{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T11:58:57Z","timestamp":1782993537325,"version":"3.54.5"},"reference-count":40,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,9,24]],"date-time":"2022-09-24T00:00:00Z","timestamp":1663977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Project","award":["2020YFB1807602"],"award-info":[{"award-number":["2020YFB1807602"]}]},{"name":"National Key Research and Development Project","award":["2020YFB1807604"],"award-info":[{"award-number":["2020YFB1807604"]}]},{"name":"National Key Research and Development Project","award":["2020Z013"],"award-info":[{"award-number":["2020Z013"]}]},{"name":"National Key Research and Development Project","award":["2020M681585"],"award-info":[{"award-number":["2020M681585"]}]},{"DOI":"10.13039\/501100010242","name":"Jiangsu Planned Projects for Postdoctoral Research Funds","doi-asserted-by":"publisher","award":["2020YFB1807602"],"award-info":[{"award-number":["2020YFB1807602"]}],"id":[{"id":"10.13039\/501100010242","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010242","name":"Jiangsu Planned Projects for Postdoctoral Research Funds","doi-asserted-by":"publisher","award":["2020YFB1807604"],"award-info":[{"award-number":["2020YFB1807604"]}],"id":[{"id":"10.13039\/501100010242","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010242","name":"Jiangsu Planned Projects for Postdoctoral Research Funds","doi-asserted-by":"publisher","award":["2020Z013"],"award-info":[{"award-number":["2020Z013"]}],"id":[{"id":"10.13039\/501100010242","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010242","name":"Jiangsu Planned Projects for Postdoctoral Research Funds","doi-asserted-by":"publisher","award":["2020M681585"],"award-info":[{"award-number":["2020M681585"]}],"id":[{"id":"10.13039\/501100010242","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2020YFB1807602"],"award-info":[{"award-number":["2020YFB1807602"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2020YFB1807604"],"award-info":[{"award-number":["2020YFB1807604"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2020Z013"],"award-info":[{"award-number":["2020Z013"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2020M681585"],"award-info":[{"award-number":["2020M681585"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Without the estimation of the intermediate parameters, the direct position determination (DPD) method can achieve higher localization accuracy than conventional two-step methods. However, multipath environments are still a key problem, and complex high-dimensional matrix operations are required in most DPD methods. In this paper, a time-difference-of-arrival-based (TDOA-based) DPD method is proposed based on the subspace orthogonality in the cross-spectra between the different sensors. Firstly, the cross-spectrum between the segmented received signal and reference signal is calculated and eigenvalue decomposition is performed to obtain the subspaces. Then, the cost functions are constructed by using the orthogonality of subspace. Finally, the location of the radiation source is obtained by searching the superposition of these cost functions in the target area. Compared with other DPD methods, our proposed DPD method leads to better localization accuracy with less complexity. The superiority of this method is verified by both simulated and real measured data when compared to other TDOA and DPD algorithms.<\/jats:p>","DOI":"10.3390\/s22197245","type":"journal-article","created":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T03:34:17Z","timestamp":1664163257000},"page":"7245","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Direct Position Determination Method Based on Subspace Orthogonality in Cross-Spectra under Multipath Environments"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0721-5787","authenticated-orcid":false,"given":"Kehui","family":"Zhu","sequence":"first","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-2919-7423","authenticated-orcid":false,"given":"Hang","family":"Jiang","sequence":"additional","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuchong","family":"Huo","sequence":"additional","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qin","family":"Yu","sequence":"additional","affiliation":[{"name":"Hai Hua Electronic Enterprise (China) Corporation, Guangzhou 510670, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianfeng","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electronic Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jie, Z., Dong, Z., Huang, X., and Shi, X. 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