The purpose of this report is to describe research in sensor fusion with statistical decision theory in the GRASP Lab, Department of Computer and Information Science, University of Pennsylvania. This report is thus a tutorial overview of the general research problem, the mathematical framework for the analysis, the results of specific research problems, and directions of future research. The intended audience for this report includes readers seeking a self-contained summary of the research as well as students considering study in this area. The prerequisite for understanding this report is familiarity with basic mathematical statistics.