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.