## 1 Introduction
In order to overcome or attenuate the cross-interfering terms present in the the quadratic TF distributions, the Choi-Williams distribution has been proposed to detect the sweep interference for GNSS receivers [16]. Appropriate image processing techniques can be also used for detection and parameter estimation of chirp signals by line detection in an image [21]. In addition, several kernel design methods have been proposed to mitigate the cross-term effect [22, 23, 24]. Unfortunately, these techniques need heavy computational complexity when they are applied in a real-time context. A reasonable method is to to introduce a window function in the time domain to reduce the undesired cross-term effects; therefore, the concept of the pseudo Wigner-Ville distribution (PWVD) is educed [20]. Consequently, the window function in PWVD can partially suppress the cross-terms to some extent; the disadvantage of the filtering window operation is the degradation of the resolution, particularly in the frequency domain. In PWVD, the time window operation is equal to frequency filtering in WVD, which can reduce the number of cross-interfering terms by suppressing the interferences between signal components sufficiently separated in time. In order to obtain a better readable result, the cross-terms between components in the frequency domain should be also minimized. Thus, an additional window function is added in order to perform a smoothing in time independently of the frequency smoothing. Therefore, the smoothed version of PWVD, namely the smoothed pseudo Wigner-Ville distribution (SPWVD), can be obtained [25]. The SPWVD is characterized by a separable kernel, which allows the time and frequency smoothing to be adjusted independently, which becomes one of the most versatile of [PERSON]'s class TF distributions. The smoothing windows can be adopted to reduce the cross-terms significantly; unfortunately, the SPWVD method also smears localized components, leading to less accurate localization of the signal auto-components in the TF plane compared to the WVD approach. Therefore, a reassignment method can be advantageously applied to improve TF localization properties in SPWVD [25, 26]. In this way, the reassigned smoothed pseudo Wigner-Ville distribution (RSPWVD) can be obtained. The RSPWVD method is used to compensate for faults in mapping the TF energy distribution by relocating the value of the neighboring energy to the gravity center rather than the geometric center. In the RSPWVD method, by the adoption of the two-dimensional low-pass filtering smoothing function, the cross-term artifacts present in the quadratic TF distribution can be efficiently eliminated; meanwhile, by the use of the reassignment, the TF localization and aggregation properties of the auto-terms of the signal can be significantly improved. In this paper, an improved TF analysis method by adopting RSPWVD has been proposed in interference detection for GNSS receivers. To the best of our knowledge, this interference detection technique based on joint TF analysis by adopting RSPWVD in the interference detection units for GNSS receivers is new. The performance of the proposed method has been deeply evaluated in comparison with the existing TF analysis approaches. Different localization properties and cross-term effects in the TF plane have been well investigated and compared among the aforementioned TF distributions adopted in interference detection for GNSS receivers. In order to prove the effectiveness of the proposed TF analysis method by adopting RSPWVD in interference detection for GNSS receivers, an experiment is accomplished in the GPS L1 signal, which is characterized in additive white Gaussian noise (AWGN) corrupted by linearly-modulated sweep interference (chirp disturbance). The analysis results show that the proposed joint TF analysis by using RSPWVD eliminates the cross-terms significantly and preserves the high resolution of time and frequency in the TF plane at the same time.