# Kalman Filter and Wavelet Cross-Correlation for VHF Broadband Interferometer Lightning Mapping
## 3 Results and discussion
### Real Data Results  
The main challenge of source localization is to identify the radiation emitted by the source out of noisy signals received by the measuring ITF system. Figure 8 shows an example of a positive narrow bipolar event (NBE). Figure 9 shows measured VHF signals related to a lightning flash triggered by the discharge process of the NBE, as observed in Figure 8. This measurement represents a time expanded window of 20 us (5000 samples). The observed signals of antenna B and D show significant similarity with possible phase shift or a time lag. However, the signal of antenna C shows slightly different noise characteristics.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c c c c c} \hline \hline
**Correlation Method** & \multicolumn{4}{c}{**CCT**} & \multicolumn{4}{c}{**CUD**} & \multicolumn{4}{c}{**CUD**} & \multicolumn{4}{c}{**CUD**} & \multicolumn{4}{c}{**CUD**} \\
**Inorg. Method** & \multicolumn{4}{c}{**Linear**} & \multicolumn{4}{c}{**CUD**} & \multicolumn{4}{c}{**CUD**} & \multicolumn{4}{c}{**CUD**} & \multicolumn{4}{c}{**CUD**} & \multicolumn{4}{c}{**CUD**} \\
**Inorg. Method** & **1** & **2**  
In the simulation results shown before, it is noted that the wavelet-based CCWD method produced the best performance of lightning mapping using the Symlet function with linear interpolation of level 8. Therefore, the same setup is implemented for real lightning data mapping.  
Figure 10 shows the constructed map of the lightning source location for positive NBE. The starting position of radiation sources was in the higher altitude about 66\({}^{\circ}\) elevation. However, these detected sources are isolated from the well-defined lightning channel and considered outliers. The colour changes in Figure 10a with time from blue to green, corresponding to the lightning progression time in Figure 9. It can be seen that the channel from the bottom (23\({}^{\circ}\) elevation) to the 32\({}^{\circ}\) elevation was approximately straight with small changes in azimuth angles range, corresponding to the trajectory of the lightning flash. Up to the 32\({}^{\circ}\) elevation, the shape and the height of the channel showed certain consistency with the observation of positive NBE. In Figure 10b, the radiation elevation angles and fast electric field change observations (black waveform) are superimposed on the VHF waveform (gray), showing the downward propagation of the VHF source. The negative electric field waveform is indicative of an upward-directed current, consistent with a positive NBE. Overall, all three filtering methods implemented in this paper show comparable accuracy for this lightning mapping with some errors that could result from the limited windowing approach conducted in this study, or due to the existing in-band hardware-interference noises when collecting the data. To avoid such noise effects, it is better to properly filter the analog signal from the antennae before the signal is digitized, such that extreme noises contaminate no portion of the bandwidth which contributes to the cross-correlation.  
Figure 8: Fast Electric field pulse relevant to a positive NBE.  
Figure 9: The VHF radiation signals associated with positive NBE received by antennae B, C, and D.