  In the context of distributed estimation, we consider the problem of sensor
collaboration, which refers to the act of sharing measurements with neighboring
sensors prior to transmission to a fusion center. While incorporating the cost
of sensor collaboration, we aim to find optimal sparse collaboration schemes
subject to a certain information or energy constraint. Two types of sensor
collaboration problems are studied: minimum energy with an information
constraint; and maximum information with an energy constraint. To solve the
resulting sensor collaboration problems, we present tractable optimization
formulations and propose efficient methods which render near-optimal solutions
in numerical experiments. We also explore the situation in which there is a
cost associated with the involvement of each sensor in the estimation scheme.
In such situations, the participating sensors must be chosen judiciously. We
introduce a unified framework to jointly design the optimal sensor selection
and collaboration schemes. For a given estimation performance, we show
empirically that there exists a trade-off between sensor selection and sensor
collaboration.
