# Improving Structural Power Content Analysis Robustness for Satellite Navigation Applications +
## 4 Filter Techniques  
Following from the analysis on the effects of jamming signals on the performance of the SPCA algorithm, different filtering techniques were considered that could enhance the robustness of the algorithm during jamming events. In this section, two types of filter application are evaluated: filtering on the DC channel of the DAM output solely and filtering on the full noise spectrum of the signal, which was described in Section 2. To start with the DC filter, it is suggested that a notch filter is used to remove the excess power from the DAM output. The transfer function for a generic notch filter is described as follows [10]:  
\[H(z)=b_{0}\frac{1-2\cos\omega_{0}z^{-1}+z^{-2}}{1-2r\cos\omega_{0}z^{-1}+r^{2} z^{-2}} \tag{10}\]  
where \(\omega_{0}\) is the desired frequency that is to be removed; \(r\) is a real, positive number that is smaller than 1 and affects the width of the notch; and \(b_{0}\) represents a gain that is often set to 1. Ideally, the width of the notch would be designed to be small to limit the removal of signal power outside of the desired frequency. However, as the spectral lines corresponding to the power of the PRN codes are spaced relatively close to each other with respect to the full bandwidth of the signal (for example, a 1 kHz spectral-line spacing compared to a 25 MHz bandwidth for GPS L1 C/A [8]), neighboring spectral lines might be affected by the DC notch filter as well. For a relatively narrowband jammer where the message frequency for AM and FM and the sweeping frequency for chirp signals are small compared to the processed bandwidth in the receiver, the jamming power after the DAM operation will be located either in or close to the DC channel. The application of a DC notch filter with sufficient width could therefore not only remove the excess power in the DC channel, but also reduce the effects of these other jamming power components. The second filter application that is suggested is an evaluation of the noise filter. As described, a comb filter is used that has its passbands centered midway between adjacent signal spectral lines. With increasing filter lengths, these passbands become narrower. For the signal filter, this can be seen as advantageous, as the signal spectral lines can be isolated more accurately. For the noise filter, however, it is desirable to capture as much of the noise as possible, which would only be reduced when increasing the comb filter length. Therefore, it is suggested to substitute the noise filter for a notch filter with repeating notches on the signal spectral lines. By increasing the quality factor of the filter, the width of the notches can be reduced, which increases the accuracy of filtering the signal spectral lines. The effects of both the DC filter and the notch noise filter are presented in Figure 2, where the AM jammer is taken as an example, as this type of signal results in multiple excess peaks across the spectrum. In this analysis, the desired false alarm rate set by the user was compared to the actually achieved false alarm rate. The desired false alarm rate was used to calculate the threshold for the SPCA test statistic. The achieved false alarm rate was computed from the truth matrix when the SPCA algorithm including the computed threshold was tested, for a scenario with an AM jammer in this case. A linear slope between the origin and coordinate \((1,1)\) would define the nominal scenario, where the SPCA method achieves exactly the desired false alarm rate. Deviation from this diagonal towards the upper left corner depicts a worse performance. From this, it can be concluded that the application of a DC notch filter greatly improves the method's resilience against AM jamming. The substitution of the comb filter for a cyclic notch filter also yields some improvements, albeit less significantly. Similar results were found for CW, chirp, and FM jamming scenarios, which was expected as all these jammers induce excess power peaks in the DC channel.