{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T15:37:28Z","timestamp":1775144248895,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,4,18]],"date-time":"2023-04-18T00:00:00Z","timestamp":1681776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Considering the problem of GNSS service interruption caused by the insufficient number of available satellites in complex environments, Low Earth Orbit (LEO) satellites can supplement GNSS effectively. To eliminate the unknown satellite clock error and the atmospheric delay error with spatial correlation in LEO observations, a Differential-Low Earth Orbit opportunistically enhancing GNSS (D-LoeGNSS) navigation framework is proposed. Firstly, because of the uncertainty of the LEO orbit, we derive the effect of the LEO orbit error on the differential measurement model. Secondly, aiming at the noise amplification and correlation in double-difference (DD), we propose a Householder-Based D-LoeGNSS (HB-DLG) algorithm, which suppresses noise by introducing an orthogonal matrix. Thirdly, in D-LoeGNSS, the typical measurement of LEO is Doppler, which is heterogeneous with the GNSS pseudorange, rendering the Dilution of Precision (DOP) evaluation method unsuitable. Given the unbiasedness of differential measurements, the Cramer Rao Lower Bound (CRLB) is derived as a metric to characterize the positioning accuracy and satellite spatial distribution. Finally, a field experiment using Orbcomm (ORB) and GPS is conducted. The experimental results show that the performance of the HB-DLG algorithm is superior to DD. Especially when the number of satellites is insufficient or the measurement redundancy is poor; the D-LoeGNSS framework has advantages of rapid convergence and high accuracy compared with a single constellation.<\/jats:p>","DOI":"10.3390\/rs15082136","type":"journal-article","created":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T01:09:22Z","timestamp":1681866562000},"page":"2136","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["A Design of Differential-Low Earth Orbit Opportunistically Enhanced GNSS (D-LoeGNSS) Navigation Framework"],"prefix":"10.3390","volume":"15","author":[{"given":"Muyuan","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Honglei","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Yu","family":"Su","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Fangchi","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Jianwu","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, L., Chen, R., Li, D., Zhang, G., Shen, X., Yu, B., and Pan, Y. (2018). Initial assessment of the LEO based navigation signal augmentation system from Luojia-1A satellite. Sensors, 18.","DOI":"10.3390\/s18113919"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1007\/s00190-018-1195-2","article-title":"LEO constellation-augmented multi-GNSS for rapid PPP convergence","volume":"93","author":"Li","year":"2019","journal-title":"J. Geod."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1671","DOI":"10.1016\/j.asr.2017.01.011","article-title":"The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS)\u2014Achievements, prospects and challenges","volume":"59","author":"Montenbruck","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_4","unstructured":"Rabinowitz, M. (2000). A Differential Carrier-Phase Navigation System Combining GPS with Low Earth Orbit Satellites for Rapid Resolution of Integer Cycle Ambiguities. [Ph.D. Thesis, Stanford University]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TAES.2013.6404114","article-title":"Ionospheric error modeling for carrier phase-based multiconstellation navigation systems","volume":"49","author":"Joerger","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1002\/navi.234","article-title":"Broadband LEO constellations for navigation","volume":"65","author":"Reid","year":"2018","journal-title":"Int. J. Navig."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2270","DOI":"10.1109\/LCOMM.2020.3003791","article-title":"Exploring implicit pilots for precise estimation of LEO satellite downlink Doppler frequency","volume":"24","author":"Wei","year":"2020","journal-title":"IEEE Commun. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ge, H., Li, B., Ge, M., Zang, N., Nie, L., Shen, Y., and Schuh, H. (2018). Initial assessment of precise point positioning with LEO enhanced global navigation satellite systems (LeGNSS). Remote Sens., 10.","DOI":"10.3390\/rs10070984"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10291-020-00977-0","article-title":"Hybrid constellation design using a genetic algorithm for a LEO-based navigation augmentation system","volume":"24","author":"Ma","year":"2020","journal-title":"GPS Solut."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s10291-022-01240-4","article-title":"Frequency design of LEO-based navigation augmentation signals for dual-band ionospheric-free ambiguity resolution","volume":"26","author":"Ma","year":"2022","journal-title":"GPS Solut."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1002\/navi.438","article-title":"Navigation using carrier Doppler shift from a LEO constellation: TRANSIT on steroids","volume":"68","author":"Psiaki","year":"2021","journal-title":"Navigation"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Khalife, J., and Kassas, Z.M. (2023). Performance-Driven Design of Carrier Phase Differential Navigation Frameworks with Megaconstellation LEO Satellites. IEEE Trans. Aerosp. Electron. Syst., 1\u201319.","DOI":"10.1109\/TAES.2023.3234521"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10291-021-01210-2","article-title":"LEO Doppler-aided GNSS position estimation","volume":"26","author":"Jiang","year":"2022","journal-title":"GPS Solut."