Measurements are never absolutely accurate, the measurement result X is, in general, different from the actual (unknown) values x of the corresponding quantity. In many practical problems, we only know upper bounds D on the measurement errors d = X - x. In such situations, once we know the measurement result, the only conclusion that we can make about the actual value x is that this value belongs to the interval [X - D, X + D]. There exist many efficient algorithms for processing such interval data. However, these algorithms usually assume that all the measurement results are valid. In reality, due to factors such as sensor malfunction, some measurement results may be way off (outliers), for which the difference between X and x is much larger than the upper bound D on the measurement error. In this paper, we overview the algorithmic problems related to processing interval sensor data in the presence of outliers. Our case study -- for which we develop and analyze these algorithms -- is localization of underwater robots, a problem in which a significant number of measurement results are outliers.