Generalized Gaussian decomposition for full waveform LiDAR processing

Waveform decomposition techniques are commonly used to extract attributes of targets from light detection and ranging (LiDAR) waveforms. Since the shape of a real LiDAR waveform varies for different systems, the conventional models (e.g. the Gaussian function, lognormal function, and generalized normal function) cannot be universally used. In this paper, we present a generalized Gaussian decomposition (GGD) algorithm, which considers the received waveform as the convolution of an arbitrary system waveform with the target response assumed as a Gaussian mixture model. The proposed method was validated using the experimental waveforms sampled from our self-designed LiDAR system with two different system responses. Metrics, including the mean absolute error (MAE) for range retrieval and the root-mean-squared error (RMSE) for waveform fitting, were used to provide a comprehensive quantitative evaluation of the performance. Three classical models for waveform decomposition-the Gaussian, lognormal, and generalized normal functions-were introduced and studied for the comparison. As for the system waveform with a right-skewed profile, the experimental results showed that the GGD algorithm provided the lowest RMSE for waveform fitting, and the most accurate range estimates with an MAE of 0.030 m. The Gaussian decomposition (GD), lognormal decomposition (LND), and generalized normal decomposition (GND) algorithms produced much worse results with MAEs of 0.362, 1.091, and 0.417 m, respectively. As for the system waveform with a negative tail, the GGD algorithm also performed best with an MAE of 0.019 m, while the GD, LND and GND algorithms provided much larger MAEs of 0.457, 0.489, and 0.354 m, respectively. Therefore, the proposed method has the potential to extract more accurate model parameters from a variety of LiDAR waveforms regardless of the shape of the system waveform.