# A Method for Autonomous Generation of High-Precision Time Scales for Navigation Constellations
## 5 Simulation Results and Analysis
### Experimental Analysis of Time-Frequency Steering Algorithm
At this time, the time-frequency steer value determined by the parameter group will expand the influence of the steered frequency standard TA(Rb), so that the signal output after being steered is biased towards the improvement of short-term stability performance, which unbalances the performance of long-term stability and increase the time control error. On the contrary, the change of the corresponding result is the opposite. Let TA(Cs) be used as the steering reference, TA(Rb) be used as the frequency standard to be steered; use the genetic algorithm to optimize the selection of steering parameters, and the time scale output after steering is TA(Streed). Figure 13 shows the phase differences of the three time scales. When the steering enters a stable state, the phase of TA(Streed) is synchronized with the steering reference TA(Cs), and the error is within 0.5 ns. Figure 14 shows the stability of the three time scales. It can be seen that the frequency stability of TA(Streed) is consistent with TA(Rb) when the sampling interval is less than \(1\times 10^{4}\) s, and is consistent with TA(Cs) when it is greater than \(2\times 10^{5}\) s. Therefore, the time-frequency signal output by the improved time-frequency steering algorithm in this paper can better comprehensively control the frequency stability advantages of the reference and the steered frequency standard. Figure 12: The steering error under the selection of different parameters. Figure 13: Phase difference of TA(Cs), TA(Rb), TA(Steered). Using the traditional KPW time scale algorithm, 24 clocks are formed into a clock group to output the time scale TA(KPW), and the time scale output by the method proposed in this paper is TA(Steered). Their frequency stability comparison is shown in Figure 15:  
It can be seen from Figure 15 that the frequency stability of TA(Steered) in this paper is better overall. When the sampling intervals are 300 s, 1 day, and 1 \(\times\) 10\({}^{-7}\) s, its frequency stability is 5.73 \(\times\) 10\({}^{-14}\), 9.17 \(\times\) 10\({}^{-15}\), 4.93 \(\times\) 10\({}^{-16}\). Compared with the frequency stability of TA(KPW), when the sampling interval is 300 s, the frequency stability is improved by 71%; when the sampling interval is 1 day, the frequency stability of the two is equivalent; when the sampling interval is 1 \(\times\) 10\({}^{6}\) s, the frequency stability is increased by 94%. Compared with the traditional KPW time-scale algorithm, the method proposed in this paper has significantly improved the short-term and long-term stability of the time-frequency signal output. The frequency stability comparison between TA(Steered) and 24 single clocks is shown in Figure 16 and Table 2:  
Figure 14: The frequency stability of TA(Cs), TA(Rb), TA(Steered). Figure 10:0 The frequency stability of TA(Steered) and TA(KPW). From Figure 16 and Table 2, it can be seen that TA(Steered) has a higher overall advantage in stability than a single atomic clock in each period. When the sampling interval is 300 s, it can reach the order of 5.73 \(\times\)\(10^{-14}\), the stability of 1000 s can reach 2.79 \(\times\)\(10^{-14}\), the stability of 1 \(\times\)\(10^{5}\) s can reach 8.38 \(\times\)\(10^{-15}\), and the level of 1 \(\times\)\(10^{6}\) s can reach 8.87 \(\times\)\(10^{-16}\). When the sampling interval is 1 \(\times\)\(10^{6}\) s, it is six times more stable than the best cesium clock and three orders of magnitude better than the worst rubidium clock. After analyzing the stability, the next step is to analyze the comprehensive atomic time TA(Steered) and the forecast clock difference of each atomic clock. The results are shown in Figure 17 and Table 3 below: