Performing detailed work on objects requires precise localization. Currently humans aid machines in localization either by direct operation, or implicitly by designing a sequence of actions a robot follows. Our approach to automate localization is to reason over many potential actions, perform the best information gathering action, and then use the mea- surement obtained to update a non-Gaussian belief. We propose a method for autonomous localization of objects with initial 6DOF uncertainty capable of reasoning about and performing measurements with low uncertainty and arbitrary error models. Surprisingly, common methods capable of modeling arbitrary belief distributions perform poorly as measurement uncertainty decreases, so we modify a particle filter to handle these accurate measurements produced by tactile or laser sensors. We then show how the expected information gain of the proposed measurement can be calculated efficiently from these particles. We present experiments, both in simulation and on hardware, that show our method is both fast and accurate.