# A Cumulant-Based Method for Acquiring GNSS Signals
## 5 Discussion  
The results of this study demonstrate the efficacy of the proposed method for GNSS signal acquisition, particularly in challenging environments, such as those involving weak signals or multipath interference. Compared to traditional methods, our approach shows improvements in both the suppression of side-peaks and the accuracy of code-phase detection.  
The problem of side-peaks in the acquisition of BOC-modulated signals, as noted in previous studies [3; 4], has been a persistent challenge due to the complex autocorrelation function of these signals. Traditional methods often fail to completely eliminate these side-peaks, which can lead to false locks and positioning errors. Our results indicate that the proposed cumulant-based method effectively addresses this issue, eliminating side-peaks and improving the robustness of the signal acquisition.  
Moreover, the higher processing gain observed in our method suggests that it may be particularly valuable for applications involving weak signals, where traditional approaches struggle to maintain reliable acquisition. This finding aligns with the hypothesis that leveraging higher-order statistical properties, such as cumulants, can enhance signal detection  
Figure 16: Acquisition results of GPS PRN5 using the traditional method in indoor conditions.  
Figure 17: Acquisition results of GPS PRN5 using the proposed method in indoor conditions.  
in low-SNR environments. The ability of our method to detect signals at levels as low as 23 dB-Hz--below the typical thresholds for standard receivers--further supports this claim and highlights its potential for indoor and urban canyon applications, where signal strength is often compromised.  
While the results are promising, there are several avenues for future research. First, further investigation is needed to optimize the algorithm's performance under various noise conditions and to ensure its scalability for real-time processing in commercial GNSS receivers. Additionally, exploring the integration of this method with advanced signal processing techniques, such as machine learning, could provide further enhancements in acquisition speed and accuracy.  
While our study demonstrates promising results for GPS signal acquisition in indoor environments, we acknowledge that our current work does not include equivalent results for Galileo signals in similar conditions. The acquisition of Galileo signals indoors presents unique challenges due to its signal structure and complex multipath effects. Our preliminary experiments in this area have not yet yielded satisfactory results, highlighting the need for further research. We identify this as a crucial area for future investigation, with the potential to significantly advance indoor GNSS positioning techniques. Future work will focus on optimizing our proposed method specifically for indoor Galileo signal acquisition, aiming to extend the benefits of our approach to this important use case.  
Finally, while our study focused on GNSS signals, the principles underlying the proposed method may have broader applications in other fields where time-delay estimation is critical, such as radar, sonar, and telecommunications. Future research could explore these potential cross-disciplinary applications, thereby extending the impact of this work beyond satellite navigation.