基于分组LM算法的全波形LiDAR高斯分解

Gaussian Decomposition of Full- waveform Li DAR Based on Grouping LM Algorithm

LM(Levenberg-Marquardt)算法是全波形机载激光雷达(Li DAR)数据高斯分解中求解模型参数的一种方法。针对其结果在一定程度上依赖初值、雅克比矩阵出现非数值导致无结果等问题,本文提出分组LM算法,以广义高斯混合函数为模型,模型参数初始化后,将参数分组并使用LM算法依次对各组参数进行优化,并生成点云。为验证结果的可靠性,以系统点云为参考,与基于改进的EM(Expectation Maximum)算法全波形分解法做对比。结果表明,本方法不仅得到较高质量的点云,而且得到回波位置和宽度等信息。

LM （Levenberg -Marquardt） algorithm is a traditional method to solve model parameters of Gaussian decomposition in full - waveform LiDAR data. This paper employs the generalized Gaussian mixture function to fit the mathematical model of waveform, and then grouping LM algorithm is used to optimize parameters of the function. It has been shown that grouping LM algorithm used in this paper overcomes the common drawbacks of the traditional LM algorithm such as the final results are influenced by the initial parameters, possible algorithm interruption caused by non -numerical entries occurred in the Jacobian matrix, etc. Precision is evaluated by comparing between the point cloud generated by the proposed algorithm and those provided by the system. The proposed algorithm in this paper is further compared to the improved EM （Expectation Maximum） based waveform decomposition algorithm. The results show that the proposed algorithm can not only generate high quality point cloud, but also extract other information such as echo location, width of the wave, etc, which could be used in further applications.