{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T03:49:12Z","timestamp":1791863352813,"version":"4.3.4"},"reference-count":31,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,4,17]],"date-time":"2025-04-17T00:00:00Z","timestamp":1744848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Open Fund Project of the Key Laboratory of Intelligent Space TTC&amp;O (Space Engineering University), Ministry of Education","award":["CYK2024-02-06"],"award-info":[{"award-number":["CYK2024-02-06"]}]},{"name":"Open Fund Project of the Key Laboratory of Intelligent Space TTC&amp;O (Space Engineering University), Ministry of Education","award":["CK-2024-0050"],"award-info":[{"award-number":["CK-2024-0050"]}]},{"name":"Shandong Key Laboratory of Space Debris Monitoring and Low-Orbit Satellite Networking","award":["CYK2024-02-06"],"award-info":[{"award-number":["CYK2024-02-06"]}]},{"name":"Shandong Key Laboratory of Space Debris Monitoring and Low-Orbit Satellite Networking","award":["CK-2024-0050"],"award-info":[{"award-number":["CK-2024-0050"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As the number of satellites and amount of space debris in Low-Earth orbit (LEO) increase, high-precision orbit determination is crucial for ensuring the safe operation of spacecraft and maintaining space situational awareness. However, ground-based optical observations are constrained by limited arc-segment angular data and dynamic noise interference, and the traditional Extended Kalman Filter (EKF) struggles to meet the accuracy and robustness requirements in complex orbital environments. To address these challenges, this paper proposes a Bayesian Adaptive Extended Kalman Filter (BAEKF), which synergistically optimizes track determination through dynamic noise covariance adjustment and Bayesian a posteriori probability correction. Experiments demonstrate that the average root mean square error (RMSE) of BAEKF is reduced by 34.7% compared to the traditional EKF, effectively addressing EKF\u2019s accuracy and stability issues in nonlinear systems. The RMSE values of UKF, RBFNN, and GPR also show improvement, providing a reliable solution for high-precision orbital determination using optical observation.<\/jats:p>","DOI":"10.3390\/s25082527","type":"journal-article","created":{"date-parts":[[2025,4,17]],"date-time":"2025-04-17T06:53:46Z","timestamp":1744872826000},"page":"2527","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Bayesian Adaptive Extended Kalman-Based Orbit Determination for Optical Observation Satellites"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6111-8438","authenticated-orcid":false,"given":"Yang","family":"Guo","sequence":"first","affiliation":[{"name":"Shandong Key Laboratory of Space Debris Monitoring and Low-Orbit Satellite Networking, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1888-8021","authenticated-orcid":false,"given":"Qinghao","family":"Pang","sequence":"additional","affiliation":[{"name":"Shandong Key Laboratory of Space Debris Monitoring and Low-Orbit Satellite Networking, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1555-7518","authenticated-orcid":false,"given":"Xianlong","family":"Yin","sequence":"additional","affiliation":[{"name":"Shandong Key Laboratory of Space Debris Monitoring and Low-Orbit Satellite Networking, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xueshu","family":"Shi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Intelligent Space TT&O (Space Engineering University), Ministry of Education, Beijing 101416, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengxu","family":"Zhao","sequence":"additional","affiliation":[{"name":"Shandong Key Laboratory of Space Debris Monitoring and Low-Orbit Satellite Networking, Qingdao University of Technology, Qingdao 266520, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Sun","sequence":"additional","affiliation":[{"name":"National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinsheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Universe Kingdom Beijing Technology Co., Ltd., Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,17]]},"reference":[{"key":"ref_1","unstructured":"Guo, Y., Cheng, Z., Zhang, Q.H., and Zhao, Z.X. (2025). Efficacy assessment method of space object cooperative monitoring system applying fuzzy theory. Mod. Radar, 1\u201310."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"25","DOI":"10.31577\/congeo.2021.51.1.2","article-title":"Extended Kalman filter based statistical orbit determination for geostationary and geosynchronous satellite orbits in BeiDou constellation","volume":"51","author":"Chipade","year":"2021","journal-title":"Contrib. Geophys. Geod."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1016\/j.actaastro.2017.04.002","article-title":"Analysis of orbit determination from Earth-based tracking for relay satellites in a perturbed areostationary orbit","volume":"136","author":"Romero","year":"2017","journal-title":"Acta Astronaut."},{"key":"ref_4","first-page":"10589","article-title":"Sustainable skies and the Earth\u2013space environment","volume":"48","author":"Williams","year":"2023","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_5","first-page":"228","article-title":"The Image Processing System for Ultra-Fast Moving Space Debris Objects","volume":"7","author":"Stanislav","year":"2024","journal-title":"Nat. Sustain."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4069","DOI":"10.1016\/j.asr.2021.07.022","article-title":"Optimization of ground tracking stations for BDS-3 satellite orbit determination","volume":"68","author":"Zhang","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Kim, S., Lim, H., Bennett, C.J., Lachut, M., Jo, J.H., Choi, J., Choi, M., Park, E., Yu, S.Y., and Sung, K.P. (2020). Analysis of Space Debris Orbit Prediction Using Angle and Laser Ranging Data from Two Tracking Sites under Limited Observation Environment. Sensors, 20.","DOI":"10.3390\/s20071950"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s42452-025-06502-7","article-title":"Enhanced YOLOv8-based method for space debris detection using cross-scale feature fusion","volume":"7","author":"Guo","year":"2025","journal-title":"Discov. Appl. Sci."