{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T06:54:09Z","timestamp":1773730449585,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T00:00:00Z","timestamp":1697587200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009145","name":"Botswana International University of Science and Technology","doi-asserted-by":"publisher","award":["S00387"],"award-info":[{"award-number":["S00387"]}],"id":[{"id":"10.13039\/100009145","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the context of Kalman filters, the predicted error covariance matrix Pk+1 and measurement noise covariance matrix R are used to represent the uncertainty of state variables and measurement noise, respectively. However, in real-world situations, these matrices may vary with time due to measurement faults. To address this issue in CubeSat attitude estimation, an adaptive extended Kalman filter has been proposed that can dynamically estimate the predicted error covariance matrix and measurement noise covariance matrix using an expectation-maximization approach. Simulation experiments have shown that this algorithm outperforms existing methods in terms of attitude estimation accuracy, particularly in sunlit and shadowed phases of the orbit, with the same filtering parameters and initial conditions.<\/jats:p>","DOI":"10.3390\/s23208549","type":"journal-article","created":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T10:36:56Z","timestamp":1697625416000},"page":"8549","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Attitude Determination System for a Cubesat Experiencing Eclipse"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9608-7670","authenticated-orcid":false,"given":"Kesaobaka","family":"Mmopelwa","sequence":"first","affiliation":[{"name":"Department of Mechanical, Energy, and Industrial Engineering, Fauculty of Engineering, Botswana International University of Science and Technology, Private Bag 16, Palapye 10071, Botswana"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6205-8131","authenticated-orcid":false,"given":"Teddy Tumisang","family":"Ramodimo","sequence":"additional","affiliation":[{"name":"Department of Mechanical, Energy, and Industrial Engineering, Fauculty of Engineering, Botswana International University of Science and Technology, Private Bag 16, Palapye 10071, Botswana"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oduetse","family":"Matsebe","sequence":"additional","affiliation":[{"name":"Department of Mechanical, Energy, and Industrial Engineering, Fauculty of Engineering, Botswana International University of Science and Technology, Private Bag 16, Palapye 10071, Botswana"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1724-9550","authenticated-orcid":false,"given":"Bokamoso","family":"Basutli","sequence":"additional","affiliation":[{"name":"Department of Electrical, Computer, and Telecommunications Engineering, Fauculty of Engineering, Botswana International University of Science and Technology, Private Bag 16, Palapye 10071, Botswana"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.actaastro.2011.12.014","article-title":"A survey and assessment of the capabilities of Cubesats for Earth observation","volume":"74","author":"Selva","year":"2012","journal-title":"Acta Astronaut."},{"key":"ref_2","unstructured":"Carrara, V., Kuga, H.K., Bringhenti, P.M., and de Carvalho, M.J. (2014, January 9). Attitude determination, control and operating modes for CONASAT Cubesats. Proceedings of the 24th International Symposium on Space Flight Dynamics (ISSFD), Laurel, MD, USA."},{"key":"ref_3","unstructured":"Mahmood, N.H., B\u00f6cker, S., Munari, A., Clazzer, F., Moerman, I., Mikhaylov, K., Lopez, O., Park, O.S., Mercier, E., and Bartz, H. (2020). White paper on critical and massive machine type communication towards 6G. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Xia, X., Sun, G., Zhang, K., Wu, S., Wang, T., Xia, L., and Liu, S. (2017, January 28\u201330). NanoSats\/CubeSats ADCS survey. Proceedings of the 2017 29th Chinese Control And Decision Conference (CCDC), Chongqing, China.","DOI":"10.1109\/CCDC.2017.7979410"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"104099","DOI":"10.1016\/j.autcon.2021.104099","article-title":"Real-time monitoring of construction sites: Sensors, methods, and applications","volume":"136","author":"Rao","year":"2022","journal-title":"Autom. Constr."},{"key":"ref_6","first-page":"439","article-title":"A survey of attitude representations","volume":"8","author":"Shuster","year":"1993","journal-title":"Navigation"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"718","DOI":"10.2514\/2.2824","article-title":"Review of attitude representations used for aircraft kinematics","volume":"38","author":"Phillips","year":"2001","journal-title":"J. Aircr."},{"key":"ref_8","unstructured":"D\u00edaz, E.O. (2019). 3D Motion of Rigid Bodies, Springer."},{"key":"ref_9","unstructured":"Parwana, H., and Kothari, M. (2017). Quaternions and attitude representation. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1515\/arsa-2017-0005","article-title":"An optimized triad algorithm for attitude determination","volume":"52","author":"Zhu","year":"2017","journal-title":"Artif. Satell."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.paerosci.2017.03.003","article-title":"Review on gyroless attitude determination methods for small satellites","volume":"90","author":"Hajiyev","year":"2017","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1515\/mms-2017-0023","article-title":"Single-Frame Attitude Determination Methods for Nanosatellites","volume":"24","author":"Conguroglu","year":"2017","journal-title":"Metrol. Meas. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"12","DOI":"10.2514\/1.22452","article-title":"Survey of nonlinear attitude estimation methods","volume":"30","author":"Crassidis","year":"2007","journal-title":"J. Guid. Control Dyn."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Markley, F.L., and Crassidis, J.L. (2014). Fundamentals of Spacecraft Attitude Determination and Control, Springer.","DOI":"10.1007\/978-1-4939-0802-8"},{"key":"ref_15","unstructured":"Reidel, D. (1999). Spacecraft Attitude Determination and Control (Astrophysics and Space Science Library 73), Springer. [1978th ed.]