{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T20:33:04Z","timestamp":1767990784054,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,15]],"date-time":"2023-06-15T00:00:00Z","timestamp":1686787200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Yunnan Fundamental Research Projects","award":["202301AT070159"],"award-info":[{"award-number":["202301AT070159"]}]},{"name":"Yunnan Fundamental Research Projects","award":["202201BE070001-035"],"award-info":[{"award-number":["202201BE070001-035"]}]},{"name":"Yunnan Fundamental Research Projects","award":["202301AU070062"],"award-info":[{"award-number":["202301AU070062"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Accurately modeling the density of atmospheric mass is critical for orbit determination and prediction of space objects. Existing atmospheric mass density models (ADMs) have an accuracy of about 15%. Developing high-precision ADMs is a long-term goal that requires a better understanding of atmospheric density characteristics, more accurate modeling methods, and improved spatiotemporal data. This study proposes a method for calibrating ADMs using sparse angular data of space objects in low-Earth orbit over a certain period of time. Applying the corrected ADM not only improves the accuracy of orbit determination, but also enhances the accuracy of orbit prediction beyond the correction period. The study compares the impact of two calibration methods: atmospheric mass density model coefficient (ADMC) calibration and high precision satellite drag model (HASDM) calibration on the accuracy of orbit prediction of space objects. One month of ground-based telescope array angular data is used to validate the results. Space objects are classified as calibration objects, participating in ADM calibration, and verification objects, inside and outside the calibration orbit region, respectively. The results show that applying the calibrated ADM can significantly increase the accuracy of orbit prediction. For objects within the calibration orbit region, the calibration object\u2019s orbit prediction error was reduced by about 55%, while that of verification objects was reduced by about 45%. The reduction in orbit prediction error outside this region was about 30%. This proposed method contributes significantly to the development of more reliable ADMs for orbit prediction of space objects with sparse angular data and can provide significant academic value in the field of space situational awareness.<\/jats:p>","DOI":"10.3390\/rs15123128","type":"journal-article","created":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T02:02:20Z","timestamp":1686880940000},"page":"3128","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Case Study on the Effect of Atmospheric Density Calibration on Orbit Predictions with Sparse Angular Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-4657-1850","authenticated-orcid":false,"given":"Junyu","family":"Chen","sequence":"first","affiliation":[{"name":"Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jizhang","family":"Sang","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenwei","family":"Li","sequence":"additional","affiliation":[{"name":"Changchun Observatory, National Astronomical Observatories, Chinese Academy of Sciences, Jilin 130017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengzhi","family":"Liu","sequence":"additional","affiliation":[{"name":"Changchun Observatory, National Astronomical Observatories, Chinese Academy of Sciences, Jilin 130017, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Puente, C., Saenz-Nuno, M.A., Villa-Monte, A., and Olivas, J.A. (2021). Satellite Orbit Prediction Using Big Data and Soft Computing Techniques to Avoid Space Collisions. Mathematics, 9.","DOI":"10.3390\/math9172040"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1007\/s10291-022-01289-1","article-title":"Satellite laser ranging to GNSS-based Swarm orbits with handling of systematic errors","volume":"26","author":"Strugarek","year":"2022","journal-title":"GPS Solut."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Najder, J., and Sosnica, K. (2021). Quality of Orbit Predictions for Satellites Tracked by SLR Stations. Remote Sens., 13.","DOI":"10.3390\/rs13071377"},{"key":"ref_4","unstructured":"Kelso, T.S. (2009, January 8\u201312). Analysis of the iridium 33 cosmos 2251 collision. Proceedings of the AAS Space Flight Mechanics Meeting, Savannah, Georgia."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.actaastro.2021.02.023","article-title":"Differential algebra enabled multi-target tracking for too-short arcs","volume":"182","author":"Pirovano","year":"2021","journal-title":"Acta Astronaut."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.actaastro.2014.06.012","article-title":"Experimental results of debris orbit predictions using sparse tracking data from Mt. Stromlo","volume":"102","author":"Sang","year":"2014","journal-title":"Acta Astronaut."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1016\/j.asr.2010.10.017","article-title":"Improved orbit predictions using two-line elements","volume":"47","author":"Levit","year":"2011","journal-title":"Adv. Space Res."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chen, J., and Lin, C. (2023). Research on Enhanced Orbit Prediction Techniques Utilizing Multiple Sets of Two-Line Element. Aerospace, 10.","DOI":"10.3390\/aerospace10060532"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2535","DOI":"10.1016\/j.asr.2022.12.056","article-title":"Advanced ensemble modeling method for space object state prediction accounting for uncertainty in atmospheric density","volume":"71","author":"Paul","year":"2023","journal-title":"Adv. Space Res."