{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T09:23:29Z","timestamp":1760606609935,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,6,24]],"date-time":"2019-06-24T00:00:00Z","timestamp":1561334400000},"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":["61601485"],"award-info":[{"award-number":["61601485"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Conservative sensor error modeling is of great significance in the field of safety-of-life. At present, the overbound method has been widely used in areas such as satellite-based augmentation systems (SBASs) and ground-based augmentation systems (GBASs) that provide integrity service. It can effectively solve the difficulties of non-Gaussian and non-zero mean error modeling and confidence interval estimation of user position error. However, there is still a problem in that the model is too conservative and leads to the lack of availability. In order to further improve the availability of SBASs, an improved paired overbound method is proposed in this paper. Compared with the traditional method, the improved algorithm no longer requires the overbound function to conform to the characteristics of the probability distribution function, so that under the premise of ensuring the integrity of the system, the real error characteristics can be more accurately modeled and measured. The experimental results show that the modified paired overbound method can improve the availability of the system with a probability of about 99%. In view of the fact that conservative error modeling is more sensitive to large deviations, this paper analyzes the robustness of the improved algorithm in the case of abnormal data loss. The maximum deviation under a certain integrity risk is used to illustrate the effectiveness of the improved paired overbound method compared with the original method.<\/jats:p>","DOI":"10.3390\/s19122826","type":"journal-article","created":{"date-parts":[[2019,6,25]],"date-time":"2019-06-25T10:52:31Z","timestamp":1561459951000},"page":"2826","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Conservative Sensor Error Modeling Using a Modified Paired Overbound Method and its Application in Satellite-Based Augmentation Systems"],"prefix":"10.3390","volume":"19","author":[{"given":"Yan","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Electronic Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhibin","family":"Xiao","sequence":"additional","affiliation":[{"name":"College of Electronic Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pengpeng","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electronic Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaomei","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Electronic Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Ou","sequence":"additional","affiliation":[{"name":"College of Electronic Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1109\/5.533954","article-title":"Wide area augmentation of the Global Positioning System","volume":"84","author":"Enge","year":"2002","journal-title":"Proc. IEEE"},{"key":"ref_2","unstructured":"Watt, G.T., La Cruz, C.L.D., Habereder, H.L., and Heine, D.R. (2003, January 9\u201312). Proving SBAS Integrity Through Fault Tree-Based Systems Engineering. Proceedings of the International Technical Meeting of the Satellite Division of the Institute of Navigation, Portland, OR, USA."},{"key":"ref_3","unstructured":"Walter, T., and Enge, P. (2019, June 23). Integrity Lessons from the WAAS Integrity Performance Panel (WIPP). Available online: http:\/\/web.stanford.edu\/group\/scpnt\/gpslab\/pubs\/papers\/Walter_IONNTM_2003.pdf."},{"key":"ref_4","unstructured":"Walter, T., Hansen, A., and Enge, P. (2007, January 27\u201330). Validation of the WAAS MOPS Integrity Equation. Proceedings of the Annual Meeting of the Institute of Navigation, Cambridge, MA, USA."},{"key":"ref_5","unstructured":"Rife, J., and Pervan, S.P.B. (2004, January 21\u201324). Core Overbounding and its Implications for LAAS Integrity. Proceedings of the ION GNSS, Long Beach, CA, USA."},{"key":"ref_6","unstructured":"Ober, P.B., Farnsworth, R., Breeuwer, E., and van Willigen, D. (2001, January 11\u201314). SBAS Integrity Verification. Proceedings of the ION GPS, Salt Lake City, UT, USA."