## 4 Narrowband Interference Suppression Algorithm Based on SVD with Guidance Signal
### Accurate Estimation of Narrowband Interference Frequency  
In order to accurately estimate the frequency of narrowband interference, this paper introduces an improved Rife method based on the frequency-amplitude mean curve of FSWT [27].  
The Rife method has high accuracy when the estimated frequency is located in the central region of two adjacent quantization frequencies, but the error may be larger than DFT when it is located near the quantization frequency point [28]. The improved Rife method uses the frequency shift technology to shift the signal frequency to the two adjacent quantized frequency center regions at one time, and then uses the Rife algorithm to estimate the frequency. The high precision and stable frequency estimation performance is obtained in the whole frequency band.  
According to the principle of the improved Rife method, this paper moves the frequency of the original signal to \(\delta\) approaching 0.5, and then the frequency of the signal after the frequency shift is accurately estimated by the Rife method, which reduces the estimation error of the whole frequency range. The algorithm is detailed as follows:  
(1) In the frequency-amplitude mean curve of FSWT, the serial number \(k\) corresponding to the peak spectral line of the narrowband interference frequency and the serial number \(k+r\) of the sub-amplitude spectral line are obtained, and the amplitude corresponding to the spectral line is found: \(R(k)\), \(R(k+r)\).  
(2) Calculate the correction value \(\sigma\), as shown in (22).  
\[\sigma=\frac{|R(k+r)|}{|R(k+r)|+|R(k)|},r=\pm 1 \tag{22}\]  
(3) Obtain the estimated frequency \(f_{r}\) of the narrowband interference. The calculation of \(f_{r}\) is given by the following:  
\[f_{r}=\frac{f_{s}}{N}\times(k+\sigma) \tag{23}\]  
In (23), \(f_{s}\) is the sampling frequency and \(N\) is the number of sampling points.  
(4) According to the estimated frequency \(f_{r}\), the frequency shift of the spectral line in \(k\) and \(k+r\) is carried out. The frequency shift distance \(f_{d}\) is given in (24), and the peak value \(R(k)\) and \(R(k+r)\) of the spectral line in \(k\) and \(k+r\) after the frequency shift is obtained.  
\[f_{d}=(k+0.5)\times\frac{f_{s}}{N}-f_{r} \tag{24}\]  
(5) Step (2) and Step (3) are carried out again to obtain the accurate frequency estimation of the narrowband interference signal.  
This improved Rife method is used to estimate the narrowband interference frequency of the noisy PD signal in Figure 1c. The estimation results are shown in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline peak point & \(\backslash\)1 & \(\backslash\)2 & \(\backslash\)3 & \(\backslash\)4 & \(\backslash\)5 & \(\backslash\)6 & \(\backslash\)7 \\ \hline skewness value & \(-0.71\) & \(-0.42\) & \(-1.16\) & \(0.46\) & \(-0.94\) & \(-0.81\) & \(2.77\) \\ \hline \end{tabular}
\end{table}
Table 3: Skewness value of peak frequency.  
According to Table 4, the improved Rife method can estimate the narrowband interference frequency well. At the same time, its calculation is simple, enhancing efficiency and fitting for PD online monitoring.