Above Ground Level Estimation for Radar Altimetry Using Proximal Hamiltonian Monte Carlo

Abstract

The parameter estimation of conventional radar altimetry waveform often suffers from overfitting due to the high dimensionality on a succession of echoes. To this end, a novel proximal Hamiltonian Monte Carlo (PHMC) algorithm is proposed in this article to estimate the altitude in a statistical manner. More specifically, the Laplace distribution is used to encode the nonsmoothness in the estimation of the elevation parameter of the detection area. However, as the nonconjugation between the sparse prior and Gaussian-likelihood function, the hierarchical Bayesian strategy is employed for the closed-form posterior solution. To overcome the difficulty of fully Bayesian inference on high-dimensional posterior, the PHMC is utilized. Specifically, in order to obtain an available gradient of the nondifferentiable potential energy, the proximal operator is adopted to provide the subgradient to estimate parameters. Both the results using simulation and practical data demonstrate the superiority of the proposed PHMC over other conventional algorithms.