{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:46:22Z","timestamp":1761597982992,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,9]],"date-time":"2018-09-09T00:00:00Z","timestamp":1536451200000},"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":["41704002"],"award-info":[{"award-number":["41704002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"China Postdoc Science Foundation","award":["2017M620337"],"award-info":[{"award-number":["2017M620337"]}]},{"name":"the Fundamental Research Funds for the Central Universities","award":["N\/A"],"award-info":[{"award-number":["N\/A"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In Global navigation satellite system (GNSS) data processing, integer ambiguity acceptance test is considered as a challenging problem. A number of ambiguity acceptance tests have been proposed from different perspective and then unified into the integer aperture estimation (IA) framework. Among all the IA estimators, the optimal integer aperture (OIA) achieves the highest success rate with the fixed failure rate tolerance. However, the OIA is of less practical appealing due to its high computation complexity. On the other hand, the popular discrimination tests employ only two integer candidates, which are the essential reason for their sub-optimality. In this study, a generalized difference test (GDT) is proposed to exploit the benefit of including three or more integer candidates to improve their performance from theoretical perspective. The simulation results indicate that the third best integer candidates contribute to more than 70% success rate improvement for integer bootstrapping success rate higher than 0.8 case. Therefore, the GDT with three integer candidates (GDT3) achieves a good trade-off between the performance and computation burden. The threshold function is also applied for rapid determination of the fixed failure rate (FF)-threshold for GDT3. The performance improvement of GDT3 is validated with real GNSS data set. The numerical results indicate that GDT3 achieves higher empirical success rate while the empirical failure rate remains comparable. In a 20 km baseline test, the success rate GDT3 increase 7% with almost the same empirical failure rate.<\/jats:p>","DOI":"10.3390\/s18093018","type":"journal-article","created":{"date-parts":[[2018,9,10]],"date-time":"2018-09-10T10:28:57Z","timestamp":1536575337000},"page":"3018","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Improving GNSS Ambiguity Acceptance Test Performance with the Generalized Difference Test Approach"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1887-6222","authenticated-orcid":false,"given":"Lei","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6683-2342","authenticated-orcid":false,"given":"Ruizhi","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"},{"name":"Collaborative Innovation Center for Geospatial Technology, Wuhan 430079, China"}]},{"given":"Lili","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6548-3347","authenticated-orcid":false,"given":"Yanming","family":"Feng","sequence":"additional","affiliation":[{"name":"Science and Engineer Faculty, Queensland University of Technology, Brisbane QLD 4000, Australia"}]},{"given":"Yuanjin","family":"Pan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0722-028X","authenticated-orcid":false,"given":"Ming","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"},{"name":"Collaborative Innovation Center for Geospatial Technology, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7257-6186","authenticated-orcid":false,"given":"Peng","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,9]]},"reference":[{"unstructured":"Teunissen, P.J.G. (1993, January 8\u201313). Least-Square Estimation of the Integer GPS Ambiguities. Proceedings of the International Association of Geodesy, Beijing, China.","key":"ref_1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/s00190-014-0780-2","article-title":"A new ambiguity acceptance test threshold determination method with controllable failure rate","volume":"89","author":"Wang","year":"2015","journal-title":"J. Geod."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF00863419","article-title":"The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation","volume":"70","author":"Teunissen","year":"1995","journal-title":"J. Geod."