},{"key":"ref_9","first-page":"155","article-title":"Orbit determination of high-orbit space targets based on space-based optical goniometry","volume":"41","author":"Liu","year":"2021","journal-title":"J. Opt."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1007\/s10712-022-09758-5","article-title":"Radial Orbit Errors of Contemporary Altimetry Satellite Orbits","volume":"44","author":"Sergei","year":"2023","journal-title":"Surv. Geophys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1016\/j.asr.2017.11.001","article-title":"Precision orbit determination performance for CryoSat-2","volume":"61","author":"Schrama","year":"2018","journal-title":"Adv. Space Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.actaastro.2013.03.009","article-title":"Nonlinear filtering methods for spacecraft navigation based on differential algebra","volume":"94","author":"Valli","year":"2014","journal-title":"Acta Astronaut."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"e2020JA028862","DOI":"10.1029\/2020JA028862","article-title":"Bayesian Model for HOPE Mass Spectrometers on Van Allen Probes","volume":"126","author":"Vira","year":"2021","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhu, R., Fu, Q., Liu, N., Zhao, F., Wen, G., Li, Y.C., and Jiang, H.L. (2024). Improved target detection method for space-based optoelectronic systems. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-51717-0"},{"key":"ref_15","first-page":"5951","article-title":"The Simple Solution for Nonlinear State Estimation of Ill-Conditioned Systems: The Normalized Unscented Kalman Filter","volume":"74","author":"Aarnes","year":"2023","journal-title":"IFAC Pap. Online"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1424","DOI":"10.1016\/j.asr.2024.05.012","article-title":"RBFNN-based angles-only orbit determination method for non-cooperative space targets","volume":"74","author":"Gong","year":"2024","journal-title":"Adv. Space Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/s42064-024-0210-z","article-title":"Initial orbit determination of some cislunar orbits based on short-arc optical observations","volume":"8","author":"Hou","year":"2024","journal-title":"Astrodynamics"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sun, C., Sun, Y., Yu, X., and Fang, Q. (2023). Rapid Detection and Orbital Parameters\u2019 Determination for Fast-Approaching Non-Cooperative Target to the Space Station Based on Fly-around Nano-Satellite. Remote Sens., 15.","DOI":"10.3390\/rs15051213"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.actaastro.2020.06.046","article-title":"Initial orbit association and long-term orbit prediction for low earth space objects using optical tracking data","volume":"176","author":"Lee","year":"2020","journal-title":"Acta Astronaut."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"David, S., Puneet, S., and Sean, O.R. (2022). Angles-Only Initial Orbit Determination via Multivariate Gaussian Process Regression. Electronics, 11.","DOI":"10.3390\/electronics11040588"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"979","DOI":"10.2514\/1.62308","article-title":"Collision Probability with Gaussian Mixture Orbit Uncertainty","volume":"37","author":"DeMars","year":"2014","journal-title":"J. Guid. Control Dyn."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1016\/j.asr.2014.11.015","article-title":"Orbit determination via adaptive Gaussian swarm optimization","volume":"55","author":"Kiani","year":"2014","journal-title":"J. Adv. Space Res."},{"key":"ref_23","first-page":"2339","article-title":"Gaussian-Mixture Kalman Filter for Orbit Determination Using Angles-Only Data","volume":"40","author":"Psiaki","year":"2017","journal-title":"J. Guid. Control Dyn."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2807","DOI":"10.2514\/1.G002615","article-title":"Gaussian Mixture Approximation of Angles-Only Initial Orbit Determination Likelihood Function","volume":"40","author":"Psiaki","year":"2017","journal-title":"J. Guid. Control Dyn."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wang, Q., Sun, T., Lyu, Z., and Gao, D. (2019). A Virtual In-Cylinder Pressure Sensor Based on EKF and Frequency-Amplitude-Modulation Fourier-Series Method. J. Sens., 19.","DOI":"10.3390\/s19143122"},{"key":"ref_26","first-page":"161","article-title":"Fault detection in a three-tank hydraulic system using unknown input observer and extended Kalman filter","volume":"9","author":"Demirkol","year":"2021","journal-title":"J. Eng. Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.protcy.2013.12.457","article-title":"Unscented Kalman Filters and Particle Filter Methods for Nonlinear State Estimation","volume":"12","author":"Kelemen","year":"2014","journal-title":"J. Procedia Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"100909","DOI":"10.1016\/j.arcontrol.2023.100909","article-title":"State of art on state estimation: Kalman filter driven by machine learning","volume":"56","author":"Bai","year":"2023","journal-title":"J. Annu. Rev. Control"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Anirudh, C., Rao, J.V., and Donghoon, K. (2021). Measurement Noise Covariance-Adapting Kalman Filters for Varying Sensor Noise Situations. Sensors, 21.","DOI":"10.3390\/s21248304"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Chen, J., Jin, X., and Hou, C. (2024). Real-Time Orbit Determination of Micro\u2013Nano Satellite Using Robust Adaptive Filtering. J. Sens., 24.","DOI":"10.3390\/s24247988"},{"key":"ref_31","first-page":"325","article-title":"A Bayesian approach to gamma storm data processing","volume":"31","author":"Bu","year":"2013","journal-title":"Prog. Astron."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/8\/2527\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:16:16Z","timestamp":1760030176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/8\/2527"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,17]]},"references-count":31,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["s25082527"],"URL":"https:\/\/doi.org\/10.3390\/s25082527","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,17]]}}}