."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"401282","DOI":"10.1155\/2013\/401282","article-title":"Attitude determination with magnetometers and accelerometers to use in satellite simulator","volume":"2013","author":"Kuga","year":"2013","journal-title":"Math. Probl. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/j.ast.2016.06.004","article-title":"Gyro-free attitude and rate estimation for a small satellite using SVD and EKF","volume":"55","author":"Hajiyev","year":"2016","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Hajiyev, C., \u00c7ilden, D., and Somov, Y. (2015, January 27\u201330). Gyroless attitude and rate estimation of small satellites using singular value decomposition and extended Kalman filter. Proceedings of the 2015 16th International Carpathian Control Conference (ICCC), Szilvasvarad, Hungary.","DOI":"10.1109\/CarpathianCC.2015.7145066"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Cilden, D., Hajiyev, C., and Soken, H.E. (2015, January 16\u201319). Attitude and attitude rate estimation for a nanosatellite using SVD and UKF. Proceedings of the 2015 7th International Conference on Recent Advances in Space Technologies (RAST), Istanbul, Turkey.","DOI":"10.1109\/RAST.2015.7208431"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Sumanth, R.M. (2019). Computation of eclipse time for low-Earth orbiting small satellites. Int. J. Aviat. Aeronaut. Aerosp., 6.","DOI":"10.15394\/ijaaa.2019.1412"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"13544","DOI":"10.1109\/JSEN.2022.3175261","article-title":"Backup Magnetometer-only Attitude Estimation Algorithm for Small Satellites","volume":"22","author":"Esit","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Hajiyev, C., Cilden-Guler, D., and Somov, Y. (2017, January 19\u201322). Attitude determination of nanosatellites in the sun-eclipse phases. Proceedings of the 2017 8th International Conference on Recent Advances in Space Technologies (RAST), Istanbul, Turkey.","DOI":"10.1109\/RAST.2017.8002990"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.ifacol.2018.11.254","article-title":"Gyroless Nanosatellite Attitude Estimation in Loss of Sun Sensor Measurements","volume":"51","author":"Hajiyev","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3875","DOI":"10.1016\/j.asr.2021.07.006","article-title":"Satellite attitude estimation using SVD-Aided EKF with simultaneous process and measurement covariance adaptation","volume":"68","author":"Hajiyev","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.isprsjprs.2022.12.010","article-title":"HE2LM-AD: Hierarchical and efficient attitude determination framework with adaptive error compensation module based on ELM network","volume":"195","author":"Cao","year":"2023","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1002\/asjc.1689","article-title":"Adaptive iterated extended Kalman filter for relative spacecraft attitude and position estimation","volume":"20","author":"Xiong","year":"2018","journal-title":"Asian J. Control"},{"key":"ref_27","first-page":"245","article-title":"Attitude determination using vector observations and the singular value decomposition","volume":"36","author":"Markley","year":"1988","journal-title":"J. Astronaut. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"417","DOI":"10.2514\/3.56190","article-title":"Kalman filtering for spacecraft attitude estimation","volume":"5","author":"Lefferts","year":"1982","journal-title":"J. Guid. Control Dyn."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Kang, C.W., and Park, C.G. (2009, January 23\u201326). Attitude estimation with accelerometers and gyros using fuzzy tuned Kalman filter. Proceedings of the 2009 European Control Conference (ECC), Budapest, Hungary.","DOI":"10.23919\/ECC.2009.7074977"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1186\/s40623-020-01288-x","article-title":"International geomagnetic reference field: The thirteenth generation","volume":"73","author":"Alken","year":"2021","journal-title":"Earth Planets Space"},{"key":"ref_31","unstructured":"Makovec, K.L. (2001). A Nonlinear Magnetic Controller for Three-Axis Stability of Nanosatellites. [Ph.D. Thesis, Virginia Tech]."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.solener.2020.10.084","article-title":"Updating the PSA sun position algorithm","volume":"212","author":"Blanco","year":"2020","journal-title":"Sol. Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1038\/nbt1406","article-title":"What is the expectation maximization algorithm?","volume":"26","author":"Do","year":"2008","journal-title":"Nat. Biotechnol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1109\/79.543975","article-title":"The expectation-maximization algorithm","volume":"13","author":"Moon","year":"1996","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.automatica.2010.10.013","article-title":"System identification of nonlinear state-space models","volume":"47","author":"Wills","year":"2011","journal-title":"Automatica"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1109\/TAES.2017.2756763","article-title":"A new adaptive extended Kalman filter for cooperative localization","volume":"54","author":"Huang","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_37","first-page":"2341","article-title":"Single image haze removal using dark channel prior","volume":"33","author":"He","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1109\/TPAMI.2015.2439281","article-title":"Image super-resolution using deep convolutional networks","volume":"38","author":"Dong","year":"2015","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/20\/8549\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:09:02Z","timestamp":1760130542000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/20\/8549"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,18]]},"references-count":38,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["s23208549"],"URL":"https:\/\/doi.org\/10.3390\/s23208549","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,18]]}}}