{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:42:48Z","timestamp":1760236968104,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,6]],"date-time":"2020-02-06T00:00:00Z","timestamp":1580947200000},"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":["6163308"],"award-info":[{"award-number":["6163308"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The solution of carrier phase ambiguity is essential for precise global navigation satellite system (GNSS) positioning. Methods of searching in the coordinate domain show their advantage over the methods based on ambiguity fixing, for example, immune to cycle slips, far fewer epochs taken for obtaining the precise solution. However, there are still some drawbacks via using the Ambiguity Function Method (AFM), such as low computation efficiency and the existence of a false global optimum. The false global optimum is a situation where the Least Square (LS) criterion achieves minimum in another place than the point of the actual position, which restricts the application of this method to single-frequency receivers. The numerical search approach derived in this paper is based on the Modified Ambiguity Function Approach (MAFA). It focuses on eliminating the false optimum solution and reducing the computation load by utilizing single-frequency receivers without solving the ambiguity fixing problem. An improved segmented simulated annealing method is used to decrease the computation load while the Kernel Density Estimator (KDE) method is used to filter out the false optimum candidates. Static experiments were carried out to evaluate the performance of the new approach. It is shown that a precise result can be obtained by handling two epochs of data with z coordinate fixed to the referenced value. Meanwhile, the new approach can achieve a millimeter level of position accuracy after dealing with nineteen epochs of observations data when searching in \r\n          \r\n            \r\n              \r\n                x\r\n                ,\r\n                y\r\n                ,\r\n                z\r\n              \r\n            \r\n          \r\n         domain. The new approach shows its robustness even if the search region is broad, and the prior position is several meters away from the referenced value.<\/jats:p>","DOI":"10.3390\/s20030856","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T03:13:27Z","timestamp":1581045207000},"page":"856","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An Improved Ambiguity-Free Method for Precise GNSS Positioning with Utilizing Single Frequency Receivers"],"prefix":"10.3390","volume":"20","author":[{"given":"Wenhao","family":"Yang","sequence":"first","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yue","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fanming","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s10291-013-0339-3","article-title":"Performance assessment of single- and dual-frequency BeiDou\/GPS single-epoch kinematic positioning","volume":"18","author":"He","year":"2014","journal-title":"GPS Solut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/s10291-014-0392-6","article-title":"The mixed-receiver BeiDou inter-satellite-type bias and its impact on RTK positioning","volume":"19","author":"Nadarajah","year":"2015","journal-title":"GPS Solut."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/s00190-015-0802-8","article-title":"Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo","volume":"89","author":"Li","year":"2015","journal-title":"J. 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