{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T16:25:14Z","timestamp":1771259114612,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,16]],"date-time":"2022-01-16T00:00:00Z","timestamp":1642291200000},"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":["42071447, 42074012"],"award-info":[{"award-number":["42071447, 42074012"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100019033","name":"Liaoning Key Research and Development Program","doi-asserted-by":"publisher","award":["2020JH2"],"award-info":[{"award-number":["2020JH2"]}],"id":[{"id":"10.13039\/501100019033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013099","name":"Scientific Research Fund of Liaoning Provincial Education Department","doi-asserted-by":"publisher","award":["LJ2019JL021"],"award-info":[{"award-number":["LJ2019JL021"]}],"id":[{"id":"10.13039\/501100013099","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In order to complete the high-precision calibration of the planetary rover navigation camera using limited initial data in-orbit, we proposed a joint adjustment model with additional multiple constraints. Specifically, a base model was first established based on the bundle adjustment model, second-order radial and tangential distortion parameters. Then, combining the constraints of collinearity, coplanarity, known distance and relative pose invariance, a joint adjustment model was constructed to realize the in orbit self-calibration of the navigation camera. Given the problem of directionality in line extraction of the solar panel due to large differences in the gradient amplitude, an adaptive brightness-weighted line extraction method was proposed. Lastly, the Levenberg-Marquardt algorithm for nonlinear least squares was used to obtain the optimal results. To verify the proposed method, field experiments and in-orbit experiments were carried out. The results suggested that the proposed method was more accurate than the self-calibration bundle adjustment method, CAHVOR method (a camera model used in machine vision for three-dimensional measurements), and vanishing points method. The average error for the flag of China and the optical solar reflector was only 1 mm and 0.7 mm, respectively. In addition, the proposed method has been implemented in China\u2019s deep space exploration missions.<\/jats:p>","DOI":"10.3390\/rs14020402","type":"journal-article","created":{"date-parts":[[2022,1,16]],"date-time":"2022-01-16T20:45:21Z","timestamp":1642365921000},"page":"402","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["An In-Orbit Stereo Navigation Camera Self-Calibration Method for Planetary Rovers with Multiple Constraints"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3822-5243","authenticated-orcid":false,"given":"Xinchao","family":"Xu","sequence":"first","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingyue","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Song","family":"Peng","sequence":"additional","affiliation":[{"name":"Beijing Institute of Spacecraft System Engineering, Beijing 100094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4076-2101","authenticated-orcid":false,"given":"Youqing","family":"Ma","sequence":"additional","affiliation":[{"name":"Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100101, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongxi","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aigong","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Geomatics, Liaoning Technical University, Fuxin 123008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,16]]},"reference":[{"key":"ref_1","first-page":"69","article-title":"Review of 2020 global deep space activities","volume":"39","author":"Shi","year":"2021","journal-title":"Sci. Technol. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1360\/SST-2020-0207","article-title":"Strategy of deep space exploration","volume":"50","author":"Liu","year":"2020","journal-title":"Sci. Sin. Technol."},{"key":"ref_3","first-page":"51","article-title":"China successfully launched its first mars mission, Tianwen 1","volume":"21","author":"Chen","year":"2020","journal-title":"Aerosp. China"},{"key":"ref_4","first-page":"1562","article-title":"Advances and applications of lunar photogrammetric mapping using orbital images","volume":"48","author":"Di","year":"2019","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_5","unstructured":"Ma, Y. (2014). Research on Navigation and Positioning Technology of Chang\u2019e-3 Lunar Patrol Probe. [Ph.D. Thesis, Wuhan University]."