As a system of ranging and positioning based on time transfer, the timekeeping ability of a navigation satellite constellation is a key factor for accurate positioning and timing services. As the timekeeping performances depend on the frequency stability and predictability of satellite clocks, we propose a method to establish a more stable and predictable space time reference, i.e., inter-satellite link time (ISLT), uniting the satellite clocks through inter-satellite links (ISLs). The joint timekeeping framework is introduced first. Based on the weighted average timescale algorithm, the optimal weights that minimize the increment of the ISLT timescale are determined and allocated to the clock ensemble to improve the frequency stability and predictability in both the long and short term. The time deviations with respect to the system time of nine BeiDou-3 satellites through multi-satellite precise orbit determination (MPOD) are used for joint timekeeping evaluation. According to the Allan deviation, the frequency of the ISLT is more stable than the nine satellite clocks in the short term (averaging time smaller than 7000 s), and its daily stability can reach 6 × 10⁻¹⁵. Meanwhile, the short-term (two hours) and long-term (10 h) prediction accuracy of the ISLT is 0.18 and 1.05 ns, respectively, also better than each satellite clock. Furthermore, the joint timekeeping is verified to be robust against single-satellite malfunction.

Global navigation satellite systems are widely used across the world because of their continuous/all-weather, global coverage, and high precision positioning. But, three-dimensional positioning accuracy, especially in the vertical direction, remains insufficient because of the geometric distribution of satellites. This is especially true for air-borne objects such as unmanned aerial vehicles, civil aviation devices, and missiles. To solve this problem, we adopt a satellite-ground joint positioning system based on a pseudo-satellite (pseudolite). The introduction of ground pseudolites can significantly reduce the vertical dilution of precision and improve positioning accuracy. This method has been proposed in the 1980s. However, we have to ask a question, as long as we add a pseudolite, can the positioning accuracy be improved? The answer is no. Pseudolites can cause time synchronization problems with satellites, and the resulting timing errors of the pseudolite are converted into pseudorange errors, reducing accuracy. Here, we seek to evaluate the impact of the reduced vertical dilution of precision and the increased range errors associated with the introduction of a pseudolite on the ground. We derive a mathematical formula to explain this relationship. We conclude that when the satellite range error and the change in the position dilution of precision associated with a pseudolite are known, we can calculate an approximate limit for the pseudolite timing accuracy to ensure that the use of the pseudolite improves the positioning accuracy. This work should be of great value in guiding engineering practice.

Equipped with inter-satellite links (ISLs), BeiDou-3 satellites are able to operate autonomously in case of ground facility malfunction. To provide reliable positioning, navigation and timing service during autonomous operation, satellites need to maintain a stable time reference. In this letter, we propose a minimal covariance distributed Kalman filter (MCDKF) to realize distributed timekeeping. The proposed algorithm overcomes the problem of network dynamics. Meanwhile, it improves the stability of the on-board time reference by minimizing the variance of the estimate errors at each update step, under the constraint of local observations. Simulation results show that the proposed algorithm reduces the estimation variance and improves the frequency stability compared to other distributed algorithms.