A Multi-Constraint Co-Optimization LQG Frequency Steering Method for LEO Satellite Oscillators
High-precision time–frequency 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 osc...
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2025-07-01
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| author | Dongdong Wang Wenhe Liao Bin Liu Qianghua Yu |
| author_facet | Dongdong Wang Wenhe Liao Bin Liu Qianghua Yu |
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| description | High-precision time–frequency 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 (Σ<sub>11</sub>, Σ<sub>22</sub>) 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 × 10<sup>−13</sup> at 100 s, and long-term frequency stability is 4.22 × 10<sup>−14</sup> 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 × 10<sup>−13</sup> 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 (1–40 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–frequency performance of OCXOs, providing a low-cost, high-precision timing–frequency reference solution for LEO satellites. |
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| institution | Kabale University |
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| spelling | doaj-art-077f08297fc546058cd4accfeb4881fc2025-08-20T03:36:34ZengMDPI AGSensors1424-82202025-07-012515473310.3390/s25154733A Multi-Constraint Co-Optimization LQG Frequency Steering Method for LEO Satellite OscillatorsDongdong Wang0Wenhe Liao1Bin Liu2Qianghua Yu3School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, ChinaSchool of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, ChinaBeijing Research Institute of Telemetry, China Aerospace Science and Technology Corporation, Beijing 100094, ChinaBeijing Research Institute of Telemetry, China Aerospace Science and Technology Corporation, Beijing 100094, ChinaHigh-precision time–frequency 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 (Σ<sub>11</sub>, Σ<sub>22</sub>) 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 × 10<sup>−13</sup> at 100 s, and long-term frequency stability is 4.22 × 10<sup>−14</sup> 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 × 10<sup>−13</sup> 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 (1–40 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–frequency performance of OCXOs, providing a low-cost, high-precision timing–frequency reference solution for LEO satellites.https://www.mdpi.com/1424-8220/25/15/4733low Earth orbit (LEO) satellitesoven-controlled crystal oscillators (OCXOs)multi-constraint co-optimizationLQG controlfrequency stability |
| spellingShingle | Dongdong Wang Wenhe Liao Bin Liu Qianghua Yu A Multi-Constraint Co-Optimization LQG Frequency Steering Method for LEO Satellite Oscillators Sensors low Earth orbit (LEO) satellites oven-controlled crystal oscillators (OCXOs) multi-constraint co-optimization LQG control frequency stability |
| title | A Multi-Constraint Co-Optimization LQG Frequency Steering Method for LEO Satellite Oscillators |
| title_full | A Multi-Constraint Co-Optimization LQG Frequency Steering Method for LEO Satellite Oscillators |
| title_fullStr | A Multi-Constraint Co-Optimization LQG Frequency Steering Method for LEO Satellite Oscillators |
| title_full_unstemmed | A Multi-Constraint Co-Optimization LQG Frequency Steering Method for LEO Satellite Oscillators |
| title_short | A Multi-Constraint Co-Optimization LQG Frequency Steering Method for LEO Satellite Oscillators |
| title_sort | multi constraint co optimization lqg frequency steering method for leo satellite oscillators |
| topic | low Earth orbit (LEO) satellites oven-controlled crystal oscillators (OCXOs) multi-constraint co-optimization LQG control frequency stability |
| url | https://www.mdpi.com/1424-8220/25/15/4733 |
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