# A Method for Autonomous Generation of High-Precision Time Scales for Navigation Constellations
## 1 Introduction  
The basic principle of the global navigation satellite system (GNSS) is timing and ranging. In order to ensure that GNSS provides users with high-precision navigation positioning and timing services, it is necessary to establish and maintain a high-precision time reference [1]. At present, the time reference of mainstream GNSS is established and maintained by the atomic clock group of the ground master station, such as GPS System Time (GPST) and Beidou System Time (BDT). The satellite-borne atomic clocks on the navigation satellites obtain the satellite-ground clock difference through the satellite-ground two-way time comparison technology, and achieves the satellite-ground time synchronization [2]. With the development of the autonomous operation technology of the navigation constellation, in order to maintain the continuity of the time-frequency signal of the GNSS and reduce the dependence on the ground station, the navigation constellation needs to independently establish and maintain a high-precision time scale as the time-frequency reference of each single satellite [3]. The time difference of an atomic clock can be composed of a deterministic trend term and a random term error:(\(x(t)=x_{0}+y_{0}t+\frac{Dt^{2}}{2}+\varepsilon(t)\)), where the deterministic trend term includes the initial time error \(x_{0}\), the initial frequency deviation is \(y_{0}\), and the linear frequency drift \(D\) is caused by aging and temperature changes. \(\varepsilon(t)\) is the random frequency deviation of different types of noise such as stationary noise and non-stationary noise, mainly including: WPM, FPM, WFM, FFM and RWFM noise. Since the atomic clock is composed of various electronic components, the five noise levels of each clock are not exactly the same, and the frequency stability and frequency accuracy are also different. Therefore, the random noise of the output time scale can be reduced by the time scale algorithm, and the frequency stability can be improved. With the development of inter-satellite link technology, the clock difference accuracy obtained by two-way measurement of the inter-satellite link is less than 0.3 ns [2; 4]. Therefore, the satellite clocks can be formed into a large clock group through the inter-satellite link, and the time scale algorithm can be used to obtain a more stable time scale [5]. Currently, commonly used time scale algorithms include weighted average algorithm (ALGOS algorithm and AT1 algorithm) [6], Kalman filter algorithm [7], Kalman plus weights (KPW) algorithm [8; 9], wavelet decomposition algorithm, etc. The core idea of the ALGOS algorithm and the AT1 algorithm is to assign a weight to each atomic clock, thereby increasing the stability of the time scale. However, without eliminating or suppressing the noise of the atomic clock, it cannot further improve the accuracy and reliability of the atomic time scale. For the Kalman filter time scale algorithm, it can model a variety of noises and suppress these noises at the same time. Its obtained time scale is significantly better than the ALGOS algorithm that can only mainly suppress one kind of noise, but its incompleteness will cause the error of the estimation result to increase with time, and the accuracy of the time scale will decrease. The KPW algorithm proposed by [PERSON] assumes that only white frequency noise (WFM) remains in the clock data after Kalman frequency correction, and adjusts the weight according to the strength of WFM, thus it can take into account both short-term and long-term stability of the time scale. Since different spaceborne atomic clocks have different time-frequency characteristics, the scheme in this paper is to divide multiple rubidium atomic clocks and cesium atomic clocks into two clock groups according to type, and use the genetic algorithm [10] to improve the KPW time scale algorithm. The two clock groups use this time scale algorithm to generate two timescales.