Control of sensing by navigation on information gradients

In estimation of parameters residing in a smooth manifold from sensor data, the Fisher information induces a Riemannian metric on the parameter manifold. If the collection of sensors is reconfigured, this metric changes. In this way, sensor configurations are identified with Riemannian metrics on the parameter manifold. The collection of all Riemannian metrics on a manifold forms a (weak) Riemannian manifold, and a smooth trajectory of sensor configurations manifests as a smooth curve in this space. This paper develops the idea of sensor management by following trajectories in the space of sensor configurations that are defined locally by gradients of the metric this space inherits from the abstract space of all Riemannian metrics on the parameter manifold. Theory is developed and computational examples that illustrate sensor configuration trajectories arising from this scheme are presented.