The Geometry of Active Sensing

An autonomous system needs “active sensing” to decide which combination of action and sensing is expected to give the largest increase in information. This paper deduces the intrinsic properties of information and sensor processing from first principles, and combines them to define active sensing in a coordinate-free way. Intrinsic properties don’t depend on the choice of coordinates, reference frames or physical units, so differential geometry is the appropriate tool to describe them. Only the most basic geometric concepts are needed to understand the principles of optimal information processing and active sensing: linear form, vector field, and metric. Classical “optimal experiment design” results, such as “D-optimality,” are derived as a simple limit case of the general geometric theory.