## 5 Numerical Results
### Experimental Result Verification  
The original data sequence with no more than 1% vacancy is selected as the experimental set, and the data are set to be empty; the data sequence is cleaned according to a random proportion. Then, the proposed method is used to clean the data sequence, and the null values in the data sequence are used as the predicted values of the gap after data cleaning. The gap predictions are compared with the original values, and the mean absolute percentage error (MAPE), root mean square error (RMSE) [25], mean absolute error (MAE) [11], and signal-to-noise ratio (\(SNR\)) are calculated. The formula for calculating SNR is as follows:  
\[SNR=\frac{\sum(y_{i}-\overline{y})^{2}-\sum(y_{i}-\hat{y}_{i})^{2}}{\sum(y_{i }-\hat{y}_{i})^{2}} \tag{25}\]  
where \(y_{i}\) represents the original data value corresponding to the moment when the set data value is empty, \(\hat{y}_{i}\) represents the predicted value of the vacancy, and \(\overline{y}\) represents the average value of the original data value.  
This study compares the data cleaning of the random forest algorithm [26], the LSTM algorithm [27], and the deep neural network algorithm [28]. It also applies the CC-VC algorithm to the traditional extended Kalman filter (EKF). The comparative experimental results are shown in Table 1. In addition, to display the comparison results more clearly, the corresponding data cleaning indicator radar chart is shown in Figure 16. The figure shows that compared with the advanced algorithms published in the past two years, the proposed data cleaning algorithm still has certain advantages in improving data cleaning accuracy and data quality, which is helpful for the processing and storage of measurement data by subsequent power distribution terminals.  
Figure 15: Comparison of the 30 th sky interval measurement deviation before and after filtering.  
In addition, for the measurement of data sequences at different measurement time points, the Gaussian filtering algorithm, the wavelet threshold algorithm [5], and the algorithm in this study are used to filter the calculated time consumption. The data are completed on a computer with a platform CPU of 2.1 GHZ and a memory of 16 GB to study the time complexity of the proposed algorithm. The results are shown in Table 2.  
The table shows that when the measurement time point is 60, the CC-VC-UKF algorithm consumes about 95% more time than the wavelet threshold algorithm. When the measurement time point is 576, the corresponding consumption time increases by about 28%. This finding shows that with the increase in measurement time points, the time complexity gap of the CC-VC-UKF algorithm compared with other algorithms gradually narrows. When the scale of the measurement data is sufficiently large, the difference of the time complexity of the algorithm compared with other algorithms can be ignored.  
In addition, given that the proposed algorithm is aimed at offline data, it can satisfy the data cleaning requirements without considering the real-time performance.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **MAPE** & **RMSE(MW)** & **MAE(MW)** & **SNR** \\ \hline Random Forest & 9.4527\% & 7.7264 & 8.0462 & 8.7561 \(\times\) 10\({}^{-5}\) \\ LSTM & 8.7819\% & 7.3861 & 7.5257 & 8.9366 \(\times\) 10\({}^{-5}\) \\ Deep Neural Network & 8.4667\% & 6.9628 & 6.4102 & 9.3422 \(\times\) 10\({}^{-5}\) \\ CC-VC-EKF & 10.0353\% & 8.4243 & 7.6343 & 9.2547 \(\times\) 10\({}^{-5}\) \\ Algorithm of this paper & 7.8918\% & 6.8967 & 5.8653 & 9.8751 \(\times\) 10\({}^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of filtering results of different algorithms.  
Figure 16: Comparison results of different algorithms.