{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:51:28Z","timestamp":1760241088412,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T00:00:00Z","timestamp":1575331200000},"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":["61701047 and 41701536"],"award-info":[{"award-number":["61701047 and 41701536"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of\u00a0Hunan Province","doi-asserted-by":"publisher","award":["2019JJ50639 and 2017JJ3322"],"award-info":[{"award-number":["2019JJ50639 and 2017JJ3322"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014472","name":"Scientific Research Foundation of Hunan Provincial Education Department","doi-asserted-by":"publisher","award":["18A148 and 16B004"],"award-info":[{"award-number":["18A148 and 16B004"]}],"id":[{"id":"10.13039\/100014472","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201800800006"],"award-info":[{"award-number":["201800800006"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Phase difference measurement of sinusoidal signals can be used for phase error calibration of the spaceborne single-pass interferometric synthetic aperture radar (InSAR) system. However, there are currently very few papers devoted to the discussion of phase difference measurement of high-frequency internal calibration signals of the InSAR system, especially the discussion of sampling frequency selection and the corresponding measuring method when the high-frequency signals are sampled under the under-sampling condition. To solve this problem, a phase difference measurement method for high-frequency sinusoidal signals is proposed, and the corresponding sampling frequency selection criteria under the under-sampling condition is determined. First, according to the selection criteria, the appropriate under-sampling frequency was chosen to sample the two sinusoidal signals with the same frequency. Then, the sampled signals were filtered by limited recursive average filtering (LRAF) and coherently accumulated in the cycle of the baseband signal. Third, the filtered and accumulated signals were used to calculate the phase difference of the two sinusoidal signals using the discrete Fourier transform (DFT), digital correlation (DC), and Hilbert transform (HT)-based methods. Lastly, the measurement accuracy of the three methods were compared respectively by different simulation experiments. Theoretical analysis and experiments verified the effectiveness of the proposed method for the phase error calibration of the InSAR system.<\/jats:p>","DOI":"10.3390\/s19235328","type":"journal-article","created":{"date-parts":[[2019,12,4]],"date-time":"2019-12-04T04:30:35Z","timestamp":1575433835000},"page":"5328","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Phase Difference Measurement of Under-Sampled Sinusoidal Signals for InSAR System Phase Error Calibration"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7100-826X","authenticated-orcid":false,"given":"Zhihui","family":"Yuan","sequence":"first","affiliation":[{"name":"Laboratory of Radar Remote Sensing Applications, Changsha University of Science and Technology, Changsha 410114, China"},{"name":"School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410114, China"},{"name":"Roy M. Huffington Department of Earth Sciences, Southern Methodist University, Dallas, TX 75275, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yice","family":"Gu","sequence":"additional","affiliation":[{"name":"Laboratory of Radar Remote Sensing Applications, Changsha University of Science and Technology, Changsha 410114, China"},{"name":"School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410114, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuemin","family":"Xing","sequence":"additional","affiliation":[{"name":"Laboratory of Radar Remote Sensing Applications, Changsha University of Science and Technology, Changsha 410114, China"},{"name":"School of Traffic and Transportation Engineering, Changsha University of Science and Technology, Changsha 410114, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lifu","family":"Chen","sequence":"additional","affiliation":[{"name":"Laboratory of Radar Remote Sensing Applications, Changsha University of Science and Technology, Changsha 410114, China"},{"name":"School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410114, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"115106","DOI":"10.1063\/1.3498897","article-title":"A simple method to measure phase difference between sinusoidal signals","volume":"81","author":"Bertotti","year":"2010","journal-title":"Rev. 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