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10291-005-0148-4","article-title":"On the probability density function of the GNSS ambiguity residuals","volume":"10","author":"Verhagen","year":"2006","journal-title":"GPS Solutions"},{"doi-asserted-by":"crossref","unstructured":"Shen, L., Guo, J., and Wang, L. (2018). A self-organizing spatial clustering approach to support large-scale network RTK system. Sensors, 18.","key":"ref_5","DOI":"10.3390\/s18061855"},{"key":"ref_6","first-page":"49","article-title":"On the generalised distance in statistics","volume":"2","author":"Mahalanobis","year":"1936","journal-title":"Proc. National Inst. Sci. India"},{"key":"ref_7","first-page":"79","article-title":"Integer aperture GNSS ambiguity resolution","volume":"38","author":"Teunissen","year":"2003","journal-title":"Artif. Satell."},{"doi-asserted-by":"crossref","unstructured":"Verhagen, S. (2005). The GNSS Integer Ambiguities: Estimation and Validation. [Ph.D. Thesis, Delft Institute of Earth Observation and Space Systems, Delft University of Technology].","key":"ref_8","DOI":"10.54419\/d0mifg"},{"key":"ref_9","first-page":"89","article-title":"A carrier phase ambiguity estimator with easy-to-evaluate fail-rate","volume":"38","author":"Teunissen","year":"2003","journal-title":"Artif. Satell."},{"unstructured":"Wang, L. (2015). Reliability Control of GNSS Carrier-Phase Integer Ambiguity Resolution. [Ph.D. Thesis, School of Electrical Engineering and Computer Science, Queensland University of Technology].","key":"ref_10"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1179\/003962609X390058","article-title":"The GNSS ambiguity ratio-test revisited: A better way of using it","volume":"41","author":"Teunissen","year":"2009","journal-title":"Surv. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1007\/s10291-012-0299-z","article-title":"The ratio test for future GNSS ambiguity resolution","volume":"17","author":"Verhagen","year":"2013","journal-title":"GPS Solutions"},{"unstructured":"Wang, L., Verhagen, S., and Feng, Y. (2014, January 8\u201312). A Novel Ambiguity Acceptance Test. Threshold Determination Method with Controllable Failure Rate. Proceedings of the ION GNSS+ 2014, Tampa, FL, USA.","key":"ref_13"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1007\/s10291-016-0550-0","article-title":"Reliability control of single-epoch RTK ambiguity resolution","volume":"21","author":"Wang","year":"2016","journal-title":"GPS Solutions"},{"unstructured":"Landau, H. (1992, January 16\u201318). On-the-Fly Ambiguity Resolution for Precise Differential Positioning. Proceedings of the ION GPS 1992, Albuquerque, NM, USA.","key":"ref_15"},{"key":"ref_16","first-page":"17","article-title":"On the discernibility of the ambiguity sets during on-the-fly ambiguity resolution","volume":"61","author":"Abidin","year":"1994","journal-title":"Aust. J. Geod. Photogramm. Surv."},{"doi-asserted-by":"crossref","unstructured":"Euler, H.J., and Schaffrin, B. (1991, January 10\u201313). On a Measure for the Discernibility Between Different Ambiguity Solutions in the Static-Kinematic GPS-Mode. Proceedings of the International Association of Geodesy Symposia, New York, NY, USA.","key":"ref_17","DOI":"10.1007\/978-1-4612-3102-8_26"},{"unstructured":"Tiberius, C.C.J.M., and De Jonge, P. (1995, January 24\u201328). Fast Positioning Using the LAMBDA Method. Proceedings of the International Symposium on Differential Satellite Navigation Systems, Bergen, Norway.","key":"ref_18"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s001900050103","article-title":"Quality-control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning","volume":"71","author":"Han","year":"1997","journal-title":"J. Geod."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1007\/s001900050204","article-title":"A discrimination test procedure for ambiguity resolution on-the-fly","volume":"72","author":"Wang","year":"1998","journal-title":"J. Geod."},{"key":"ref_21","first-page":"119","article-title":"Some Remarks on GPS Ambiguity Resolution","volume":"32","author":"Teunissen","year":"1998","journal-title":"Artif. Satell."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s00190-005-0481-y","article-title":"Integer aperture bootstrapping: A new GNSS ambiguity estimator with controllable fail-rate","volume":"79","author":"Teunissen","year":"2005","journal-title":"J. Geod."},{"key":"ref_23","first-page":"219","article-title":"Integer aperture least-squares estimation","volume":"40","author":"Teunissen","year":"2005","journal-title":"Artif. Satell."