# A Precise and Stable Space-Based Time System for Navigation in Smart Cities
###### Abstract  
The high-accuracy and high-stability space-based time system is necessary for satellite navigation systems to achieve high quality of service (QoS) on navigation and positioning in smart city applications. This paper proposes a precise and high-stability space-based time system established under the autonomous time scale of navigation satellites. The generation, maintenance, and transfer of high-precision space-based time references are researched. A centralized time comparison method based on the ALGOS algorithm conducts the two-way time comparison of the inter-satellite link. Specifically, using the relative clock difference observations of all links between satellites for a certain period of time, the clock difference, clock speed, and clock drift parameters of \(n-1\) stars in a constellation of \(n\) stars relative to the same reference can be estimated simultaneously. Simulations are conducted on real collected data from the Beidou navigation systems when providing services to smart cities around the world. The simulation results show the  
long-term stability is better than \(1\times 10^{-14}/\mathrm{d}\). The long-term stability of the high-precision passive hydrogen clock is even better than \(5\times 10^{-15}/\mathrm{d}\)[9; 12], which is equivalent to that of the GPS-3 space-borne pulsed light-pumped cesium clock [13]. The performance of new space-borne atomic clocks such as microwave clocks and integrating sphere cold atomic clocks is also improving [14; 15; 16]. An accurate time measurement system is key to determining the target position and providing precise positioning services for the navigation satellite system. The nowadays commonly used space-based time offset measurement methods, including the satellite-ground two-way time comparison method (TWTT) [17] and the orbit determination and time synchronization method (ODTS) [18; 19], still have room for improvement in terms of precision. Therefore, this paper mainly focuses on the research of a space-based time system established under the autonomous time scale of navigation satellites. Specifically, it researches the generation, maintenance, and transfer of high-precision space-based time references. First of all, this paper proposes a scheme establishing a space-based time system for navigation constellations. The establishment follows the inter-satellite link two-way ranging, ranging information exchange, and data pre-processing to obtain the time comparison data of the entire network, and we use the time comparison data to obtain the space-based time with an integrated atomic time algorithm. The space-based integrated atomic time algorithm is realized based on the ALGOS algorithm [20]. For the evaluation of the stability of atomic clocks in orbit, the current satellite-ground time comparison method and the precise orbit determination and time synchronization method are compared, and a centralized time comparison method based on the two-way time comparison of the inter-satellite link is proposed. Using the relative clock difference observations of all links between satellites for a certain period of time, the clock difference, clock speed, and clock drift parameters of \(n-1\) stars in a constellation of \(n\) stars relative to the same reference can be estimated simultaneously. Simulations are conducted on real collected data from the Beidou navigation systems when providing services to smart cities around the world. The accuracy and stability of the proposed space-based time system are evaluated. The results show that the satellite clock offset has higher short-term and long-term prediction accuracy and stability under the autonomous time scale reference. Specifically, the residual error of the hydrogen clock offset prediction is decreased from 0.47 ns to 0.20 ns, and the residual error of the rubidium clock offset prediction is decreased from 0.50 ns to 0.38 ns. Based on the KA measurement data of the 18 MEO + 1 GEO satellites and an anchor station in orbit, an accuracy analysis is carried out.