## 7 Positioning Performance of LEO NR Signal
### Positioning Performance  
This section compares the three-dimensional (3D) positioning performance between the proposed ZPC navigation receiver and the CON receiver. As described in Section 4, the simulation of the LEO NR system consists of three core components: the NR transmitter, the LEO satellite channel, and the NR navigation receiver. The NR navigation receiver contains two sequential operational phases: signal acquisition and tracking. The acquisition module initially estimates the pseudo-random noise (PRN) sequence identifier, code phase delay, and carrier frequency offset. Like conventional GNSS receivers, the acquisition process detects peaks generated by correlating local replica and received signals. For brevity, the acquisition module is not expanded upon. After successful acquisition, the receiver enters tracking mode. The DLL and FLL in the NR receiver estimate the pseudorange and pseudorange rate, respectively. Based on these measurements, the EKF output receiver's state vector is in real time. The simulation experiment includes six viewed satellites, as described in Section 7.1, and their tracking errors are plotted in Figure 14. All the tracking error curves have a similar trend: There are transient responses at the beginning of the tracking (0-0.2 s), then the error curves tend to stabilize. The settling time is determined by the tracking loop bandwidth \(B_{L}\) and is about \(4.24/B_{L}\)[2]. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Parameter** & **Sat 1** & **Sat 2** & **Sat 3** & **Sat 4** & **Sat 5** & **Sat 6** \\ \hline Semi-major Axis \(a\) (km) & 7136 & 6980 & 6970 & 7050 & 6820 & 7130 \\ Eccentricity \(e\) & 0.0001568 & 0.0001459 & 0.0001603 & 0.0001432 & 0.0001464 & 0.0001406 \\ Inclination \(i\) (\({}^{\circ}\)) & 53.0531 & 53.2146 & 53.2157 & 43.0039 & 43.0019 & 53.1584 \\ RAAN \(\Omega\) (\({}^{\circ}\)) & 189.0089 & 191.0164 & 305.9367 & 291.2627 & 294.6071 & 192.7046 \\ Argument of Perigee \(\omega\) (\({}^{\circ}\)) & 63.1495 & 78.6725 & 89.8188 & 270.5086 & 262.0388 & 61.5981 \\ Mean Anomaly \(M\) (\({}^{\circ}\)) & 82.5489 & 166.1697 & 347.1216 & 212.3624 & 208.9401 & 164.3645 \\ Altitude \({}^{1}\) (km) & 765 & 609 & 599 & 679 & 449 & 759 \\ \hline \hline \end{tabular} \({}^{\dagger}\) The radius of Earth is 6371 km.  
\end{table} 
Table 4: Orbital data from Starlink satellites [77]. Figure 13: The trajectory of LEO satellites and receiver. The proposed ZPC and CON receiver's tracking accuracy comparison is plotted in Figure 15. All simulation parameters for the ZPC and CON receivers are identical except for the replica signal and correlation process. This simulation configuration helps to compare the difference of receivers with high repeatability. The tracking accuracy is quantified through the standard deviation (STD) of ranging and velocity errors. The comparison results show that (1) significant differences exist in ranging and velocity error STD for different satellites, with this difference being caused by distinct orbital characteristics, leading to different Doppler shifts and carrier-to-noise ratios; and (2) the CON architecture ranging accuracy ranges from 17.8 to 27.9 cm, and velocity precision ranges from 3.66 to 4.93 cm/s. In contrast, the ZPC receiver demonstrates superior ranging accuracy (3.0-4.5 cm) and velocity accuracies (0.7-1.14 cm/s). ZPC achieves about an 80% improvement in both ranging and velocity accuracy. The CON receiver has two shortages: Omitting the CP process leads to inter-carrier interference (ICI), and it cannot identify PBCH signals decreasing the output power of correlation. The ZPC receiver addresses these shortages, and all known NR reference signals are utilized as local replica signals. Next, we analyze the positioning performance of the LEO NR system, considering only the receiver noise while excluding other error sources. Four navigation reception strategies are utilized: static ZPC, mobile ZPC, static CON, and mobile CON.