## 5 Multipath Mitigation Results  
According to the analysis above, the implementation of segmentation and time averaging helps the frequency domain multipath estimation method achieve better performance. Even in poor C/N\({}_{0}\) conditions, we can further improve the estimation accuracy by reducing the length of \(L\). Since multipath parameter estimation serves the goal of multipath mitigation on BOC signals, it is meaningful to evaluate the final ranging accuracy improvement in the multipath conditions using the proposed technique. So in this section, we plotted the root-mean-square error (RMSE) curves of code tracking and presented the comparison results of different multipath mitigation techniques. However, as our target signals are BOC-modulated signals, even high-order BOC signals, the TEXBAT dataset of GPS C/A signals would not be appropriate. So, the performance evaluation in this section was implemented by simulations. This scheme for performance evaluation had also be adopted in papers, such as [16; 36]. One of the benefits of such process is any other error sources can be excluded except multipath error. Figure 7: Impulse responses of the proposed averaging-FFT method over TEXBAT dataset. In this part, we mainly consider three different methods which can be used for multipath mitigation for BOC signals, i.e., the proposed method, MEDLL, and CCRW. They are classified into two groups. The first two techniques are parametric. Particularly, the MEDLL is among the most popular approaches of this type. CCRW is non-parametric and the best representative of this type. As mentioned in the Introduction section, there are various local reference waveforms among the CCRW family. Without loss of generality, the CCRW method here is implemented by reference to [7; 37]. Figures 8 and 9 show the local waveform signal and the cross correlation function between the reference waveform and the nominal BOC(1,1) signal, respectively. Non-zero values of the local CCRW signal appear only at the PN code transitions. The width of these gated waveform \(w\) is set to n/m PN code chips for a BOC(\(m\),\(n\)) signal. So for BOC(1,1), \(w\) is one PN code chip. Besides, it is should be noted that the two parametric techniques, MEDLL and aFFT method, achieve the goal of multipath mitigation by means of estimating the multipath parameters. We can obtain the code phase observations by directly estimating the time delay \(\tau_{0}\) of LOS. This is equivalent to the output of prompt correlator in a conventional tracking loop. The estimate of \(\tau_{0}\) will be further used to calculate the range estimates. As mentioned above, RMSE was used in this paper to indicate the multipath estimator performance. In order to calculate the RMSE, the trial of multipath estimation  
Figure 8: Illustration of CCRW method used in the following simulations. Figure 9: The CCF between BOC(1,1) signal and local CCRW signal. has been performed for a large number of times, such as 1000 times here. The mathematical expression of RMSE is generally defined as follows:  
\[\text{RMSE}=\sqrt{\frac{\sum\limits_{p=1}^{P}\left(\hat{r}_{p}-r_{0}\right)^{2}} {P}} \tag{26}\]  
where \(P\) denotes the total times of trails, \(\hat{r}_{p}\) represents the range estimate of the p-th trail. \(r_{0}\) is the actual rang value defined directly as \(r_{0}=\tau_{0}\cdot c\), where \(\tau_{0}\) is the pre-set delay of LOS and \(c\) is the speed of light. In the simulations of section \"Multipath Mitigation Results\", \(\tau_{0}\) was set to 0 for convenience. But if we try to estimate the delay of a multipath signal, it should be set to the actual code delay of that path. At the same time, in order to show the universality and practicality of the proposed method, we set up three different simulation scenarios in this section: (1) single-path channel; (2) three-path channel; and (3) high-order BOC signals. They are all static scenarios. Most of the multipath mitigation algorithms in the previous literatures are tested in the presence of a few secondary paths (three or less).