Optimal topological design for distributed estimation over sensor networks

The topological structure of sensor network possesses distinctive and interesting characteristics that are important for many applications. In the previous work by Liu et al. (Y. Liu, C. Li, W.K.S. Tang, Z. Zhang, Distributed estimation over complex networks, Inform. Sci. 197(8) (2012) 91-104) the effects of network topology on distributed estimation have been addressed. In this paper, we further focus on the optimal topological design of sensor networks, which targets for improving the performance of distributed estimation. Based on spectral analysis, it is shown that this design problem is equivalent to finding an optimal topology that maximizes the eigenratio of the second smallest and the largest eigenvalues of the respective network Laplacian matrix. To tackle this optimization problem, a computational algorithm combining a local greedy algorithm and tabu search is proposed, in which the constraint on the distance of two communicated sensors is incorporated. As shown in the numerical simulations, the proposed algorithm outperforms other optimization strategies in the viewpoints of accuracy, robustness and complexity. Consequently, the quality of distributed estimation can be improved by obtaining a better network topology.