# Positioning Using IRIDIUM Satellite Signals of Opportunity in Weak Signal Environment
## 5 Experimental Results
### Positioning Based on Iridium Satellite SOPs in Weak Signal Environment
Figure 8: Doppler-shift estimation results of the IRIDIUM NEXT signals obtained by the traditional method: (**a**) Iridium ring alert signal Doppler-shift estimation results; (**b**) Iridium primary message signal Doppler-shift estimation results. These four IRIDIUM NEXT satellites are simulated with the satellite tool kits (STK). The simulation time is in accordance with the time of the real IRIDIUM NEXT collected. The simulation results corresponding to the starting time of the real IRIDIUM NEXT collected are shown in Figure 10a,b. The red point denotes the receiver location and the yellow point denotes the satellite locations. The satellites are IRIDIUM 41918U, IRIDIUM 41919U, IRIDIUM 41917U, and IRIDIUM 43479U. We can see that the first satellite, 41918U, just comes into view at a low elevation location, then following the other three Iridium satellites. These four satellites are located at the same orbit and the corresponding sub-tracks are near the receiver. The conclusion is in accordance with the analysis results from the real Doppler-shift curves discussed above. We give the sky plot by taking the first IRIDIUM NEXT satellite for example, as shown in Figure 11. The red point denotes the Iridium satellite position corresponding to the starting time of the real Iridium data collected and the receiver locates at the central of the circle. In this case, although the receiver is located at an occlusion environment, we can still estimate the Iridium Doppler-shift. Figure 10: Simulation results of the four visible IRIDIUM NEXT satellites based on STK: (**a**) Three-dimensional (3D) graphics of the simulation result; (**b**) two-dimensional (2D) graphics of the simulation result. Figure 9: Doppler-shift estimation results of the IRIDIUM NEXT signals obtained by the new method: (**a**) Iridium ring alert signal Doppler-shift estimation results; (**b**) Iridium primary message signal Doppler-shift estimation results. After obtaining the Doppler-shift measurements, we can realize the receiver positioning. The IRIDIUM NEXT TLE data downloaded from the NOARD web are obtained as the satellite ephemerides and the orbital prediction model is used to calculate the Iridium satellite position and velocity. The Doppler positioning and height aiding are used for receiver position calculation. For the static receiver, the multi-epoch positioning method is used here. We use total 25 Doppler-shift measurements to form the positioning solution equations and the least squares (LS) is used to calculate the receiver position. These 25 measurements come from four different satellites. As a result, for every satellite, the measurements corresponding to different moments are used together. The receiver solutions calculated with different Doppler-shift measurement combinations are different. The Doppler-shift measurement accuracy corresponding to different satellites and different moments are different. Here, the positioning results with different Doppler measurement combinations are shown. Every combination has 25 Doppler measurements from four satellites, and the receiver position calculations are run for a total of 800 times. The positioning error statistic results with the ring alert signal are carried out first. The mean error and root mean square (RMS) are calculated, as shown in Table 1.  
It can be seen that compared with the north-direction and the up-direction, the receiver has a larger positioning error in the east-direction. The east-direction average position error reaches 147 m, and the error is with large fluctuations. The mean value of up-direction position error is optimistic, however, the fluctuation range is about 10 m more than the north-error. The 3D position error RMS in this case is about 400 m. The statistical results of height aiding are shown in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **East-Error/m** & **North-Error/m** \\ \hline Mean value & 147 & \(-\)162 & 58 \\ RMS value & 371 & 149 & 161 \\ \hline \hline \end{tabular}
\end{table}