{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T18:58:06Z","timestamp":1757617086134,"version":"3.44.0"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T00:00:00Z","timestamp":1726272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T00:00:00Z","timestamp":1726272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Youth Project of Basic Research Program (Free Exploration) of Shanxi Province","award":["202203021222245"],"award-info":[{"award-number":["202203021222245"]}]},{"name":"General Project of Basic Research Program (Free Exploration) of Shanxi Province","award":["20210302124303"],"award-info":[{"award-number":["20210302124303"]}]},{"name":"Shanxi Key Laboratory of Intelligent Optimization Computing and Blockchain Technology"},{"name":"special fund for Science and Technology Innovation Teams of Shanxi Province","award":["202204051002018"],"award-info":[{"award-number":["202204051002018"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12171021"],"award-info":[{"award-number":["12171021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1007\/s11075-024-01935-4","type":"journal-article","created":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T00:01:55Z","timestamp":1726272115000},"page":"1855-1870","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Globally solving the fractional squared least squares model for GPS localization"],"prefix":"10.1007","volume":"99","author":[{"given":"Xiaoli","family":"Cen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Xia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,9,14]]},"reference":[{"issue":"3","key":"1935_CR1","doi-asserted-by":"publisher","first-page":"928","DOI":"10.1109\/7.303764","volume":"30","author":"JS Abel","year":"1994","unstructured":"Abel, J.S.: A variable projection method for additive components with application to GPS. IEEE Trans. Aerosp. Electron. Syst. 30(3), 928\u2013930 (1994)","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"issue":"6","key":"1935_CR2","doi-asserted-by":"publisher","first-page":"952","DOI":"10.1109\/7.104271","volume":"27","author":"JS Abel","year":"1991","unstructured":"Abel, J.S., Chaffee, J.W.: Existence and uniqueness of GPS solutions. IEEE Trans. Aerosp. Electron. Syst. 27(6), 952\u2013956 (1991)","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"1935_CR3","doi-asserted-by":"crossref","unstructured":"Bancroft, S.: An algebraic solution of the GPS equations. IEEE Trans. Aerosp. Electron. Syst. AES-21(1), 56\u201359 (1985)","DOI":"10.1109\/TAES.1985.310538"},{"issue":"1","key":"1935_CR4","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1137\/100809908","volume":"22","author":"A Beck","year":"2012","unstructured":"Beck, A., Pan, D.: On the solution of the GPS localization and circle fitting problems. SIAM J. Optim. 22(1), 108\u2013134 (2012)","journal-title":"SIAM J. Optim."},{"key":"1935_CR5","doi-asserted-by":"crossref","unstructured":"Boutin,\u00a0M., Kemper,\u00a0G.: Global Positioning: the uniqueness question and a new solution method. arXiv:2310.09261 (2023)","DOI":"10.1016\/j.aam.2024.102741"},{"issue":"4","key":"1935_CR6","first-page":"1368","volume":"33","author":"X Cen","year":"2021","unstructured":"Cen, X., Xia, Y.: A new global optimization scheme for quadratic programs with low-rank nonconvexity. Informs J. Comput. 33(4), 1368\u20131383 (2021)","journal-title":"Informs J. Comput."},{"issue":"4","key":"1935_CR7","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1109\/7.328767","volume":"30","author":"J Chaffee","year":"1994","unstructured":"Chaffee, J., Abel, J.: On the exact solutions of pseudorange equations. IEEE Trans. Aerosp. Electron. Syst. 30(4), 1021\u20131030 (1994)","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"issue":"3","key":"1935_CR8","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s10291-022-01237-z","volume":"26","author":"M Hou","year":"2022","unstructured":"Hou, M.: Uniqueness and hyperconic geometry of positioning with biased distance measurements. GPS Solutions. 26(3), 79 (2022)","journal-title":"GPS Solutions."},{"key":"1935_CR9","doi-asserted-by":"crossref","unstructured":"Schmidt, R.O.: A new approach to geometry of range difference location. IEEE Trans. Aerosp. Electron. Syst. AES-8(6), 821\u2013835 (1972)","DOI":"10.1109\/TAES.1972.309614"},{"issue":"3","key":"1935_CR10","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1007\/s11081-019-09470-1","volume":"21","author":"XH Wang","year":"2020","unstructured":"Wang, X.H., Zhang, H., Xia, Y.: GPS localization problem: a new model and its global optimization. Optim. Eng. 21(3), 851\u2013866 (2020)","journal-title":"Optim. Eng."},{"issue":"1","key":"1935_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40305-019-00286-5","volume":"8","author":"Y Xia","year":"2020","unstructured":"Xia, Y.: A survey of hidden convex optimization. J. Oper. Res. Soc. China. 8(1), 1\u201328 (2020)","journal-title":"J. Oper. Res. Soc. China."},{"issue":"2","key":"1935_CR12","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/s10898-018-0719-x","volume":"73","author":"Y Xia","year":"2019","unstructured":"Xia, Y., Wang, L.F., Yang, M.J.: A fast algorithm for globally solving Tikhonov regularized total least squares problem. J. Glob. Optim. 73(2), 311\u2013330 (2019)","journal-title":"J. Glob. Optim."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01935-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-024-01935-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01935-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T22:22:35Z","timestamp":1757110955000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-024-01935-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,14]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["1935"],"URL":"https:\/\/doi.org\/10.1007\/s11075-024-01935-4","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2024,9,14]]},"assertion":[{"value":"23 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 September 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}]}}