We present an iterative overlap estimation technique to augment existing point cloud registration algorithms that can achieve high performance in difficult real-world situations where large pose displacement and non-overlapping geometry would otherwise cause traditional methods to fail. Our approach estimates overlapping regions through an iterative Expectation Maximization procedure that encodes the sensor field-of-view into the registration process. The proposed technique, Expected Overlap Estimation (EOE), is derived from the observation that differences in field-of-view violate the iid assumption implicitly held by all maximum likelihood based registration techniques. We demonstrate how our approach can augment many popular registration methods with minimal computational overhead. Through experimentation on both synthetic and real-world datasets, we find that adding an explicit overlap estimation step can aid robust outlier handling and increase the accuracy of both ICP-based and GMM-based registration methods, especially in large unstructured domains and where the amount of overlap between point clouds is very small.