Optimal experiment design with diffuse prior information

In system identification one always aims to learn as much as possible about a system from a given observation period. This has led to on-going interest in the problem of optimal experiment design. Not surprisingly, the more one knows about a system the more focused the experiment can be. Indeed, many procedures for `optimal´ experiment design depend, paradoxically, on exact knowledge of the system parameters. This has motivated recent research on, so called, `robust´ experiment design where one assumes only partial prior knowledge of the system. Here we go further and study the question of optimal experiment design when the a-priori information about the system is diffuse. We show that band-limited `1/f´ noise is optimal for a particular choice of cost function.