  In problems of parameter estimation from sensor data, the Fisher Information
provides a measure of the performance of the sensor; effectively, in an
infinitesimal sense, how much information about the parameters can be obtained
from the measurements. From the geometric viewpoint, it is a Riemannian metric
on the manifold of parameters of the observed system. In this paper we consider
the case of parameterized sensors and answer the question, "How best to
reconfigure a sensor (vary the parameters of the sensor) to optimize the
information collected?" A change in the sensor parameters results in a
corresponding change to the metric. We show that the change in information due
to reconfiguration exactly corresponds to the natural metric on the infinite
dimensional space of Riemannian metrics on the parameter manifold, restricted
to finite-dimensional sub-manifold determined by the sensor parameters. The
distance measure on this configuration manifold is shown to provide optimal,
dynamic sensor reconfiguration based on an information criterion. Geodesics on
the configuration manifold are shown to optimize the information gain but only
if the change is made at a certain rate. An example of configuring two
bearings-only sensors to optimally locate a target is developed in detail to
illustrate the mathematical machinery, with Fast-Marching methods employed to
efficiently calculate the geodesics and illustrate the practicality of using
this approach.
