Dimensionality Reduction for Distributed Estimation in the Infinite Dimensional Regime

Distributed estimation of an unknown signal is a common task in sensor networks. The scenario usually envisioned consists of several nodes, each making an observation correlated with the signal of interest. The acquired data is then wirelessly transmitted to a fusion center that aims at estimating the desired signal within a prescribed accuracy. Motivated by the obvious processing limitations inherent to such distributed infrastructures, we seek to find efficient compression schemes that account for limited available power and communication bandwidth. We propose a transform-based approach to this problem where each sensor provides the fusion center with a low-dimensional approximation of its local observation by means of a suitable linear transform. Under the mean-squared error criterion, we derive the optimal solution to apply at one sensor assuming all else being fixed. This naturally leads to an iterative algorithm whose optimality properties are exemplified using a simple though il...

• Type: Journal
• Year: 2008
• Where: TIT
• Authors: Olivier Roy, Martin Vetterli
• Keywords: Fusion Center, Obvious Processing Limitations, Sensor, TIT 2008