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"103","DOI":"10.14358\/PERS.81.2.103","article-title":"Direct linear transformation from comparator coordinates into object space coordinates in close-range photogrammetry","volume":"81","author":"Karara","year":"2015","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1109\/JRA.1987.1087109","article-title":"A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses","volume":"3","author":"Tsai","year":"2003","journal-title":"IEEE J. Robot. Autom."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1109\/34.159901","article-title":"Camera calibration with distortion models and accuracy evalution","volume":"14","author":"Weng","year":"1992","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Faugeras, O.D., Luong, Q.T., and Maybank, S.J. (1992, January 19\u201322). Camera self-calibration: Theory and experiments. Proceedings of the European Conference on Computer Vision, Santa Margherita Ligure, Italy.","DOI":"10.1007\/3-540-55426-2_37"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/BF00127171","article-title":"A theory of self-calibration of a moving camera","volume":"8","author":"Maybank","year":"1992","journal-title":"Int. J. Comput. Vis."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"11451","DOI":"10.1364\/OE.20.011451","article-title":"Three-dimensional reconstruction blood vessels extracted from retinal fundus images","volume":"20","year":"2012","journal-title":"Opt. Express"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4101","DOI":"10.1016\/j.proeng.2012.01.627","article-title":"Research on camera self-calibration of high-precision in binocular vision","volume":"29","author":"Jiang","year":"2012","journal-title":"Procedia Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Merras, M., Akkad, N.E., Saaidi, A., Nazih, A.G., and Satori, K. (2013, January 8\u20139). A new method of camera self-calibration with varying intrinsic parameters using an improved genetic algorithm. Proceedings of the 2013 8th International Conference on Intelligent Systems: Theories and Applications (SITA), Rabat, Morocco.","DOI":"10.1109\/SITA.2013.6560799"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1109\/34.888718","article-title":"A flexible new technique for camera calibration","volume":"22","author":"Zhang","year":"2000","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_15","first-page":"138","article-title":"An improved method of stereo camera calibration","volume":"35","author":"Tan","year":"2006","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1007\/s11340-021-00726-5","article-title":"DLT-lines based camera calibration with lens radial and tangential distortion","volume":"61","author":"Shi","year":"2021","journal-title":"Exp. Mech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/BF00127813","article-title":"Using vanishing points for camera calibration","volume":"4","author":"Caprile","year":"1990","journal-title":"Int. J. Comput. Vis."},{"key":"ref_18","unstructured":"Wei, G.Q., He, Z., and Ma, S.D. (1989, January 23\u201326). Camera calibration by vanishing point and cross ratio. Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Glasgow, UK."},{"key":"ref_19","unstructured":"Fan, H. (2015). Research and Application of Wide Angle Camera Calibration based on Concentric Circles. [Master\u2019s Thesis, Xidian University]."},{"key":"ref_20","first-page":"363","article-title":"Camera calibration method based on circular points","volume":"3","author":"Zhao","year":"2007","journal-title":"J. Xidian Univ."},{"key":"ref_21","first-page":"1","article-title":"High precision camera calibration method based on plane transformation","volume":"9","author":"Peng","year":"2021","journal-title":"J. Beijing Univ. Aeronaut. Astronaut."},{"key":"ref_22","unstructured":"Brown, D.C. (1958). A Solution to the General Problem of Multiple Station Analytical Stereotriangulation, Patrick Airforce Base. Rca-mtp Data Reduction Technical Report no. 43."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Huang, W., Jiang, S., and Jiang, W. (2021). Camera self-calibration with GNSS constrained bundle adjustment for weakly structured long corridor UAV images. Remote Sens., 13.","DOI":"10.3390\/rs13214222"},{"key":"ref_24","first-page":"877","article-title":"Stereo-camera calibration with restrictive constraints","volume":"41","author":"Zheng","year":"2012","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.isprsjprs.2016.03.017","article-title":"An asymmetric re-weighting method for the precision combined bundle adjustment of aerial oblique images","volume":"117","author":"Xie","year":"2016","journal-title":"J. Photogramm. