Distributed Relaxation on Augmented Lagrangian for Consensus based Estimation in Sensor Networks

This paper presents several new distributed algorithms to solve consensus based estimation problems in a decentralized way by adopting the well-known relaxation methods Jacobi, Gauss-Seidel and successive over-relaxation within a sensor network. In distributed estimation, all nodes collaborate to estimate the signals emitted from some common sources, employing iterative processing with one-hop data exchange. Consequently, the Jacobi-based consensus estimation algorithm produces a considerable communication effort due to its parallel processing. On the contrary, significant overhead can be saved by the Gauss-Seidel based consensus estimation algorithm with sequential update and exchange of local information. Additionally, both distributed algorithms can be accelerated by successive over-relaxation, resulting in further reduction of the communication effort for the distributed estimation. The evaluation of all the algorithms has been carried out in presence of both ideal and erroneous inter-node links in a randomly generated network. Moreover, the influence of the network topology on the distributed estimation has also been investigated, and the simulative results indicate that a network with low connectivity is preferred by the proposed algorithms.