Calculation Methods and Comparison for Lightning Optical Return-Stroke Speed

The optical return-stroke speed calculation is vital to analyze the lightning development process. The traditional calculation methods of lightning optical return-stroke speed, including the slope-intercept and percentage-of-peak methods, usually have considerable calculation errors in noise cases. In this article, we generate the simulated optical return-stroke signal within 100 m above the starting point along the lightning channel and use four cross-correlation methods and six traditional methods to calculate the return-stroke speed at different observation points along the channel. We optimize the cross-correlation method and reduce the calculation error to within +/- 10% by selecting a part of the waveform to participate in the cross-correlation operation and performing the exponential operation on the frequency-domain cross-correlation sequence. The calculation results of the quadratic-correlation method and two optimized cross-correlation methods do not change significantly at different observation points along the channel. Different channel-base waveforms affect the return-stroke speed variation trend. The smaller the dispersion factor $\lambda_p$ is, the more pronounced the variation of the calculation result is, and the greater the calculation error is. The optical waveform with generated Gaussian noise will significantly affect the traditional calculation method. In contrast, the cross-correlation calculation method with noise has only a tiny calculation error.