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1360\/N972014-00455","article-title":"High precision localization of the Chang\u2019E-3 lunar rover","volume":"60","author":"Liu","year":"2015","journal-title":"Chin. Sci. Bull."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/0146-664X(78)90112-0","article-title":"A system for extracting three-dimensional measurements from a stereo pair of TV cameras","volume":"7","author":"Yakimovsky","year":"1978","journal-title":"Comput. Graph. Image Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1002\/2016EA000219","article-title":"The Mars science laboratory curiosity rover mast camera (mastcam) instruments: Pre-flight and in-flight calibration, validation, and data archiving: Msl\/mastcam calibration","volume":"4","author":"Bell","year":"2017","journal-title":"Earth Space Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s00190-011-0524-5","article-title":"On weighted total least-squares for geodetic transformations","volume":"86","author":"Mahboub","year":"2011","journal-title":"J. Geod."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s11263-006-5168-1","article-title":"Generalized camera calibration including fish-eye lenses","volume":"68","author":"Gennery","year":"2006","journal-title":"Int. J. Comput. Vis."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Workman, S., Mihail, R.P., and Jacobs, N. (2014, January 6\u201312). A pot of gold: Rainbows as a calibration cue. Proceedings of the European Conference on Computer Vision, Zurich, Switzerland.","DOI":"10.1007\/978-3-319-10602-1_53"},{"key":"ref_32","first-page":"159","article-title":"A stereo rectification algorithm for planetary rover visual navigation system","volume":"38","author":"Wang","year":"2017","journal-title":"J. Astronaut."},{"key":"ref_33","first-page":"32","article-title":"A positioning method of rover based on descent image and navigation image","volume":"5","author":"Xu","year":"2017","journal-title":"J. Navig. Position."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"971","DOI":"10.11834\/jrs.20144072","article-title":"Remote sensing mapping and localization techniques for teleoperation of Chang\u2019e-3 rover","volume":"18","author":"Liu","year":"2014","journal-title":"Natl. Remote Sens. Bull."},{"key":"ref_35","first-page":"259","article-title":"The historical development of analytical photogrammetry","volume":"30","author":"Doyle","year":"1964","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_36","first-page":"27","article-title":"Seed point optimal selection method of PTD algorithm based on confidence interval estimation theory","volume":"29","author":"Xing","year":"2020","journal-title":"Eng. Surv. Mapp."},{"key":"ref_37","first-page":"17","article-title":"Restore of Mathematical detail: The process of gauss deriving the probability density function of normal distribution","volume":"34","author":"Yang","year":"2019","journal-title":"J. Stat. Inf."},{"key":"ref_38","first-page":"213","article-title":"Research on modeling of probability density distribution of transverse wind power time series based on gaussian mixture distribution","volume":"34","author":"Yang","year":"2016","journal-title":"Water Resour. Power"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"35","DOI":"10.5201\/ipol.2012.gjmr-lsd","article-title":"LSD: A line segment detector","volume":"2","author":"Jakubowicz","year":"2012","journal-title":"Image Process. Line"},{"key":"ref_40","unstructured":"Feng, P. (2014). Research on Camera Calibration by Self Checking Beam Adjustment Based on Sparse Matrix. [Master\u2019s Thesis, Xi\u2019an University of Science and Technology]."},{"key":"ref_41","unstructured":"Wang, B., and Liu, C. (2016). Computer Vision Technology in Lunar Rover Teleoperation, National Defense Industry Press."},{"key":"ref_42","unstructured":"Tsai, R.Y. (1986, January 22\u201326). An efficient and accurate camera calibration technique for 3D machine vision. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Miami Beach, FL, USA."},{"key":"ref_43","unstructured":"Team E (2016). MathWorks releases release2016b with MATLAB and Simulink product families. Appl. Electron. Tech., 42, 10."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/2\/402\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:02:13Z","timestamp":1760133733000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/2\/402"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,16]]},"references-count":43,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["rs14020402"],"URL":"https:\/\/doi.org\/10.3390\/rs14020402","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,16]]}}}