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 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 (Σ₁₁, Σ₂₂) 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^-13 at 100 s, and long-term frequency stability is 4.22 × 10^-14 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^-13 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.