Consider an unmanned aerial vehicle (UAV) that searches for an unknown number of targets at unknown positions in 3D space. A particle filter uses imperfect measurements about the targets to update an intensity function that represents the expected number of targets. We propose a receding-horizon planner that selects the next UAV position by maximizing a joint, exploration and target-refinement objective. Confidently localized targets are saved and removed from consideration. A nonlinear controller with an obstacle-avoidance component is used to reach the desired waypoints. We demonstrate the performance of our approach through a series of simulations, as well as in real-robot experiments with a Parrot Mambo drone that searches for targets from a constant altitude. The proposed planner works better than a lawnmower and a target-refinement-only method.