基于近端算子PHMC的机载雷达高度表参数估计

Elevation parameter estimation for radar altimetry using Proximal Hamiltonian Monte Carlo

摘要:

传统雷达高度表参数估计算法在面对参数的高维特性时会出现过拟合情况，导致参数估计精确度降低。为此，提出一种新颖的基于近端算子修正的哈密顿蒙特卡洛(PHMC)算法，通过统计学的手段估计高程参数。首先假设高程参数具有稀疏特性，并使用拉普拉斯分布对其进行表征，这种稀疏先验可表征高程突变的地形场景。稀疏先验与似然函数之间为非共轭关系，使用分层贝叶斯的方法获得后验分布函数的闭合解，采用哈密顿蒙特卡洛(HMC)方法通过采样的方式解决贝叶斯推论中的参数估计问题，引入近端算子提供次梯度完成参数估计。仿真数据验证了所提PHMC算法优于其他传统算法。

Abstract:

Conventional radar altimetry parameter estimation algorithms often suffer from overfitting due to the high dimensionality of the parameters to be estimated. To this end, a novel Proximal Hamiltonian Monte Carlo(PHMC) algorithm is proposed to estimate the elevation parameters in a statistical way. More specifically, Laplace distribution is employed to characterize the sparse prior to achieve the confidence estimation for the elevation parameters. This prior can depict the terrain scenes with abrupt elevation changes. However, due to the non-conjugation between the sparse prior and Gaussian likelihood function, the hierarchical Bayesian is employed to obtain the closed-form solution of posterior distribution function. To overcome the difficulty of the Bayesian inference of high-dimensional posterior, the Hamiltonian Monte Carlo(HMC) is utilized to solve the parameter estimation problem in fully Bayesian inference. Since the potential energy obtained by posterior distribution does not satisfy the differentiable requirement of HMC, the proximal operator is applied to provide the sub-gradient to estimate parameters. Comparisons with the results using synthesis and practical data have demonstrated the superiority of the proposed PHMC over other conventional algorithms.