Linear quadratic Gaussian-based clock steering system for GNSS real-time precise point positioning timing receiver

Clock steering is crucial for Global Navigation Satellite System (GNSS) timing receivers to provide high-performance time and frequency. However, the lack of theoretical analysis and design methods makes it difficult to apply an existing controller to the emerging real-time precise point positioning (RT-PPP) timing receiver. In this research, a Linear Quadratic Gaussian (LQG)-based clock steering method for the RT-PPP timing receiver is proposed with a detailed design process. We theoretically derive the transfer function of the system first. Then, the relationship between the system bandwidth and the control parameter is present. As for the parametric design, based on the analysis of the free-running oscillator instability, the RT satellite clock reference variation, and the GNSS observation noise, the parameters of the Kalman estimator are set, and the optimal bandwidth of the system is estimated. Under the constraint of the bandwidth and the damping ratio, the control parameters of the LQG controller are determined finally. Simulated results show that the parametric design method is feasible for different noise conditions. And finally, we evaluate the performance of the proposed clock steering method on a Rubidium clock RT-PPP timing receiver. Experimental results show that the timing receiver realizes the optimal combination of the short-term stability of the Rubidium clock and the long-term stability of the RT-PPP reference expectedly. The precision of the output one pulse per second (1PPS) is 0.21 ns over 24 h. And the frequency stabilities can reach 3.59E-12@1s and 2.43E-14@10000s, which is more stable than a high-quality Cesium clock.