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Approximate Inference for Localization

This document outlines a sensor network situation where approximate inference is used for localization. The basic assumptions made for simplification are described, however the locations are not explicitly denoted. This is the first of several lectures on this topic. The next few lectures revolve around a sensor network example, where the goal is to determine the location and number of targets in a field with sound sensors scattered in that field. This particular example can be extended or modified to apply to just about virtually every type of sensor data used for localization, with only the mathematical models for propagation needing to be modified. This document is not intended to walk someone through the entire process of an aproximate inference problem. Rather, our goal here is to set up the framework for thinking about these problems, and provide an example of what a problem would look like. The notation outlined will be followed through this document.