An information-driven autonomous robotic exploration method on a continuous representation of unknown environments is proposed in this paper. The approach conveniently handles sparse sensor measurements to build a continuous model of the environment that exploits structural dependencies without the need to resort to a fixed resolution grid map. A gradient field of occupancy probability distribution is regressed from sensor data as a Gaussian process providing frontier boundaries for further exploration. The resulting continuous global frontier surface completely describes unexplored regions and, inherently, provides an automatic stop criterion for a desired sensitivity. The performance of the proposed approach is evaluated through simulation results in the well-known Freiburg and Cave maps.