},{"key":"ref_7","unstructured":"DeCleene, B. (2000, January 19\u201322). Defining Pseudorange Integrity\u2014Overbounding. Proceedings of the ION GPS, Salt Lake City, UT, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1109\/TAES.2006.314579","article-title":"Paired Overbounding for Nonideal LAAS and WAAS Error Distributions","volume":"42","author":"Rife","year":"2006","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Blanch, J., Walter, T., and Enge, P. Gaussian Bounds of Sample Distributions for Integrity Analysis. IEEE Trans. Aerosp. Electron. Syst., 2018.","DOI":"10.1109\/TAES.2018.2876583"},{"key":"ref_10","unstructured":"Rife, J., Walter, T., and Blanch, J. (2004, January 6\u20138). Overbounding SBAS and GBAS error distributions with excess-mass functions. Proceedings of the 2004 International Symposium on GPS\/GNSS, Sydney, Australia."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1002\/navi.303","article-title":"From pseudorange overbounding to integrity risk overbounding","volume":"66","author":"Nikiforov","year":"2019","journal-title":"Navigation"},{"key":"ref_12","unstructured":"Shively, C.A., and Braff, R. (2019, June 23). An overbound concept for pseudorange error from the LAAS ground facility. Available online: https:\/\/www.mitrecaasd.org\/library\/tech_docs\/2000\/mp00w0000138.pdf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1017\/S0373463304003029","article-title":"A Method of over Bounding Ground Based Augmentation System (GBAS) Heavy Tail Error Distributions","volume":"58","author":"Braff","year":"2005","journal-title":"J. Navig."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1109\/TAES.2008.4655357","article-title":"Position error bound calculation for GNSS using measurement residuals","volume":"44","author":"Blanch","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_15","unstructured":"Koehler, K. (2001). Characteristic Function. Handbook of Probability, John Wiley & Sons."},{"key":"ref_16","unstructured":"Sayim, I., and Pervan, B. (2005, January 9\u201311). Overbounding non-zero mean Gaussian ranging error for navigation integrity of LAAS. Proceedings of the 2nd International Conference on Recent Advances in Space Technologies, Istanbul, Turkey."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1262","DOI":"10.1109\/TAES.2009.5310297","article-title":"Sigma Overbounding using a Position Domain Method for the Local Area Augmentaion of GPS","volume":"45","author":"Lee","year":"2009","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Schempp, T., and Peck, S. (2010, January 4\u20136). Incremental benefits of dual frequency signals for the Wide Area Augmentation System. Proceedings of the Position Location & Navigation Symposium, Indian Wells, CA, USA.","DOI":"10.1109\/PLANS.2010.5507217"},{"key":"ref_19","unstructured":"Walter, T., Blanch, J., and Enge, P. (2019, June 23). Vertical Protection Level Equations for Dual Frequency SBAS. Available online: http:\/\/web.stanford.edu\/group\/scpnt\/gpslab\/pubs\/papers\/Walter_IONGNSS_2010_VPL_EquationsForL1L5_SBAS_paper.pdf."},{"key":"ref_20","first-page":"528","article-title":"Optimization of a Vertical Protection Level Equation for Dual Frequency SBAS","volume":"23","author":"Blanch","year":"2013","journal-title":"J. Mod. Afr. Stud."},{"key":"ref_21","unstructured":"Celada, J., P\u00e9rez, D., Pericacho, J., Lera, J., Fern\u00e1ndez, M., Barrios, J., Ostolaza, J., and Caro, J. (2015, January 14\u201318). Multi-Constellation, Dual-Frequency SBAS. Proceedings of the 28th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2015), Tampa, FL, USA."},{"key":"ref_22","unstructured":"ICAO (International Civil Aviation Organization) (2019, June 23). Proposed Amendment to Annex 10, Standards and Recommended Practices for GNSS. GNSSP\/3. Available online: https:\/\/www.icao.int\/safety\/acp\/ACPWGF\/ACP-WG-M-9\/WGM09WP22Appendix_AMCP-7%20rep3appA%20NGSS%20SARPs.pdf."},{"key":"ref_23","unstructured":"RTCA (Radio Technical Commission for Aeronautics), Inc (2019, June 23). Minimum Operational performance Standards for Global Positioning System\/Wide Area Augmentation System Airborne Equipment. RTCA DO-229D. Available online: http:\/\/read.pudn.com\/downloads775\/ebook\/3071458\/RTCA%20DO-229D.pdf."},{"key":"ref_24","first-page":"854","article-title":"A behavioral approach to GNSS positioning and DOP determination","volume":"7","author":"Wang","year":"2008","journal-title":"WSEAS Trans. Syst."},{"key":"ref_25","first-page":"350","article-title":"Characteristic Functions","volume":"69","author":"Lukacs","year":"1962","journal-title":"Am. Math. Mon."},{"key":"ref_26","unstructured":"FAA (2019, June 23). Wide Area Augmentation System Performance Analysis Report, Available online: https:\/\/www.nstb.tc.faa.gov\/reports\/waaspan68.pdf."