  We consider the problem of collaborative distributed estimation in a large
scale sensor network with statistically dependent sensor observations. In
collaborative setup, the aim is to maximize the overall estimation performance
by modeling the underlying statistical dependence and efficiently utilizing the
deployed sensors. To achieve greater sensor transmission and estimation
efficiency, we propose a two step group-based collaborative distributed
estimation scheme, where in the first step, sensors form dependence driven
groups such that sensors in the same group are highly dependent, while sensors
from different groups are independent, and perform a copula-based maximum a
posteriori probability (MAP) estimation via intragroup collaboration. In the
second step, the estimates generated in the first step are shared via
inter-group collaboration to reach an average consensus. A merge based K-medoid
dependence driven grouping algorithm is proposed. Moreover, we further propose
a group-based sensor selection scheme using mutual information prior to the
estimation. The aim is to select sensors with maximum relevance and minimum
redundancy regarding the parameter of interest under certain pre-specified
energy constraint. Also, the proposed group-based sensor selection scheme is
shown to be equivalent to the global/non-group based selection scheme with high
probability, but computationally more efficient. Numerical experiments are
conducted to demonstrate the effectiveness of our approach.
