Many tasks in active perception require that we be able to combine different information from a variety of sensors that relate to one or more features of the environment. Prior to combining these data, we must test our observations for consistency. The purpose of this paper is to examine sensor fusion problems for linear location data models using statistical decision theory (SDT). The contribution of this paper is the application of SDT to obtain: (i) a robust test of the hypothesis that data from different sensors are consistent; and (ii) a robust procedure for combining the data that pass this preliminary consistency test. Here, robustness refers to the statistical effectiveness of the decision rules when the probability distributions of the observation noise and the a priori position information associated with the individual sensors are uncertain. The standard linear location data model refers to observations of the form: Z = ϴ + V, where V represents additive sensor noise and ϴ denotes the "sensed" parameter of interest to the observer. While the theory addressed in this paper applies to many uncertainty classes, the primary focus of this paper is on asymmetric and/or multimodal models, that allow one to account for very general deviations from nominal sampling distributions. This paper extends earlier results in SDT and multi-sensor fusion obtained by [Zeytinoglu and Mintz, 1984], [Zeytinoglu and Mintz, 1988], and [McKendall and Mintz, 1988].