{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T03:28:29Z","timestamp":1781926109160,"version":"3.54.5"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,14]],"date-time":"2018-09-14T00:00:00Z","timestamp":1536883200000},"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":["61573368,11172323"],"award-info":[{"award-number":["61573368,11172323"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The integration of a star tracker and gyroscope units (GUs) can take full advantage of the benefits of each, and provide continuous and accurate attitude information with a high update rate. The systematic error calibration of the integrated system is a crucial step to guarantee its attitude accuracy. In this paper, a comprehensive calibration method for the star tracker and GUs integrated system is proposed from a global perspective. Firstly, the observation model of the predicted star centroid error (PSCE) with respect to the systematic errors including the star tracker intrinsic parameter errors, GUs errors and fixed angle errors is accurately established. Then, the systematic errors are modeled by a series of differential equations, based on which the state-space model is established. Finally, the systematic errors are decoupled and estimated by a Kalman filter according to the established state-space model and observation model. The coupling between the errors of the principal point and subcomponents of the fixed angles (i.e.,     \u03a8 x     and     \u03a8 y    ) is analysed. Both simulations and experiments indicate that the proposed method is effective at estimating the systematic errors of the star tracker and GUs integrated system with high accuracy and robustness with respect to different star centroid accuracies and gyroscope noise levels.<\/jats:p>","DOI":"10.3390\/s18093106","type":"journal-article","created":{"date-parts":[[2018,9,14]],"date-time":"2018-09-14T10:57:59Z","timestamp":1536922679000},"page":"3106","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["A Comprehensive Calibration Method for a Star Tracker and Gyroscope Units Integrated System"],"prefix":"10.3390","volume":"18","author":[{"given":"Wenfeng","family":"Tan","sequence":"first","affiliation":[{"name":"College of Opto-Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3595-2592","authenticated-orcid":false,"given":"Dongkai","family":"Dai","sequence":"additional","affiliation":[{"name":"College of Opto-Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Opto-Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingshu","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Opto-Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shiqiao","family":"Qin","sequence":"additional","affiliation":[{"name":"College of Opto-Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1109\/TAES.2002.1008988","article-title":"Accuracy performance of star trackers\u2014A tutorial","volume":"38","author":"Liebe","year":"2002","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/62.387971","article-title":"Star trackers for attitude determination","volume":"10","author":"Liebe","year":"1995","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"20096","DOI":"10.1364\/OE.21.020096","article-title":"Motion-blurred star acquisition method of the star tracker under high dynamic conditions","volume":"21","author":"Sun","year":"2013","journal-title":"Opt. Express"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6009","DOI":"10.1364\/OE.22.006009","article-title":"Smearing model and restoration of star image under conditions of variable angular velocity and long exposure time","volume":"22","author":"Sun","year":"2014","journal-title":"Opt. Express"},{"key":"ref_5","unstructured":"Liu, C., Liu, G., Wang, X., and Li, A. (2010). Principles and Systematic Applications of Missile-Borne Star Sensor, National Defense Industry Press."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.actaastro.2004.09.011","article-title":"The proba satellite star tracker performance","volume":"56","author":"Denver","year":"2005","journal-title":"Acta Astronaut."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7559","DOI":"10.1364\/AO.54.007559","article-title":"Attitude-correlated frames approach for a star sensor to improve attitude accuracy under highly dynamic conditions","volume":"54","author":"Ma","year":"2015","journal-title":"Appl. Opt."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"10187","DOI":"10.1364\/AO.55.010187","article-title":"Multiexposure imaging and parameter optimization for intensified star trackers","volume":"55","author":"Yu","year":"2016","journal-title":"Appl. Opt."