Linear Coherent Estimation with Spatial Collaboration

TL;DR

This paper introduces a method for sensor networks to collaboratively estimate a parameter by optimizing linear updates and power allocation, improving accuracy especially in low SNR conditions.

Contribution

It develops an optimal collaborative strategy for sensor networks with partial connectivity, considering power constraints and imperfect information, enhancing estimation accuracy.

Findings

Significant reduction in estimation distortion with moderate network connectivity.

Performance gains are notable under low local-SNR conditions.

Analytical and numerical results validate the proposed approach.

Abstract

A power constrained sensor network that consists of multiple sensor nodes and a fusion center (FC) is considered, where the goal is to estimate a random parameter of interest. In contrast to the distributed framework, the sensor nodes may be partially connected, where individual nodes can update their observations by (linearly) combining observations from other adjacent nodes. The updated observations are communicated to the FC by transmitting through a coherent multiple access channel. The optimal collaborative strategy is obtained by minimizing the expected mean-square-error subject to power constraints at the sensor nodes. Each sensor can utilize its available power for both collaboration with other nodes and transmission to the FC. Two kinds of constraints, namely the cumulative and individual power constraints are considered. The effects due to imperfect information about observation and channel gains are also investigated. The resulting performance improvement is illustrated analytically through the example of a homogeneous network with equicorrelated parameters. Assuming random geometric graph topology for collaboration, numerical results demonstrate a significant reduction in distortion even for a moderately connected network, particularly in the low local-SNR regime.