The multi-echo decomposition algorithm for LiDAR based on the Asymmetric Generalized Gaussian function

Waveform decomposition technology is one of the core technologies in full-waveform LiDAR ranging. When using a multi-echo decomposition algorithm based on traditional mathematical functions to decompose multi-echo pulses, issues such as low ranging accuracy, limited scope of application, and poor practicality often arise. To address these challenges, a multi-echo decomposition algorithm based on the Asymmetric Generalized Gaussian (ASGG) function is proposed. This algorithm determines the bilateral shape coefficients of the ASGG function based on the response of the lidar system, resulting in an echo pulse model that accurately describes the morphology of the echo pulse and features parameters with high interpretability. This enables high-accuracy and high-robustness multi-echo decomposition. Indoor experiments were conducted using two LiDAR systems with different response characteristics to collect multi-echo data of various shapes for validation. The results demonstrate that the multi-echo decomposition algorithm based on the ASGG function exhibits stable and superior decomposition performance. Specifically, when dealing with asymmetric echo pulses and the presence of small-amplitude echoes that are difficult to detect, the decomposition algorithm based on the ASGG function improves the absolute ranging accuracy by 20.69 times, 22.07 times, and 17.38 times, respectively compared to decomposition algorithms based on the Gaussian function, generalized Gaussian function, and exponential Gaussian function. Additionally, the ranging repeatability accuracy is enhanced by 2.46 times, 3.02 times, and 2.13 times. The root mean square error (RMSE) of the waveform fitting is reduced by 1.14 times, 1.14 times, and 0.83 times, respectively, and the goodness of fit R² reaches 0.9995. When processing multi-echo data of different shapes collected by the same device or similar shapes collected by different devices, the degradation of the absolute ranging accuracy is only about 30% of that of other functions.