Abstract: Range imaging of laser radar can reflect the targets geometry structure, and different poses of the same target lead to a tremendous variety of range imaging. Thus pose estimation is especially important for automated target recognition (ATR). Ulf Grenander's pattern theory makes use of deformable template to represent observed image and model the variability of target pose via the actions of the matrix special orthogonal group. In Bayesian estimation framework, it samples from posterior to empirically generate the estimates using jump-diffusion process. Error analysis of pose estimation makes use of the Hilbert-Schmidt norm as an error metric. Our work focuses on pose estimation of ground-based targets of range imaging, using Ulf Grenander's pattern theory to estimate vehicle in differe