Linear Coherent Estimation With Spatial Collaboration

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 signal-to-noise ratio regime.Index Terms-Constrained optimization, distributed estimation, linear minimum mean square estimation (LMMSE), wireless sensor networks.

Distributed Two-Step Quantized Fusion Rules Via Consensus Algorithm for Distributed Detection in Wireless Sensor Networks

“…(25) P roof : The proof is given in Appendix A. Now, the convergence of (25) It is worth mentioning that the condition (f (α i ) ≤ 1, ∀i) does not affect the optimality of the fusion rule defined in (15) for the structure considered in (14) and the condition can be satisfied by scaling the centralized weighting vector (α) by a positive constant c. Clearly, the distributed system (22) achieves the performance of the unquantized centralized approach in section III-A2.…”

“…What we require now is a distributed approach that will converge to the equivalent of the optimum weighted linear combining FC solution in (15).…”

“…We have now stated the necessary and sufficient conditions for the time evolution (22) to converge to the weighted centralized optimum linear fusion rule (15). The exchange of information between SNs is assumed error free and the bandwidth between two connected SNs is considered unlimited.…”

“…After the collaboration stage, the SNs (which in general can be a subset of all SNs) report to a FC where the final decision is made. Reference [13] proposes an ef f icient collaboration strategy in a distributed fashion (as opposed to [15] where this optimal collaboration strategy is computed at a FC) by means of using only local SNs observations. While the authors in [13] claim to reduce the FC control overhead, [14] derives the optimum power allocation scheme constraint on the maximum total network power budget in order to improve the quality of the estimation back at the FC.…”

Wireless Power Transfer for Distributed Estimation in Sensor Networks

“…The effects of channel estimation error were reported in [10] for orthogonal MACs adopting a linear minimum meansquared error estimator, while in [13], the sensing noise uncertainty was investigated by adopting the BLUE. Recently, the optimal transmit strategy for cooperative linear estimation was studied in [4].…”