# Cross-Correlation Wavelet-Domain-Based Particle Swarm Optimization for Lightning Mapping
###### 1 Introduction  
Accurate lightning mapping is a key step to real-time detection of lightning strikes. There has been a growing interest in understanding the process in which lightning propagates. Researchers often study lightning over a specific range of frequencies such as very high frequency (VHF). The lightning mapping is then performed using, magnetic direction finder, time of arrival, or interferometer (ITF) [1]. The ITF has been recognized as superior, compared to the other techniques, due to its capability of scanning more lightning events and performing continuous and quasi-continuous emission mapping from lightning pulses for enhanced 2D visualization [2]. Several ITF-based techniques have been proposed to estimate the lightning maps [3, 4, 5, 6, 7]. Some of these techniques implement phase difference of arrival (PDOA) for windowed signals arriving at each pair of ITF sensors, such as the work proposed by [7]. Others used the time difference of arrival (TDOA) and cross-correlation in both time and frequency domains [3, 5, 8]. Similar to Stock [4], the TDOA was used in [3], with the implementation of wavelet-domain cross-correlation. Despite the major progress made in this field, there is still a need for further enhancement, especially in developing more robust techniques that are able to locate the lightning emissions and optimize the process of lightning mapping. These improvements include but are not limited to (1) automatic extraction of the exact lightning events from ITF signals; (2) in the preprocessing phase, particularly the noise filtering, it must be carefully designed so that the relevant lightning information is not destroyed and reserved for the next processing steps; (3) tuning of different parameters involved in the cross-correlation procedure such as the sliding window length. In this context, some optimization techniques have been shown to be successful in hyperparameter tuning. Among these methods, particle swarm optimization (PSO) is a simple yet powerful optimization algorithm and has been applied to numerous applications in various fields of science and engineering, such as machine learning, image processing, data mining operation research, etc. [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. However, PSO has some characteristics that, in some sense and to a certain extent, have some similarity to those found in other population-based computational models, such as genetic algorithms (GAs) and other evolutionary computing techniques. A key underlying feature of the PSO algorithm is that it is a simple- to implement, powerful tool that has only a few parameters to be set. Additionally, it is effective in global search, and it is easily parallelized for concurrent processing. In fact, its simplicity and apparent competence in finding optimal solutions in complex search spaces led the PSO algorithm to become well known among the scientific community, which contributed to its study and improvement [20]. Several studies have used optimization-based techniques in related lightning research. [PERSON] et al. [21] applied the PSO optimization method to find the optimum value of the lightning position and the occurrence time. [PERSON] et al. [22] proposed a two-step procedure that uses the PSO algorithm to optimize the lightning positions (i.e., 2D space). Alternatively, [PERSON] et al. [23] proposed a PSO-based technique to optimize the reconstruction process of the return stroke current waveform. For the cross-correlation-based methods, the selection of appropriate sliding widow length could influence the performance of the lightning mapping system. However, the optimal window length for lightning has not been explored. In this paper, we proposed a cross-correlation wavelet-domain-based particle swarm optimization (CCWD-PSO) technique to improve the performance of lightning mapping. Additionally, we proposed a lightning-event extraction method, which reduces the overall computational cost of the lightning mapping process.