We address the problem of robot localization using ground penetrating radar (GPR) sensors. Current approaches for localization with GPR sensors require a priori maps of the system's environment as well as access to approximate global positioning (GPS) during operation. In this paper, we propose a novel, real-time GPR-based localization system for unknown and GPS-denied environments. We model the localization problem as an inference over a factor graph. Our approach combines 1D single-channel GPR measurements to form 2D image submaps. To use these GPR images in the graph, we need sensor models that can map noisy, high-dimensional image measurements into the state space. These are challenging to obtain a priori since image generation has a complex dependency on subsurface composition and radar physics, which itself varies with sensors and variations in subsurface electromagnetic properties. Our key idea is to instead learn relative sensor models directly from GPR data that map non-sequential GPR image pairs to relative robot motion. These models are incorporated as factors within the factor graph with relative motion predictions correcting for accumulated drift in the position estimates. We demonstrate our approach over datasets collected across multiple locations using a custom designed experimental rig. We show reliable, real-time localization using only GPR and odometry measurements for varying trajectories in three distinct GPS-denied environments. For our supplementary video, see https://youtu.be/HXXgdTJzqyw.