Sensor management via riemannian geometry

Abstract

In estimation of scenario parameters from sensor data, the Fisher information induces a Riemannian metric on the manifold of parameters. 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 smooth changes in configuration of the sensor suite manifests as a smooth curve in this space. This paper examines the idea of sensor management via navigation along geodesics in a sub-manifold of this space corresponding to physically viable sensor configurations; i.e., curves that optimize an energy integral in the sub-manifold. In addition to development of the theory, computational examples that illustrate sensor configuration trajectories arising from this scheme in small-scale scenarios are presented.