# A Novel GNSS Interference Detection Method Based on Smoothed Pseudo-Wigner-Hough Transform
## 8 Conclusions  
This paper has proposed a novel smoothed pseudo-Wigner-Hough transform-based GNSS interference detection method. To demonstrate the validity and effectiveness of the proposed technique, real GPS L1-C/A data in the presence of sweep interference have been used in the GNSS interference detection tests, and full performance analysis and comprehensive comparison with the conventional time-frequency analysis-based approaches have been undertaken. From the experimental results, it has been shown that spectrogram has a time-frequency resolution trade-off problem and Wigner-Ville distribution exhibits an undesired cross-term problem in the GNSS interference detection process, resulting in serious interference detection performance degradation. However, employing the Hough transform-based GNSS interference detection methods developed in this paper converts the original problem of global detection of the straight line of frequency modulation law of the sweep interference present in the received GNSS signal in the time-frequency space to the new problem of locally searching for the Hough-transformed energy peak positioned in a small intersecting area of concurrent sinusoidal curves in the \(\rho-\theta\) transform space. As evident in the results, the developed Hough transform-based GNSS interference detection methods have been shown to be effective in the suppression of undesirable cross interfering terms present in the quadratic time-frequency distributions, and the developed methods enhance the properties of energy aggregation, facilitating improved GNSS interference detection performance over the conventional time-frequency analysis-based approaches. Among the Hough transform-based GNSS interference detection techniques, the Wigner-Hough transform approach can be used to partially suppress the cross-terms within the quadratic time-frequency distribution; the pseudo-Wigner-Hough transform method improves interference detection performance over the Wigner-Hough transform technique; in the case of the smoothed pseudo-Wigner-Hough transform method, the Hough-transformed energy distributions are effectively strengthened and highly concentrated in a particular area of intersection within the parameter space. This enables the smoothed pseudo-Wigner-Hough transform method to be much superior to the Wigner-Hough transform and pseudo-Wigner-Hough transform techniques, as can be verified from the zero Hough-transformed energy percentage analysis results of the Hough transform-based GNSS interference detection methods. In summary, the developed Hough transform-based GNSS interference detection methods are superior to the traditional time-frequency analysis-based approaches, and in particular, the proposed novel smoothed pseudo-Wigner-Hough transform method provides supreme interference detection performance among the developed Hough transform-based techniques. The proposed smoothed pseudo-Wigner-Hough transform method is with moderate computational complexity, which is very promising to be effectively used in the practical interference detection design for GNSS receivers in interfering environments. [PERSON] conceived the work, designed the methodologies, developed the software, analyzed the results, and wrote the manuscript; [PERSON] reviewed the manuscript; [PERSON] reviewed the manuscript and gave comments to the research work; [PERSON] reviewed the manuscript and gave comments to the research work; [PERSON] edited the format of the manuscript; [PERSON] reviewed the manuscript. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Natural Science Foundation of China (Grant No. 41774029), Open Foundation of State Key Laboratory of Satellite Navigation System and Equipment Technology, China (Grant No. W2018 JSKF0402) and Chinese Fundamental Research Funds for the Central Universities (Grant No. JD2019 GYP0019). Not applicable. The authors would like to thank the anonymous reviewers for their thoughtful comments and constructive suggestions.