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Sun, Y., Wang, B., Meng, X., Tang, X., Yan, F., Zhang, X., Bai, W., Du, Q., Wang, X., and Cai, Y. (2022). Analysis of Orbital Atmospheric Density from QQ-Satellite Precision Orbits Based on GNSS Observations. Remote Sens., 14.","DOI":"10.3390\/rs14163873"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Yin, L., Wang, L., Tian, J., Yin, Z., Liu, M., and Zheng, W. (2023). Atmospheric Density Inversion Based on Swarm-C Satellite Accelerometer. Appl. Sci., 13.","DOI":"10.3390\/app13063610"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yin, L., Wang, L., Zheng, W., Ge, L., Tian, J., Liu, Y., Yang, B., and Liu, S. (2022). Evaluation of Empirical Atmospheric Models Using Swarm-C Satellite Data. Atmosphere, 13.","DOI":"10.3390\/atmos13020294"},{"key":"ref_13","unstructured":"Jacchia, L.G. (1971). Revised Static Models of the Thermosphere and Exosphere with Empircial Temperature Profiles, Smithsonian Inatitution Astrophysical Observatory Cambridge."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1016\/j.jastp.2007.10.002","article-title":"The JB2006 empirical thermospheric density model","volume":"70","author":"Bowman","year":"2008","journal-title":"J. Atmos. Sol. Terr. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"SIA-15","DOI":"10.1029\/2002JA009430","article-title":"NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues","volume":"107","author":"Picone","year":"2002","journal-title":"J. Geophys. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1029\/2020EA001321","article-title":"NRLMSIS 2.0: A Whole-Atmosphere Empirical Model of Temperature and Neutral Species Densities","volume":"8","author":"Emmert","year":"2021","journal-title":"Earth Space Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1051\/swsc\/2021032","article-title":"The operational and research DTM-2020 thermosphere models","volume":"11","author":"Bruinsma","year":"2021","journal-title":"J. Space Weather Space Clim."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.actaastro.2013.10.005","article-title":"A critical assessment of satellite drag and atmospheric density modeling","volume":"95","author":"Vallado","year":"2014","journal-title":"Acta Astronaut."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1051\/swsc\/2021002","article-title":"Thermosphere modeling capabilities assessment: Geomagnetic storms","volume":"11","author":"Bruinsma","year":"2021","journal-title":"J. Space Weather Space Clim."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"942","DOI":"10.2514\/1.A35197","article-title":"Atmospheric Density Estimation Techniques for Aerocapture","volume":"60","author":"Roelke","year":"2023","journal-title":"J. Spacecr. Rocket."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"8503011","DOI":"10.1109\/TIM.2023.3273665","article-title":"A Novel Tightly-Coupled SINS\/RCNS Integrated Navigation Method Considering Atmospheric Density Error","volume":"72","author":"Zhao","year":"2023","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/BF03546389","article-title":"Precision low Earth orbit determination using atmospheric density calibration","volume":"46","author":"Marcos","year":"1998","journal-title":"J. Astronaut. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1002\/2016SW001562","article-title":"New density estimates derived using accelerometers on board the CHAMP and GRACE satellites","volume":"15","author":"Mehta","year":"2017","journal-title":"Space Weather"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1016\/j.asr.2006.12.025","article-title":"Use of two-line element data for thermosphere neutral density model calibration","volume":"41","author":"Doornbos","year":"2008","journal-title":"Adv. Space Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2497","DOI":"10.1016\/j.asr.2004.02.020","article-title":"High accuracy satellite drag model (HASDM)","volume":"36","author":"Storz","year":"2005","journal-title":"Adv. Space Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"e2020SW002682","DOI":"10.1029\/2020SW002682","article-title":"The SET HASDM Density Database","volume":"19","author":"Tobiska","year":"2021","journal-title":"Space Weather Int. J. Res. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"e2021SW002915","DOI":"10.1029\/2021SW002915","article-title":"Machine-Learned HASDM Thermospheric Mass Density Model With Uncertainty Quantification","volume":"20","author":"Licata","year":"2022","journal-title":"Space Weather Int. J. Res. Appl."},{"key":"ref_28","first-page":"104","article-title":"A New Concept of Real Time Improvement of Atmospheric Mass Density Models and Its Validation Using CHAMP GPS-Derived Precision Orbit Data","volume":"9","author":"Sang","year":"2010","journal-title":"J. Glob. Position. Syst."},{"key":"ref_29","first-page":"9","article-title":"Thermospheric basis functions for improved dynamic calibration of semi-empirical models","volume":"10","author":"Sutton","year":"2012","journal-title":"Space Weather Int. J. Res. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.actaastro.2014.12.018","article-title":"Neural Network based calibration of atmospheric density models","volume":"110","author":"Perez","year":"2015","journal-title":"Acta Astronaut."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.asr.2020.07.030","article-title":"Identification of uncatalogued LEO space objects by a ground-based EO array","volume":"67","author":"Lei","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/j.asr.2015.05.038","article-title":"Thermospheric mass density: A review","volume":"56","author":"Emmert","year":"2015","journal-title":"Adv. Space Res."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/12\/3128\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:55:37Z","timestamp":1760126137000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/12\/3128"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,15]]},"references-count":32,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["rs15123128"],"URL":"https:\/\/doi.org\/10.3390\/rs15123128","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,15]]}}}