Filtering and Planning in Information Spaces

This tutorial presents a fresh perspective on modeling sensors and then using them for filtering and planning. The concepts and tools are motivated by many problems of current interest, such as tracking, monitoring, navigation, pursuit-evasion, exploration, and mapping. First, an overview of sensors that appear in numerous systems is presented. Following this, the notion of a virtual sensor is explained, which provides a mathematical way to model numerous sensors while abstracting away their particular physical implementation. Dozens of useful models are given. In the next part, a new perspective on filtering is given based on information spaces. This includes classics such as the Kalman and Bayesian filters; however, it also opens up a new family of reduced-complexity filters that try to maintain as little information as possible while performing their required task. Finally, the planning problem is presented in terms of filters and information spaces.