针对传统方法难以实现全波激光雷达数据中非对称波形分解的问题, 本文提出一种结合可变分量偏正态模型和可逆跳马尔科夫链蒙特卡洛(RJMCMC)算法的波形分解方法。首先, 利用能量函数刻画服从偏正态分布的理想波形与实际波形间的差异程度, 并用Gibbs分布定义其似然函数; 然后, 定义理想波形参数模型的先验分布; 在贝叶斯定理框架下, 建立具有分量可变性的波形分解模型; 设计RJMCMC的移动操作, 确定偏正态分布中的分量数以及求解模型参数。利用提出算法, 对不同波形特征(偏态、正态)的ICESat-GLAS全波激光雷达数据进行可变分量分解实验。实验结果表明: 实验波形结果与实际波形数据相关系数达到0.989以上, 所提方法不仅能够同时实现对偏态数据和正态数据的拟合, 还能更为准确地确定波形分量数。证明了该方法能实现全波激光雷达数据的精确分解, 且分解结果与对应地物高程信息相符。

To decompose asymmetric full-waveform LiDAR data with unknown number of components, a full-waveform LiDAR decomposition method was proposed based on skew-normal distribution and reversible-jump Markov Chain Monte Carlo (RJMCMC) algorithm, which can automatically determine the numbers of components. First, the energy function was used to describe the differences between the actual waveform and the ideal waveform that obeyed the skew-normal distribution, and the likelihood function was defined by Gibbs distribution. Second, the parameter models of the ideal waveform were established using the prior distribution. Then the Bayesian paradigm was followed to build the ideal waveform model. Third, an RJMCMC algorithm was designed to determine the numbers of components and decompose the waveform. The proposed algorithm was used to decompose ICESat-GLAS waveform data in various typical regions. Experimental results indicate that the cross-correlation of the true data and the result is up to 98.9%. The proposed method can not only fit the skewed waveform data and normal waveform data, but also more accurately determine the number of components in comparison to other methods. It can realize the accurate decomposition of full-waveform LiDAR data, and the decomposition result is consistent with the corresponding elevation information.