# A Method for Autonomous Generation of High-Precision Time Scales for Navigation Constellations
## 1 Introduction
Then, the improved time-frequency steering algorithm is used to obtain a comprehensive time scale that takes into account the time-frequency characteristics of the two types of atomic clocks. In the steering experiment, the deterministic trend items, \(x_{0}\), \(y_{0}\), \(D\), are removed first. The random noise of the atomic clock (including: five kinds of noise) is controlled, and the purpose is to combine the steering reference in the frequency domain with the excellent near-end noise level and the controlled frequency. Target good far-end noise levels. In terms of time domain, it is mainly reflected in the advantages of both frequency stability and long-term stability. Short-term stability and long-term stability correspond to the five types of noise corresponding to different sampling intervals. The time-frequency steering algorithm includes open-loop control and closed-loop control. The general open-loop control adopts the clock difference prediction method of the Kalman filter, and corrects the model prediction parameters to obtain the adjustment value. It does not depend on the measurement, but it can only improve the time synchronization accuracy. In the closed-loop control algorithm, the early zero-return phase modulation method will cause phase jumps, resulting in discontinuous time error data and deteriorating signal stability. The early ping-pong frequency modulation method based on two-state control used a specific frequency offset to make the time error signal oscillate between two thresholds to achieve phase continuity, but the result was not smooth [11]. The classic position-type PID closed-loop driving algorithm has a simple control structure, but the three parameters (proportional, integral and differential) that affect the degree of steering adjustment need to be adjusted manually and rely more on empirical values [12; 13; 14; 15]. The traditional optimal quadratic Gaussian control algorithm (LQG) adjusts WQ and WR parameters through numerical simulation, and iteratively calculates the optimal time-frequency steer value, which hashigher reliability [16; 17], but its parameter selection process is more complicated. The Kalman filter combined with the delay structure can be equivalent to the closed-loop control method of the digital phase-locked loop (DPLL), which expands the application mode of the traditional DPLL [18; 19]. The authors of references [20; 21] selected the observable Kalman filter system, and verified the stability of the equivalent DPLL control system with a delay structure. In references [21; 22], the standard second-order type 2 DPLL and the third-order type 3 DPLL are equivalently constructed. Because the adjustment parameters in references [21; 23] need to be adjusted many times, there are precision limitations and self-adaptive approximate selection. Therefore, there is still room for optimization and improvement in the parameter selection of the algorithm. In this paper, the genetic optimization algorithm is used to realize the adaptive adjustment of parameters, and to promote the system to achieve the desired optimal steering goal with higher parameter selection accuracy and reliability. In the second section, this paper will introduce the overall architecture of the navigation constellation high-precision time scale generation scheme. In the third section, the existing time scale algorithm is improved to obtain a time scale with higher stability than a single clock. In the fourth section, an improved time-frequency steering algorithm is introduced to generate a comprehensive time scale that takes into account both short-term and long-term stability. In the fifth section, the simulation results of the analytical scheme are summarized.