全波形LiDAR数据分解的可变分量高斯混合模型及RJMCMC算法

传统激光雷达(light detection and ranging,LiDAR)数据处理均采用固定数的波形分解方法,容易遗漏部分重叠的返回波,降低波形拟合精度。为了实现可变数波形分解,本文提出了一种自动确定波形分解数的方法。假定波形数据服从混合高斯分布,并以此建立理想的波形模型;定义用于控制理想模型与实际波形拟合程度的能量函数,用吉布斯分布构建或然率;根据贝叶斯定理构建刻画波形分解的后验概率模型;设计可逆跳转马尔科夫链蒙特卡洛(reversible jump Markov chain Monte Carlo,RJMCMC)算法模拟该后验概率模型,以确定波形分解数并同时完成波形分解。为了验证提出算法的正确性,分别对不同区域的ICESat-GLAS波形数据进行了波形分解试验,定性和定量分析结果验证了本文方法的有效性、可靠性和准确性。

Gaussian Mixture Model with Variable Components for Full Waveform LiDAR Data Decomposition and RJMCMC Algorithm

Full waveform LiDAR data record the signal of the backscattered laser pulse. The elevation and the energy information of ground targets can be effectively obtained by decomposition of the full waveform LiDAR data. Therefore, waveform decomposition is the key to full waveform LiDAR data processing. However, in waveform decomposition, determining the number of the components is a focus and difficult problem. To this end, this paper presents a method which can automatically determine the number. First of all, a given full waveform LiDAR data is modeled on the assumption that energy recorded at elevation points satisfy Gaussian mixture distribution. The constraint function is defined to steer the model fitting the waveform. Correspondingly, a probability distribution based on the function is constructed by Gibbs. The Bayesian paradigm is followed to build waveform decomposition model. Then a RJMCMC (reversible jump Markov chain Monte Carlo) scheme is used to simulate the decomposition model, which determines the number of the components and decomposes the waveform into a group of Gaussian distributions. In the RJMCMC algorithm, the move types are designed, including updating parameter vector, splitting or merging Gaussian components, birth or death Gaussian component. The results obtained from the ICESat-GLAS waveform data of different areas show that the proposed algorithm is efficient and promising.