Echo decomposition of full-waveform LiDAR based on a digital implicit model and a particle swarm optimization

In the waveform decomposition of full-waveform LiDAR, the Gaussian model (GSM) and the generalized Gaussian model (GGSM) are widely used to extract echoes from return waveforms. However, those models have explicit functions that follow specific distribution shapes, so they are suitable only for decomposing echo waveforms with similar shapes. This paper introduces a digital implicit model (DIM) and presents a universal decomposition method for the full-waveform LiDAR. In this method, the decomposition model is considered to be an implicit function, associated with a digital template waveform library, whose optimization is implemented by a modified particle swarm algorithm. The template waveform library is a customized fingerprint for any special full-waveform LiDAR, so the DIM can deal effectively with infinite echoes with arbitrary shapes. A full-waveform LiDAR system with asymmetric echo distribution is designed to compare the decomposition performances among the GSM, GGSM, and DIM. Experimental results show that, when decomposing the return waveform containing a single echo, the normalized sum of squares due to fitting error (SSE) of the DIM can be 60 times lower than the GSM and the GGSM. By comparing the estimation accuracies of the amplitude, the FWHM and the location of the echo component, the DIM has the best decomposition performance and the best ranging accuracy (subcentimeter level) among the three models; when decomposing the return waveform containing three overlapping echoes, the normalized SSE of the DIM can be 28 times lower than the GSM and 12 times lower than the GGSM. By comparing the estimation accuracies of the amplitude, FWHM, and location of echoes components, the DIM has the best decomposition performance and best ranging accuracy (centimeter level) among the three models.