An information-geometric approach to sensor management is introduced that is
based on following geodesic curves in a manifold of possible sensor
configurations. This perspective arises by observing that, given a parameter
estimation problem to be addressed through management of sensor assets, any
particular sensor configuration corresponds to a Riemannian metric on the
parameter manifold. With this perspective, managing sensors involves navigation
on the space of all Riemannian metrics on the parameter manifold, which is
itself a Riemannian manifold.
Multiple-channel detection is considered in the context of a sensor network
where raw data are shared only by nodes that have a common edge in the network
graph. Established multiple-channel detectors, such as those based on
generalized coherence or multiple coherence, use pairwise measurements from
every pair of sensors in the network and are thus directly applicable only to
networks whose graphs are completely connected.
Sensor systems typically operate under resource constraints that prevent the
simultaneous use of all resources all of the time. Sensor management becomes
relevant when the sensing system has the capability of actively managing these
resources; i.e., changing its operating configuration during deployment in
reaction to previous measurements. Examples of systems in which sensor
management is currently used or is likely to be used in the near future include
autonomous robots, surveillance and reconnaissance networks, and waveform-agile
radars.
A statistical framework is introduced for a broad class of problems involving
synchronization or registration of data across a sensor network in the presence
of noise. This framework enables an estimation-theoretic approach to the design
and characterization of synchronization algorithms. The Fisher information is
expressed in terms of the distribution of the measurement noise and standard
mathematical descriptors of the network's graph structure for several important
cases.
A geometric perspective is used to derive the entire family of Welch bounds.
This perspective unifies a number of observations that have been made regarding
tightness of the bounds and their connections to symmetric k-tensors, tight
frames, homogeneous polynomials, and t- designs.
A geometric perspective is used to derive the entire family of Welch bounds.
This perspective unifies a number of observations that have been made regarding
tightness of the bounds and their connections to symmetric k-tensors, tight
frames, homogeneous polynomials, and t- designs.