## 5 Experimental and Simulation Results  
Assuming that the one-way measurement period of the ISL is 1.5 s (GPS assigns 1.5 s to each satellite in ISLs) [14]. The clock, \(f_{c}\), is 50 MHz and the system initial phase, \(p_{0}\), is \(2^{N-1}\) (namely, \(\pi\)). Assuming that the two satellites remain stationary, \(\Delta t\) can be monitored in real-time; the inter-satellite pseudo-range delay is 78 ms, the pseudo-code ranging accuracy of the ISL is 0.5 ns, the coefficients \(\omega_{n}\) and \(\xi\) of the PLL's system function are 37.3 and 0.7, respectively, and the data update rate, \(T_{s}\), is 1 ms. Then, the response of the second-order PLL error system function under a frequency and phase step excitation is shown in the Figure 7.  
Assuming that the DDS frequency division coefficient, \(n\), is 4, the initial phase, \(\phi_{0}\), is \(2^{N-1}+\frac{2^{N-1}}{n}\) and the bit width of the phase accumulator, \(N\), is 32. Then, the phase compensation of the ranging results in case of the FPA of the 10.23 MHz and the change in the \(p^{\prime}_{0}\) of the 1 PPS are simulated. When the 1 PPS is in the non-skip-area, the pseudo-range measurement results with and without the phase compensation are shown in Figure 8. When the 1 PPS is in the skip area, the pseudo-range measurement results are shown in Figure 9. Table 1 lists the expansion of the abbreviations in Figures 8 and 9, and the FPA values of the 10.23 MHz and the initial phase values of the 1 PPS are listed in the headers of Figures 8 and 9. As can be seen from Figure 7, the PLL only needs 200 ms to output the convergent locked phase after the FPA, which can guarantee the validity of the phase compensation data in a one-way measurement period (1.5 s). Figure 7: Error response of the frequency and phase step excitation. From Figure 8, if there is no phase compensation, the pseudo-range values have an approximately 20 ns periodic jitter caused by the frequency adjustment as shown in Figure 8a, an approximately 12 ns fixed offset caused by the phase adjustment as shown in Figure 8b, an approximately 24.43 ns fixed offset caused by the change in the \(p^{\prime}_{0}\) of the 1 PPS depicted in Figure 8c, and a 24.43 ns fixed offset and a 20 ns periodic jitter caused by the FPA and the changed \(p^{\prime}_{0}\) as shown in Figure 8d. However, the ranging results with a phase compensation by tracking the 10.23 MHz directly or by tracking the \(f_{n}\) are maintained at approximately 78 ms in Figure 8a-d. \begin{table}
\begin{tabular}{c c} \hline \hline
**Abbreviations** & **Definition** \\ \hline \(F\) & Frequency adjustment of the 10.23 MHz, unit: mHz \\ \(P\) & Phase adjustment of the 10.23 MHz, unit: ns \\ \(p^{\prime}_{0}\) & Initial phase of the 1 PPS, unit: rad \\ No P-C & Ranging results without phase compensation \\
10.23 MHz P-C & Phase compensation by tracking the 10.23 MHz \\ \(f_{n}\) P-C & phase compensation by tracking \(f_{n}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Expansion of the abbreviation in Figures 8 and 9. Figure 8: Ranging results with the 1 PPS in the non-skip-area. (**a**) only frequency adjustment; (**b**) only phase adjustment; (**c**) only change \(p^{\prime}_{0}\); (**d**) the FPA and the changed \(p^{\prime}_{0}\). Particularly, in Figure 9, when the 1 PPS is in the skip area, the measurement pseudo-range has an approximately 97.75 ns periodic jump with a phase compensation by directly tracking the 10.23 MHz. Nonetheless, after the proposed phase compensation sensor, the inter-satellite measurement results are maintained at approximately 78 ms.  
To verify that the proposed phase compensation method is valid, we used an ISL engineering prototype for a field data acquisition and ranging comparison. We connected by coaxial cables the ISL ground simulation unit to the ISL engineering prototype via the intermediate frequency signal. The phase compensation sensor was realized by the field programmable gate array (FPGA) inside the prototype. The PLL setting parameters were the same as the simulation parameters.