{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T15:31:58Z","timestamp":1789140718074,"version":"build-2803163510"},"reference-count":39,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2025,7,31]],"date-time":"2025-07-31T00:00:00Z","timestamp":1753920000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>High-precision time\u2013frequency systems are essential for low Earth orbit (LEO) navigation satellites to achieve real-time (RT) centimeter-level positioning services. However, subject to stringent size, power, and cost constraints, LEO satellites are typically equipped with oven-controlled crystal oscillators (OCXOs) as the system clock. The inherent long-term stability of OCXOs leads to rapid clock error accumulation, severely degrading positioning accuracy. To simultaneously balance multi-dimensional requirements such as clock bias accuracy, and frequency stability and phase continuity, this study proposes a linear quadratic Gaussian (LQG) frequency precision steering method that integrates a four-dimensional constraint integrated (FDCI) model and hierarchical weight optimization. An improved system error model is refined to quantify the covariance components (\u03a311, \u03a322) of the LQG closed-loop control system. Then, based on the FDCI model that explicitly incorporates quantization noise, frequency adjustment, frequency stability, and clock bias variance, a priority-driven collaborative optimization mechanism systematically determines the weight matrices, ensuring a robust tradeoff among multiple performance criteria. Experiments on OCXO payload products, with micro-step actuation, demonstrate that the proposed method reduces the clock error RMS to 0.14 ns and achieves multi-timescale stability enhancement. The short-to-long-term frequency stability reaches 9.38 \u00d7 10\u221213 at 100 s, and long-term frequency stability is 4.22 \u00d7 10\u221214 at 10,000 s, representing three orders of magnitude enhancement over a free-running OCXO. Compared to conventional PID control (clock bias RMS 0.38 ns) and pure Kalman filtering (stability 6.1 \u00d7 10\u221213 at 10,000 s), the proposed method reduces clock bias by 37% and improves stability by 93%. The impact of quantization noise on short-term stability (1\u201340 s) is contained within 13%. The principal novelty arises from the systematic integration of theoretical constraints and performance optimization within a unified framework. This approach comprehensively enhances the time\u2013frequency performance of OCXOs, providing a low-cost, high-precision timing\u2013frequency reference solution for LEO satellites.<\/jats:p>","DOI":"10.3390\/s25154733","type":"journal-article","created":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T16:41:54Z","timestamp":1754325714000},"page":"4733","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Multi-Constraint Co-Optimization LQG Frequency Steering Method for LEO Satellite Oscillators"],"prefix":"10.3390","volume":"25","author":[{"given":"Dongdong","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"},{"name":"Beijing Research Institute of Telemetry, China Aerospace Science and Technology Corporation, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenhe","family":"Liao","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Liu","sequence":"additional","affiliation":[{"name":"Beijing Research Institute of Telemetry, China Aerospace Science and Technology Corporation, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qianghua","family":"Yu","sequence":"additional","affiliation":[{"name":"Beijing Research Institute of Telemetry, China Aerospace Science and Technology Corporation, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"83971","DOI":"10.1109\/ACCESS.2022.3194050","article-title":"Position, navigation, and timing (PNT) through low earth orbit (LEO) satellites: A survey on current status, challenges, and opportunities","volume":"10","author":"Prol","year":"2022","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1080\/10095020.2021.1917310","article-title":"LEO satellite clock analysis and prediction for positioning applications","volume":"25","author":"Wang","year":"2022","journal-title":"Geo-Spat. 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