## 4 Performance Evaluation of Parameter Estimation
### Tests with Real Data  
In the previous section we showed the theoretical parameter estimation capability of the proposed method. To make the results more persuasive, we verified it with real GPS signals. The dataset used here is the so-called Texas Spoofing Test Battery (TEXBAT) [33]. It is a test battery of real cases publicly provided by the University of Texas at Austin. It is originally collected to demonstrate the vulnerability of GNSS in face of a spoofing attack and test the capability of spoofing detection techniques. However, numerous papers have mentioned that the structure of the spoofing signals is quite similar with multipath signals [34; 35]. Even the same mathematic model is employed to characterize multipath and spoofing signals. This allows us to use the TEXBAT dataset as a set of multipath signal records for real data tests. Besides, the dataset only contains one secondary path signal and its behavior is known to us, which makes it quite appropriate for the verification of the performance of the proposed aFFT method. Signals were tracked using a GPS software receiver. The setting of parameters is concluded in Table 2. The signal modulation type used here is BPSK modulation (GPS C/A signal). The data was collected by a sampling rate of 25 MHz. The total signal length to perform one time multipath estimation is set to 20 ms, and the window size \(L\) is 128 points. The scenario we used is number 6 of a total of six different cases. In this scenario, a signal with the same structure as the real GPS signal is broadcast to reach the antenna of the victim receiver. The mixture of the LOS signal and the counterfeit signal can be seen as multipath signals. The behavior of the mixture signal in I channel is illustrated in Figure 6. This scenario includes a dynamic secondary path signal with a matched power advantage over the LOS signal (+0.8 dB). Compared with static scenarios, the receiver used to collect this GPS data is moving or dynamic. Thus, it can be used to verify the performance of the proposed method in dynamic conditions. In order to reduce the effect, \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Signal modulation type & BPSK(1) \\ Signal length & 20 ms \\ Sampling rate & 25 MHz \\ Window length \(L\) & 128 points \\ Window function & Hamming \\ C/N\({}_{0}\) & Larger than 45 dB-Hz \\ \hline \end{tabular}
\end{table} 
Table 2: Setting of Multipath Parameter Estimation. Figure 5: Estimation deviation of estimated code delay with \(\tau\) varying from 0.1 to 1 chip. the total signal length for one time process should not be too long, and the renewal cycle and noise bandwidth of the code and carrier loop should be a little larger. The LOS signal and multipath signal starts separating at the 150 th second. In order to show the parameter estimation ability of the proposed aFFT method, we provide the impulses at the 140 th, 235 th, and 250 th seconds, respectively as shown in Figure 7. The three subfigures on the left side show the in-phase and quadrature phase impulses after IFFT operation, and the subfigures on the right side illustrate the amplitude (absolute value) of the IQ composite impulses. Employing both the impulses of I/Q channel, we can easily obtain the current carrier phase difference between LOS signal and multipath signals. From Figure 7, we can see clearly the total changing process, which demonstrates the effectiveness of the proposed method. The impulses of both LOS signal and the extra ray can be easily detected by a threshold, and we can characterize and distinguish both LOS signal and multipath signals using the averaging-FFT method. Besides, the carrier phase difference between LOS signal and multipath signal has much effect on the I/Q channel energy distribution.