## 7 Positioning Performance of LEO NR Signal
### Positioning Performance
Figure 16 and Table 5 present the state estimation results from the EKF: the positioning and velocity error in the north-south, east-west, and altitude dimensions (the ECEF coordinate is generally used in the EKF filter; for clarity, ECEF outputs are converted to the ENU coordinate). The experiment results show the following. (1) The static ZPC receiver exhibits positioning error fluctuation during initial operation, stabilizing after 3 s of continuous operation. The means of positioning errors in the north, east, and horizontal directions measure  
Figure 14: ZPC receiver tracking errors over time: (**a**) ranging error; (**b**) velocity error. \(-1.84\) cm, \(2.51\) cm, and \(4.54\) cm, respectively. Moreover, the mean of the three-dimensional positioning accuracy is approximately \(5.61\) cm. (2) For static and mobile ZPC receivers, the difference of position and velocity errors is lower than \(4\%\). Hence, they have similar position performances, and the ZPC receiver is robust in mobile scenarios. Moreover, the CON receiver demonstrates a similar position performance in both static and mobile scenarios. (3) The CON receiver demonstrates lower positioning accuracies: \(5.85\) cm, \(-17.33\) cm, and \(-44.38\) cm in the north, east, and horizontal directions. Compared to the CON receiver, our proposed ZPC receiver achieves \(88.3\%\) improvement in positioning accuracy. (4) The ZPC receiver also demonstrates a significantly enhanced velocity measurement compared to the CON receiver. The 3D velocity error mean of ZPC is \(0.59\) cm/s, while CON exhibits more significant errors of \(2.42\) cm/s. This corresponds to a \(75.62\%\) improvement in velocity accuracy. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Mean**} & \multicolumn{3}{c}{**Std**} \\  & & **North** & **East** & **Down** & **3D** & **North** & **East** & **Down** & **3D** \\ \hline \multirow{4}{*}{Position error (m)} & ZPC (Static) & \(-0.0184\) & \(0.0251\) & \(-0.0454\) & \(0.0561\) & \(0.0055\) & \(0.0050\) & \(0.0096\) & \(0.0059\) \\  & ZPC (Mobile) & \(-0.0152\) & \(0.0184\) & \(-0.0507\) & \(0.0585\) & \(0.0087\) & \(0.0097\) & \(0.0139\) & \(0.0091\) \\ \cline{1-1}  & CON (Static) & \(0.0585\) & \(-0.1733\) & \(-0.4438\) & \(0.4807\) & \(0.0184\) & \(0.0172\) & \(0.0249\) & \(0.0242\) \\ \cline{1-1}  & CON (Mobile) & \(0.0570\) & \(-0.1765\) & \(-0.4327\) & \(0.4717\) & \(0.0199\) & \(0.0270\) & \(0.0231\) & \(0.0288\) \\ \hline \multirow{4}{*}{Velocity error (m/s)} & ZPC (Static) & \(0.0005\) & \(-0.0039\) & \(0.0069\) & \(0.0487\) & \(0.0169\) & \(0.0267\) & \(0.0459\) & \(0.0281\) \\ \cline{1-1}  & ZPC (Mobile) & \(-0.0012\) & \(-0.0009\) & \(0.0115\) & \(0.0484\) & \(0.0160\) & \(0.0265\) & \(0.0465\) & \(0.0301\) \\ \cline{1-1}  & CON (Static) & \(0.0189\) & \(-0.0126\) & \(0.0351\) & \(0.2157\) & \(0.0760\) & \(0.1361\) & \(0.1876\) & \(0.1212\) \\ \cline{1-1}  & CON (Mobile) & \(0.0171\) & \(-0.0099\) & \(0.0414\) & \(0.2200\) & \(0.0762\) & \(-0.1383\) & \(0.1918\) & \(0.1240\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Position and velocity error statistics: ZPC and CON receiver. Figure 15: Stable tracking accuracy for different LEO satellites in static scenario: (**a**) ranging accuracy; (**b**) velocity accuracy.