The Analytical Expression of Lightning Channel Base Current by Lorentzian Pulse Fitting

Aiming for the robustness improvement in a noisy environment, we propose a new representation method based on Lorentzian pulse fitting for the analytical expression process of the measured lightning channel base current (LCBC) in this article. The Lorentzian pulse train is determined only by a finite number of free parameters, which can be estimated from the high-energy part of the LCBC signal spectrum. To obtain Fourier coefficients from the LCBC measurements, we design a sum-of-sinc digital filter. In addition, we propose a denoising algorithm based on nuclear norm minimization to improve the accuracy of the parameter estimation process. By using only the high-energy spectrum region, our method is more resistant to noise during the fitting process. Furthermore, although the Lorentzian pulse fitting method cannot strictly achieve the value of LCBC as 0 at the time of
$t=0_+$
, it provides a simple and integrable expression form in the time domain, which has great application value in the analysis of lightning magnetic field characteristics. Simulation results demonstrate that our proposed method achieves higher analytical expression accuracy for LCBC signal in noisy environments than the classical versions, both in terms of the signal itself and its first derivative.