},{"key":"ref_27","unstructured":"Seynat, C., Flament, D., and Brocard, D. (2009, January 22\u201325). EGNOS Status Update. Proceedings of the 22nd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2009), Savannah, GA, USA."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Nandulal, S., Rao, C.B., Indi, C.L., Irulappan, M., Arulmozhi, S., and Soma, P. (2008, January 3\u20135). Evaluation of real-time position accuracy and LNAV\/VNAV service availability of GAGAN SBAS (Wide Area Differential GPS) over Indian region. Proceedings of the Tyrrhenian International Workshop on Digital Communications\u2014Enhanced Surveillance of Aircraft and Vehicles, Capri, Italy.","DOI":"10.1109\/TIWDC.2008.4649025"},{"key":"ref_29","unstructured":"Manabe, H. (2008, January 16\u201319). Status of MSAS: MTSAT Satellite-based Augmentation System. Proceedings of the International Technical Meeting of the Satellite Division of the Institute of Navigation, Savannah, GA, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s10291-015-0496-7","article-title":"Modernization milestone: BeiDou M2-S initial signal analysis","volume":"20","author":"Wei","year":"2016","journal-title":"GPS Solutions"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.asr.2005.05.125","article-title":"The International GPS Service: Celebrating the 10th anniversary and looking to the next decade","volume":"36","author":"Dow","year":"2005","journal-title":"Adv. Space Res."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zinkiewicz, D., Buszke, B., and Houdek, M. (2010, January 8\u201310). SISNeT as a source of EGNOS information: Overview of functionalities and applications. Proceedings of the Satellite Navigation Technologies & European Workshop on Gnss Signals & Signal Processing, Noordwijk, Netherlands.","DOI":"10.1109\/NAVITEC.2010.5708036"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/S1290-0958(99)80041-0","article-title":"EGNOS: project status overview","volume":"1","author":"Benedicto","year":"1999","journal-title":"Air Space Eur."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1017\/S037346330600381X","article-title":"An Efficient Worst User Location Algorithm for the Generation of the Galileo Integrity Flag","volume":"59","author":"Feng","year":"2006","journal-title":"J. Navig."},{"key":"ref_35","first-page":"1","article-title":"Exact Kolmogorov and total variation distances between some familiar discrete distributions","volume":"1","author":"Adell","year":"2006","journal-title":"J. Inequalities Appl."},{"key":"ref_36","first-page":"21","article-title":"Kullback-Leibler distances for quantifying clutter and models","volume":"38","author":"Lanterman","year":"1999","journal-title":"Opt. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1080\/10485252.2017.1285029","article-title":"Cram\u00e9r\u2013von Mises distance: probabilistic interpretation, confidence intervals, and neighbourhood-of-model validation","volume":"29","author":"Baringhaus","year":"2017","journal-title":"J. Nonparametric Stat."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Blanch, J., Walter, T., and Enge, P. (2017, January 25\u201329). A MATLAB Toolset to Determine Strict Gaussian Bounding Distributions of a Sample Distribution. Proceedings of the 30th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2017), Portland, OR, USA.","DOI":"10.33012\/2017.15392"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Wu, Q., Sun, M., Zhou, C., and Zhang, P. (2019). Precise Point Positioning Using Dual-Frequency GNSS Observations on Smartphone. Sensors, 19.","DOI":"10.3390\/s19092189"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Robustelli, U., Baiocchi, V., and Pugliano, G. (2019). Assessment of Dual Frequency GNSS Observations from a Xiaomi Mi 8 Android Smartphone and Positioning Performance Analysis. Electronics, 8.","DOI":"10.3390\/electronics8010091"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Zhu, F., Tao, X., Liu, W., Shi, X., Wang, F., and Zhang, X. (2019). Walker: Continuous and Precise Navigation by Fusing GNSS and MEMS in Smartphone Chipsets for Pedestrians. Remote Sens., 11.","DOI":"10.3390\/rs11020139"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/12\/2826\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:00:54Z","timestamp":1760187654000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/12\/2826"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,24]]},"references-count":41,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["s19122826"],"URL":"https:\/\/doi.org\/10.3390\/s19122826","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,6,24]]}}}