## 3 CC-VC-UKF
### Relationship between the CC-VC and the UKF  
When the noise does not satisfy the Gaussian distribution and the mean value is non-zero, the UKF is insensitive to the above noise and is prone to large estimation errors. The center of the variable center cross-correlation entropy criterion can be located at any position [20]; thus, it can effectively match the non-zero mean non-Gaussian deviation distribution. As a result, the VC cross-correlation entropy criterion is used to replace the mean square error criterion in the unscented Kalman filter.  
As shown in Figure 2, in the measurement update of the unscented Kalman filtering algorithm, the covariance matrix can be obtained by the weighted summation of the observed and predicted values of the Sigma point set in the time update. According to the mean square error criterion, the Kalman gain can be obtained directly from the following equation: \(\widetilde{\text{K}}_{i}=\widetilde{P}_{xy,i}\widetilde{P}_{yy,i}^{-1}\). The CC-VC-UKF algorithm obtains the indeterminate-point iterative equation according to the minimized cross-correlation entropy, as well as the Kalman gain through indeterminate-point iteration.  
Figure 2: UKF algorithm derivation flowchart.  
Combined Spatiotemporal Cleaning of Measurement Data in the Distribution Network Based on the CC-VC-UKF Algorithm  
Complex physical connections exist between various nodes and lines in the power grid, with a strong correlation [23]. Therefore, the measurement data collected by the measurement device also have a time and space correlation, as shown in Figure 3.  
The active daily load curve of FTU measurement for 30 days is obtained from the field measured data, as shown in Figure 4. The change trend of the measured data changes periodically in time. The time series shows that the observation points after a time interval are similar, and the daily load curves of adjacent days are similar. At the same time, network topology constraints and power flow constraints are found between various nodes of the power grid [24]. In addition, as shown in the schematic topology diagram of the power flow in Figure 5, the measurement data have a spatial correlation. Therefore, this study introduces the variable center cross-correlation entropy function into the unscented Kalman filter algorithm and performs filtering and cleaning based on the spatiotemporal correlation of the measurement data, which allows for significant improvements in the accuracy and data quality of the final cleaned data in the presence of non-zero mean non-Gaussian distributed spatial measurement deviations.  
Figure 4: FTU that measures the 30-day active power daily load curve.  
Figure 3: Temporal and spatial correlation of distribution network measurement data.  
The specific process of the multilevel data filtering and cleaning technology based on space and time is shown in Figure 6. In the whole process, all filtering algorithms adopt the CC-VC-UKF algorithm to deal with the measurement deviation of a non-zero mean and non-Gaussian distribution. The measurement data of the measurement equipment at different positions of the line are temporally filtered according to the respective reference time series to improve the quality of the measurement data. After filtering the data by the measuring equipment, the spatial measurement deviation after filtering and the line end measurement data after secondary filtering can be obtained. Finally, according to the network topology relationship in the figure, the measurement data of the head end of the line can be obtained after the spatiotemporal joint filtering and cleaning.