},{"key":"ref_9","first-page":"711","article-title":"Laboratory calibration of star tracker with brightness independent star identification strategy","volume":"45","author":"Dong","year":"2006","journal-title":"Opt. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4598","DOI":"10.3390\/s130404598","article-title":"Optical system error analysis and calibration method of high-accuracy star trackers","volume":"13","author":"Sun","year":"2013","journal-title":"Sensors"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"034112","DOI":"10.1117\/1.OE.54.3.034112","article-title":"High-accuracy star sensor calibration based on intrinsic and extrinsic parameter decoupling","volume":"54","author":"Xiong","year":"2015","journal-title":"Opt. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Boone, B.G., Bruzzi, J.R., Dellinger, W.F., Kluga, B.E., and Strobehn, K.M. (2005). Optical simulator and testbed for spacecraft star tracker development. Proc. SPIE, 5867.","DOI":"10.1117\/12.619133"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/s00340-013-5637-5","article-title":"Laboratory calibration of star sensor with installation error using a nonlinear distortion model","volume":"115","author":"Li","year":"2014","journal-title":"Appl. Phys. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.measurement.2014.04.026","article-title":"Star sensor calibration based on integrated modelling with intrinsic and extrinsic parameters","volume":"55","author":"Wei","year":"2014","journal-title":"Measurement"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"18393","DOI":"10.1364\/OE.25.018393","article-title":"On-orbit calibration for star sensors without priori information","volume":"25","author":"Zhang","year":"2017","journal-title":"Opt. Express"},{"key":"ref_16","unstructured":"Samaan, M.A., Griffith, T., Singla, P., and Junkins, J.L. (2001, January 28\u201330). Autonomous on-orbit calibration of star trackers. Proceedings of the 2001 Core Technologies For Space Systems Conference, Colorado Springs, CO, USA."},{"key":"ref_17","unstructured":"Singla, P., Griffith, D.T., Crassidis, J.L., and Junkins, J.L. (2002, January 27\u201330). Attitude determination and autonomous on-orbit calibration of star tracker for GIFTS mission. Proceedings of the AAS\/AIAA Spaceflight Mechanics Meeting, Advances in Aerospace Sciences, San Antonio, TX, USA."},{"key":"ref_18","first-page":"68","article-title":"Autonomous on-orbit calibration of a star tracker camera","volume":"50","author":"Liu","year":"2011","journal-title":"Opt. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"043101","DOI":"10.1063\/1.4979360","article-title":"A star tracker on-orbit calibration method based on vector pattern match","volume":"88","author":"Li","year":"2017","journal-title":"Rev. Sci. Instrum."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5536","DOI":"10.1364\/OE.24.005536","article-title":"On-orbit calibration approach for optical navigation camera in deep space exploration","volume":"24","author":"Wang","year":"2016","journal-title":"Opt. Express"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Kaplan, G.H. (2005). The iau resolutions on astronomical reference systems, time scales, and earth rotation models (draft 4). arXiv.","DOI":"10.21236\/ADA434096"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Jiang, J., Yu, W., and Zhang, G. (2017). High-accuracy decoupling estimation of the systematic coordinate errors of an INS and intensified high dynamic star tracker based on the constrained least squares method. Sensors, 17.","DOI":"10.3390\/s17102285"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"33559","DOI":"10.1364\/OE.25.033559","article-title":"Centroid error compensation method for a star tracker under complex dynamic conditions","volume":"25","author":"Tan","year":"2017","journal-title":"Opt. Express"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Titterton, D., and Weston, J.L. (2004). Strapdown Inertial Navigation Technology, The American Institute of Aeronautics and Astronautics.","DOI":"10.1049\/PBRA017E"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5914","DOI":"10.1364\/AO.49.005914","article-title":"Lens distortion models evaluation","volume":"49","year":"2010","journal-title":"Appl. Opt."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1115\/1.3662552","article-title":"A new approach to linear filtering and prediction problems","volume":"82","author":"Kalman","year":"1960","journal-title":"J. Basic Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"24321","DOI":"10.1364\/OE.24.024321","article-title":"High-accuracy calibration of low-cost camera using image disturbance factor","volume":"24","author":"Liu","year":"2016","journal-title":"Opt. 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