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s00190-004-0393-2","article-title":"Penalized GNSS Ambiguity Resolution","volume":"78","author":"Teunissen","year":"2004","journal-title":"J. Geod."},{"key":"ref_25","first-page":"219","article-title":"GNSS ambiguity resolution with optimally controlled failure-rate","volume":"40","author":"Teunissen","year":"2005","journal-title":"Artif. Satell."},{"doi-asserted-by":"crossref","unstructured":"Wang, L., Verhagen, S., and Feng, Y. (2014, January 21\u201323). Ambiguity Acceptance Testing: A Comparison of the Ratio Test. And Difference Test. Proceedings of the China Satellite Navigation Conference (CSNC) 2014, Nanjing, China.","key":"ref_26","DOI":"10.1007\/978-3-642-54743-0_26"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1007\/s10291-015-0465-1","article-title":"Integer aperture estimation comparison between ratio test and difference test: From theory to application","volume":"20","author":"Li","year":"2016","journal-title":"GPS Solutions"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1098\/rsta.1933.0009","article-title":"On the problem of the most efficient tests of statistical hypotheses","volume":"231","author":"Neyman","year":"1933","journal-title":"Philos. Trans. R. Soc. London"},{"doi-asserted-by":"crossref","unstructured":"Wang, L., and Feng, Y. (2013, January 15\u201317). Fixed Failure Rate Ambiguity Validation Methods for GPS and COMPASS. Proceedings of the China Satellite Navigation Conference (CSNC) 2013, Wuhan, China.","key":"ref_29","DOI":"10.1007\/978-3-642-37404-3_34"},{"doi-asserted-by":"crossref","unstructured":"De Jonge, P.J., and Tiberius, C.C.J.M. (1996). The LAMBDA Method for Integer Ambiguity Estimation: Implementation Aspects, Delft University of Technology.","key":"ref_30","DOI":"10.1007\/978-3-642-80133-4_45"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1007\/s00190-015-0826-0","article-title":"GNSS integer ambiguity validation based on posterior probability","volume":"89","author":"Wu","year":"2015","journal-title":"J. Geod."},{"key":"ref_32","first-page":"41","article-title":"An approach to validate the resolved ambiguities in GPS rapid positioning","volume":"22","author":"Chen","year":"1997","journal-title":"J. Wuhan Tech. Univ. Surv. Mapping"},{"doi-asserted-by":"crossref","unstructured":"Hou, Y., Verhagen, S., and Wu, J. (2016). An efficient implementation of fixed failure-rate ratio test for GNSS ambiguity resolution. Sensors, 16.","key":"ref_33","DOI":"10.3390\/s16070945"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s00190-010-0418-y","article-title":"Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates","volume":"85","author":"Feng","year":"2011","journal-title":"J. Geod."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s001900050269","article-title":"An optimality property of the integer least-squares estimator","volume":"73","author":"Teunissen","year":"1999","journal-title":"J. Geod."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1017\/S0373463316000047","article-title":"Impact of decorrelation on success rate bounds of ambiguity estimation","volume":"69","author":"Wang","year":"2016","journal-title":"J. Navig."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/BF03655480","article-title":"The invertible GPS ambiguity transformations","volume":"20","author":"Teunissen","year":"1995","journal-title":"Manuscr. Geod."},{"unstructured":"Gavin, H. (2018, July 10). The Levenberg-Marquardt Method for Nonlinear Least Squares Curve-Fitting Problems. Available online: http:\/\/een.iust.ac.ir\/profs\/Farrokhi\/Neural%20Networks\/Levenberg-Marquardt\/lm.pdf.","key":"ref_38"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/0111030","article-title":"An algorithm for least-squares estimation of nonlinear parameters","volume":"11","author":"Marquardt","year":"1963","journal-title":"J. Soc. Ind. Appl. Math."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/9\/3018\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:19:37Z","timestamp":1760195977000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/9\/3018"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,9]]},"references-count":39,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2018,9]]}},"alternative-id":["s18093018"],"URL":"https:\/\/doi.org\/10.3390\/s18093018","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,9,9]]}}}