{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:18:09Z","timestamp":1760145489150,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T00:00:00Z","timestamp":1722297600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A high-precision time reference is fundamental to the positioning, navigation, and timing (PNT) of global navigation satellite systems (GNSS). The precision of clock steering determines the accuracy of practical applications that rely on the time\u2013frequency reference. With the invention of direct digital synthesizer (DDS) technology, digital clock steering (DCS) has gradually become a mainstream technology. However, the key factor limiting DCS accuracy is the system quantization noise, which leads to a low frequency and phase adjustment accuracy. Here we propose a DCS method based on \u03a3-\u0394 modulation to address the issue of low resolution of DAC through shaping the quantization noise. A simulated GNSS time\u2013frequency reference system experimental platform is constructed to validate the effectiveness of the proposed method. The experimental results demonstrate that this method achieves a phase adjustment accuracy of 0.48 ps and a frequency adjustment accuracy better than 0.48 pHz, which is two orders of magnitude higher than that of existing GNSS time\u2013frequency reference systems. Thus, the proposed method offers a significant improvement in time\u2013frequency reference systems, leading to better performance, reliability, and accuracy in a wide range of practical applications.<\/jats:p>","DOI":"10.3390\/rs16152794","type":"journal-article","created":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T15:25:23Z","timestamp":1722353123000},"page":"2794","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["High-Precision Digital Clock Steering Method Based on Discrete \u03a3-\u0394 Modulation for GNSS"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-3085-1697","authenticated-orcid":false,"given":"Mingkai","family":"Liu","sequence":"first","affiliation":[{"name":"College of Intelligent Science and Technology, National University of Defense Technology (NUDT), Changsha 410073, China"}]},{"given":"Zhijun","family":"Meng","sequence":"additional","affiliation":[{"name":"College of Intelligent Science and Technology, National University of Defense Technology (NUDT), Changsha 410073, China"}]},{"given":"Enqi","family":"Yan","sequence":"additional","affiliation":[{"name":"College of Intelligent Science and Technology, National University of Defense Technology (NUDT), Changsha 410073, China"}]},{"given":"Suyang","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Intelligent Science and Technology, National University of Defense Technology (NUDT), Changsha 410073, China"}]},{"given":"Yinhong","family":"Lv","sequence":"additional","affiliation":[{"name":"College of Intelligent Science and Technology, National University of Defense Technology (NUDT), Changsha 410073, China"}]},{"given":"Xiye","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Intelligent Science and Technology, National University of Defense Technology (NUDT), Changsha 410073, China"}]},{"given":"Jun","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Intelligent Science and Technology, National University of Defense Technology (NUDT), Changsha 410073, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1186\/s43020-020-00012-0","article-title":"Precise time scales and navigation systems: Mutual benefits of timekeeping and positioning","volume":"1","author":"Tavella","year":"2020","journal-title":"Satell. 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