# An Anti-Interference Method Based on Energy Residual Searching in GNSS Positioning Applications
## 2 Related Work  
When discussing the relevant work on counteracting GNSS interference, time-frequency domain analysis techniques emerge as particularly significant. Linear frequency modulation (LFM) wideband or continuous-wave narrowband interference signals can generate highly concentrated energy distributions on the time-frequency (TF) plane. The short-time Fourier transform (STFT) decomposes a long signal into multiple short segments, performing Fourier transforms on each segment, thereby providing simultaneous information about both the time and frequency of the signal. Consequently, many researchers [13; 14; 15; 16] have developed a series of interference suppression algorithms based on STFT and its variants. For instance, [PERSON] [13] proposed an adaptive interference cancellation technique based on STFT, effectively mitigating non-stationary and rapidly varying interference in direct sequence/spread spectrum (DS/SS) communication systems. [PERSON] [14] introduced an interference detection method utilizing time-frequency statistical analysis based on STFT, discussing the impact of traditional STFT and block STFT techniques on detection effectiveness. However, the application of STFT for interference detection and mitigation still faces several limitations. Firstly, STFT suffers from an inherent trade-off between time and frequency resolution, making it challenging to achieve high resolution in both domains simultaneously [16; 17]. Additionally, the computational complexity of STFT presents challenges for real-time processing of long time series or high-sampling-rate signals. To circumvent the trade-off issue in time-frequency resolution, many scholars have employed the Wigner-Ville distribution (WVD) for detecting linear frequency-modulation interference. The WVD offers many advantageous properties, providing nearly the best resolution among all time-frequency distributions. However, due to the interaction of different components, it exhibits significant cross terms in the time-frequency plane, leading to considerable errors in the instantaneous frequency estimation of interference signals. Techniques such as smoothing can be utilized to mitigate the impact of these cross terms. [PERSON] proposed a novel frequency-sweep interference detection and suppression method based on the Radon-Wigner transform (RWT), which effectively alleviates the cross-term issues prevalent in traditional time-frequency analysis techniques. [PERSON] [18] introduced a pseudo Wigner-Ville distribution that effectively addresses both narrowband and wide-band interference while possessing a degree of cross-term suppression capability. [PERSON] [19] proposed a pseudo Wigner-Ville distribution (PWVD) that partially suppresses cross terms by employing window functions in the time domain, although this approach can lead to a decrease in resolution. [PERSON] [20] introduced a smoothed pseudo Wigner-Ville distribution (SPWVD), which allows for independent and progressive control in both the time and frequency directions, offering flexibility in alleviating poor cross-term conditions in the WVD. While this method can suppress interference terms, it requires careful parameter tuning, resulting in a relatively complex implementation. [PERSON] [21] proposed a new joint hybrid time-frequency analysis method based on the Choi-Williams transform, the Hadamard product, and the smoothed pseudo-Wigner-Ville distribution, effectively eliminating cross terms present in bilinear TF distributions. In addition, he also proposed several variants of the Wigner distribution [22; 23; 24].Furthermore, combining the Wigner transform with the Hough transform has facilitated the development of GNSS interference detection techniques based on the Wigner-Hough transform [25; 26; 23].