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Hsu, W., and Jan, S. (2014, January 5\u20138). Assessment of using Doppler shift of LEO satellites to aid GPS positioning. Proceedings of the 2014 IEEE\/ION Position, Location and Navigation Symposium\u2014PLANS 2014, Monterey, CA, USA.","DOI":"10.1109\/PLANS.2014.6851486"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2606","DOI":"10.1109\/TAES.2021.3127488","article-title":"Acquisition, Doppler Tracking, and Positioning With Starlink LEO Satellites: First Results","volume":"58","author":"Neinavaie","year":"2022","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1109\/TAES.2021.3113880","article-title":"The First Carrier Phase Tracking and Positioning Results With Starlink LEO Satellite Signals","volume":"58","author":"Khalife","year":"2022","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1002\/9781119458555.ch43a","article-title":"Navigation from Low Earth Orbit: Part 1: Concept, Current Capability, and Future Promise","volume":"Volume 43","author":"Reid","year":"2020","journal-title":"Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s10291-012-0286-4","article-title":"Satellite clock bias estimation for iGPS","volume":"17","author":"Pratt","year":"2013","journal-title":"GPS Solut."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Reid, T., Neish, A., Walter, T., and Enge, P. (2016, January 12\u201316). Leveraging commercial broadband LEO constellations for navigating. Proceedings of the 29th International Technical Meeting of the Satellite Division of the Institute of Navigation (Ion Gnss+ 2016), Portland, OR, USA.","DOI":"10.33012\/2016.14729"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Khalife, J., and Kassas, Z.M. (2019, January 16\u201320). Assessment of Differential Carrier Phase Measurements from Orbcomm LEO Satellite Signals for Opportunistic Navigation. Proceedings of the International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2019), Miami, FL, USA.","DOI":"10.33012\/2019.17031"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7670","DOI":"10.1109\/TWC.2016.2606099","article-title":"Anchor-Aided Joint Localization and Synchronization Using SOPs: Theory and Experiments","volume":"15","author":"Leng","year":"2016","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Thompson, S., Martin, S., and Bevly, D. (2021, January 25\u201328). Single Differenced Doppler Positioning with Low Earth Orbit Signals of Opportunity and Angle of Arrival Estimation. Proceedings of the 2021 International Technical Meeting of the Institute of Navigation, Manassas, VA, USA.","DOI":"10.33012\/2021.17845"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Neinavaie, M., Shadram, Z., Kozhaya, S., and Kassas, Z.M. (2022, January 5\u201312). First Results of Differential Doppler Positioning with Unknown Starlink Satellite Signals. Proceedings of the IEEE Aerospace Conference (AERO), Big Sky, MT, USA.","DOI":"10.1109\/AERO53065.2022.9843493"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1007\/s10291-003-0077-z","article-title":"Code and carrier phase based short baseline GPS positioning: Computational aspects","volume":"7","author":"Chang","year":"2004","journal-title":"GPS Solut."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"McLemore, B., and Psiaki, M.L. (2021, January 20\u201324). GDOP of Navigation using Pseudorange and Doppler Shift from a LEO Constellation. Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021), St. Louis, MO, USA.","DOI":"10.33012\/2021.18008"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4295","DOI":"10.1109\/TAES.2022.3162772","article-title":"Navigation Using Doppler Shift From LEO Constellations and INS Data","volume":"58","author":"McLemore","year":"2022","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Vallado, D.A., and Crawford, P. (2016, September 14). SGP4 Orbit Determination. Available online: http:\/\/www.centerforspace.com\/downloads\/files\/pubs\/AIAA-2008-6770.pdf.","DOI":"10.2514\/6.2008-6770"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"B\u00f6hm, J., and Schuh, H. (2013). Atmospheric Effects in Space Geodesy, Springer.","DOI":"10.1007\/978-3-642-36932-2"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10291-021-01189-w","article-title":"Bottomside ionospheric snapshot modeling using the LEO navigation augmentation signal from the Luojia-1A satellite","volume":"26","author":"Li","year":"2022","journal-title":"GPS Solut."},{"key":"ref_30","unstructured":"Xie, G. (2009). Principles of GPS and Receiver Design, Publishing House of Electronics Industry."},{"key":"ref_31","unstructured":"(2023, April 16). Total Electron Content. Wikipedia. Available online: https:\/\/en.wikipedia.org\/wiki\/Total_electron_content."},{"key":"ref_32","unstructured":"(2023, March 10). Ionospheric and Atmospheric Remote Sensing, Available online: https:\/\/iono.jpl.nasa.gov\/."},{"key":"ref_33","unstructured":"(2023, March 10). National Meteorological Information Center\u2014China Meteorological Data Network. Available online: http:\/\/data.cma.cn\/."},{"key":"ref_34","unstructured":"(2022, December 20). Ever Wondered What Is on the Orbcomm Satellite Downlink?. Available online: http:\/\/mdkenny.customer.netspace.net.au\/Orbcomm.pdf."},{"key":"ref_35","unstructured":"(2019, February 07). Rockwell Collins MPE-I Specification Sheet. Available online: http:\/\/www.collins.rockwell.com\/content\/pdf\/826.pdf."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1177\/09544100221113123","article-title":"High-order pseudorange rate measurement model for multi-constellation LEO\/INS integration: Case of Iridium-NEXT, Orbcomm, and Globalstar","volume":"237","author":"Farhangian","year":"2023","journal-title":"Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/8\/2136\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:18:26Z","timestamp":1760123906000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/8\/2136"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,18]]},"references-count":36,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["rs15082136"],"URL":"https:\/\/doi.org\/10.3390\/rs15082136","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,18]]}}}