# A Novel GNSS Interference Detection Method Based on Smoothed Pseudo-Wigner-Hough Transform
## 1 Introduction
Therefore, detecting sweep interference may be formulated as the problem of searching for a particular pattern of a linear form in the time-frequency domain. Furthermore, the detection of sweep interference can be completed by combining the Hough transform (HT) with the Wigner-Ville distribution, producing the Wigner-Hough transform (WHT) [17; 18], which is a kind of straight-line integral projective transformation. In this way, Wigner-Hough transform can be adopted for the detection of linear patterns corresponding to the linear frequency modulation signal [19; 20; 21; 22]. According to our knowledge, the Wigner-Hough transform was historically used for detecting GNSS interfering signals for the first time [23]. Hough transform-based techniques have played increasingly important roles in GNSS interference detection and have received more attention [24; 25]; several reassigned time-frequency analyses have been used in combination with the Hough transform to construct improved interference detection methods for GNSS receivers [16; 26], but the reassignment operations with these techniques require heavy computational complexities in the detection of GNSS interference. In addition, Hough transform-based techniques were also used in other navigation and radar-related applications [27; 28]. Since pseudo-Wigner-Ville distribution (PWVD) is capable of suppressing the cross-interfering term in the quadratic time-frequency distributions by using a low-pass filtering window function [9; 15], the pseudo-Wigner-Ville distribution has been combined with the Hough transform to obtain pseudo-Wigner-Hough transform (PWHT) to detect GNSS interference [25]. However, there are still residual cross-term components emerged in the parameter space, which limits the improvement of GNSS interference detection performance. Since smoothed pseudo-Wigner-Ville distribution (SPWVD) employs a low-pass filtering function in the two-dimensional form, the effect of the cross-interfering terms occurring between the multiple signal components can be effectively suppressed [9; 11; 15]; therefore, in order to break through the limitation of the pseudo-Wigner-Hough transform used in GNSS interference detection, in this paper, it's reasonable to combine the smoothed pseudo-Wigner-Ville distribution with the Hough transform to propose a novel smoothed pseudo-Wigner-Hough transform (SPWHT) to further improve interference detection performance for GNSS receivers. In order to analyze the properties of energy distribution concentration and cross-term suppression of the Hough transform-based techniques used in GNSS interference detection, a novel metric known as zero Hough-transformed energy percentage has been proposed in this paper. To the best of our knowledge, the proposed criteria of zero Hough-transformed energy percentage used for evaluating the Hough transform-based GNSS interference detection techniques are new. We employ Wigner-Hough transform, pseudo-Wigner-Hough transform and smoothed pseudo-Wigner-Hough transform, respectively, for the detection of linear patterns corresponding to the type of sweep interference existing in the GNSS useful signal, and compare the performance of these Hough transform-based methods in GNSS interference detection. To verify the validity and effectiveness of these GNSS interference detection methods, we use real GPS L1-C/A data captured in an experimental scenario with a sweep interfering signal, which is a relatively common and typical nonstationary interference impeding the performance of GNSS receivers. The results show that the Hough transform-based techniques suppress the cross-interfering terms within the quadratic time-frequency distributions and improve GNSS interference detection performance compared with the traditional approaches based on time-frequency analyses.