKO World Congress, Rio de Janeiro, Brazil."},{"key":"ref_16","first-page":"715","article-title":"Calibration of inertial measurement unit with simultaneous estimation of the temperature time-derivative variations","volume":"10","author":"Tarygin","year":"2019","journal-title":"Math. Eng. Sci. Aerosp."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12192","DOI":"10.3390\/s130912192","article-title":"Fast thermal calibration of low-grade inertial sensors and inertial measurement units","volume":"13","author":"Niu","year":"2013","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"505","DOI":"10.3182\/20100906-5-JP-2022.00086","article-title":"On GPS\/GLONASS\/INS tight integration for gimbal and strapdown systems of different accuracy","volume":"43","author":"Golovan","year":"2010","journal-title":"IFAC Proc. Vol."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Skog, I., and Handel, P. (2008, January 5\u20138). Effects of time synchronization errors in GNSS-aided INS. Proceedings of the 2008 IEEE\/ION Position, Location and Navigation Symposium, Monterey, CA, USA.","DOI":"10.1109\/PLANS.2008.4570010"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1134\/S207510872103007X","article-title":"INS\/GNSS Integration with Compensated Data Synchronization Errors and Displacement of GNSS Antenna. Experience of Practical Realization","volume":"12","author":"Vavilova","year":"2021","journal-title":"Gyroscopy Navig."},{"key":"ref_21","unstructured":"Petovello, M. (Inside GNSS, 2015). How does a GNSS receiver estimate velocity?, Inside GNSS."},{"key":"ref_22","unstructured":"Kailath, T., Sayed, A.H., and Hassibi, B. (2000). Linear Estimation, Prentice Hall."},{"key":"ref_23","unstructured":"Thornton, C.L. (1976). Triangular Covariance Factorizations for Kalman Filtering. [Ph.D. Thesis, California Institute of Technology]."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Baram, Y., and Kailath, T. (1987, January 9\u201311). Estimability and regulability of linear systems. Proceedings of the 26th IEEE Conference on Decision and Control, Los Angeles, CA, USA.","DOI":"10.1109\/CDC.1987.272760"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/77\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:47:22Z","timestamp":1760147242000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/77"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,21]]},"references-count":24,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["s23010077"],"URL":"https:\/\/doi.org\/10.3390\/s23010077","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,21]]}}}