# Positioning Using IRIDIUM Satellite Signals of Opportunity in Weak Signal Environment
## 5 Experimental Results
### Estimating Doppler-Shift of Iridium Satellite Signal in Weak Signal Environment  
In this section, we will show the Doppler-shift estimation results of the real IRIDIUM NEXT signals by the new QSA-IDE algorithm. The Iridium 7 channel simplex signal, ring alert, can be obtained after filtering the IF data from RFFN. The signal standard frequency is 1626.270833 MHz and the corresponding IF is 28.270833 MHz. We first give the Iridium signal time-domain plot, then Doppler-shift estimation results are carried out. The Iridium signals are the discontinuous burst signals. The time length of the most bursts is about 6.5 ms, and the maximum time length is 20.32 ms. The time domain plot of a 9 ms collected signal after filtering (the filter bandwidth is corresponding to the Iridium ring alert signal bandwidth) is shown in Figure 5a. An Iridium burst signal exists in this 9 ms data. The first 2 ms data is the pure noise signal, then the following 6.6 ms data is the Iridium burst signal, the last 0.4 ms data is the pure noise signal. The amplitude of the Iridium signal is not significantly higher than for noise since  
Figure 4: IRIDIUM NEXT data collection in weak signal environment. the power of the Iridium signal is decreased due to the occlusion environment. The Doppler-shift of this Iridium signal cannot be obtained by the traditional Doppler-shift estimation method since the signal fails to detect, even the tone signal of the Iridium signal that is used by traditional Doppler-shift estimation method cannot be correctly locked. As a result, the Doppler-shift cannot be estimated by the traditional method in weak signal environment. However, Doppler-shift can be estimated by the QSA-IDE algorithm proposed above. The first step of the new method is the quadratic square processing, this can be finished by Equations (1)-(7). Squaring this 9 ms data twice, that is, to multiply it by itself three times. The time domain plot of the quadratic square data after filtering is shown in Figure 5b. It can be seen that the power of the quadratic square Iridium signal is stronger than for noise signal power. The signal-to-noise ratio is very optimistic after quadratic square processing. The quadratic square Iridium signal near the baseband after filtering can be used for Doppler-shift estimation once it was detected by the matched filter. The Doppler-shift estimation result is shown in the following. After detecting the quadratic square Iridium signal and locking the starting time, the quadratic square Iridium signal is intercepted and sent into the FFT process module. The FFT results of the quadratic square signal are shown in Figure 6. The center frequency of the quadratic square Iridium signal is about 1,192,618.629174 Hz. With the help of the standard frequency of ring alert, we can get the Doppler-shift coarse estimation. However, the Doppler-shift fine estimation is necessary since the error of the Doppler-shift coarse estimation caused by the FFT resolution is insupportable. Generating a local carrier based on the FFT results according to Equation (9). Let it correlate with the quadratic square signal according to Equation (10). The fine center frequency of the quadratic square Iridium signal can be received by using the MLE discussed above. The correlation results can be obtained by Equations (11)-(15), and are shown in Figure 7. The frequency corresponding to the correlation peak is 1,192,697.914173989 Hz, which means the fine frequency estimation of the quadratic square Iridium signal is obtained. The real quadratic square signal of ring alert near the baseband is 1,083,332 Hz. Then, the Doppler-shift of this ring alert burst signal is 27.34147854349727 Hz after simple numerical calculation. Figure 5: Magnitude of collected 9 ms data: (**a**) Magnitude of the collected data after filtering with the Iridium ring alert signal frequency band; (**b**) magnitude of collected data after square quadratic square processing and filtering with the Iridium ring alert signal frequency band.