Decomposition of small-footprint full waveform LiDAR data based on generalized Gaussian model and grouping LM optimization

Full waveform airborne Light Detection And Ranging(LiDAR) data contains abundant information which may overcome some deficiencies of discrete LiDAR point cloud data provided by conventional LiDAR systems. Processing full waveform data to extract more information than coordinate values alone is of great significance for potential applications. The Levenberg-Marquardt (LM) algorithm is a traditional method used to estimate parameters of a Gaussian model when Gaussian decomposition of full waveform LiDAR data is performed. This paper employs the generalized Gaussian mixture function to fit a waveform, and proposes using the grouping LM algorithm to optimize the parameters of the function. It is shown that the grouping LM algorithm overcomes the common drawbacks which arise from the conventional LM for parameter optimization, such as the final results being influenced by the initial parameters, possible algorithm interruption caused by non-numerical elements that occurred in the Jacobian matrix, etc. The precision of the point cloud generated by the grouping LM is evaluated by comparing it with those provided by the LiDAR system and those generated by the conventional LM. Results from both simulation and real data show that the proposed algorithm can generate a higher-quality point cloud, in terms of point density and precision, and can extract other information, such as echo location, pulse width, etc., more precisely as well.