# Positioning Using IRIDIUM Satellite Signals of Opportunity in Weak Signal Environment
## 3 The Estimation of Iridium Satellite Signal Doppler-Shift in Weak Signal Environment
### The Principle of Estimating Iridium Satellite Signal Doppler-Shift in Weak Signal Environment  
Considering the Iridium satellite SOPs are non-cooperative and non-navigational radio signals, the quadratic square accumulating instantaneous Doppler estimation (QSA-IDE) algorithm is proposed in this paper to realize the Doppler-shift accuracy estimation in weak signal environment. The algorithm squares the signal twice before estimating Doppler-shift. An open-loop measurement method is used to measure Doppler-shift in weak signal environment since the Iridium signals are discontinuous bursts. The QSA-IDE has two parts: Signal detection and signal acquisition. The Iridium bursts in the continuously received data are funded by detection part and the start times of the bursts are locked. The bursts are then intercepted and sent to the acquisition process for Doppler-shift estimation. The principle of QSA-IDE is shown in Figure 2.  
The Iridium signals from the antenna are transformed into an intermediate frequency (IF) digital sequence after processing by radio frequency front end (RFFE). The pre-processing module first divides the IF data into consecutive multiple data blocks \(d_{i}(i=1,\ldots,M)\). The length of time of \(d_{i}\) is longer than a TDMA frame time. The IF signals in every data block are squared twice and filtered to remove the high frequency part. The new data blocks are denoted by \(s_{i}(i=1,\ldots,M)\). \(s_{i}\) may include the quadratic square Iridium signals and the quadratic square noise signals, or only includes the quadratic square noise signals. The quadratic square Iridium signals remove the situation of phase flip caused by the unique word (BPSK) and the information (QPSK). Then, the \(s_{i}\) is sent into detection module for detecting whether the Iridium burst is existing or not. In the detection module, the matched filter is used to judge whether there is a quadratic square Iridium signal. Once finding the target signal, it enters the capture process. At the same time, the quadratic square Iridium signal is intercepted after locking its start and time, and its time stamp and the number of \(s_{i}\) are marked. The detection threshold value can be obtained from the pure noise signal in the actual environment. It assumed that total \(N\) data blocks have Iridium signals, the first one and the last one are block \(p\) and block \(q\), respectively. These Iridium signals are denoted by \(r_{k}(k=1,\ldots,\mathrm{N};\mathrm{N}<\mathrm{M})\). \(\mathrm{N}\) target signals \(S_{k}=r_{k}^{4}(k=1,\ldots,\mathrm{N};\mathrm{N}<\mathrm{M})\) are received after finishing the above processing. Then, the quadratic square Iridium signals \(S_{k}(k=1,\ldots,\mathrm{N};\mathrm{N}<\mathrm{M})\) are sent to acquisition module. Figure 2: Principle of the quadratic square accumulating instantaneous Doppler estimation algorithm. The main work of acquisition module is Doppler-shift estimation. The center frequency of the quadratic square Iridium signals can be obtained by fast Fourier transform (FFT) processing. The Doppler-shift can be directly calculated since the standard frequency is known. However, the Doppler-shift measurement accuracy is affected by the FFT resolution. This process is called Doppler-shift coarse estimation. The maximum likelihood estimator (MLE) algorithm [14] can be used to realize Doppler-shift fine estimation. This needs a receiver to search the target signals in frequency space. Multiplying the incoming signals with the locally generated duplicated signals, the correlation between the duplicated signals and the incoming signals is detected by signal power that is calculated by coherent integration and squaring. If the frequency of the local carrier matches the incoming signal frequency, the output will be significantly greater than if any of these criteria were not fulfilled. During the search process, the local carrier frequency parameter can be searched within the FFT resolution bandwidth or a wider frequency range.