| We study the problem of distributed estimation, where a group of nodes are required to cooperate with each other to estimate some parameter of interest from noisy measurements without a fusion center. Distributed estimation algorithms are useful in several areas, including wireless sensor networks, where robustness, scalability, flexibility, and low power consumption are desirable. In this dissertation, we mainly focus on the cases where the node measurements are correlated. First, we consider the problem of fusing multiple estimates from different nodes. Cases of both known and unknown correlation are investigated. A Bayesian approach and a convex optimization approach are proposed. Second, we study the sequential estimation problem where all the nodes in the network cooperate to estimate a static parameter recursively, and where the correlation between measurements from different nodes are known. We propose an efficient distributed algorithm and prove that it is optimal in the sense that the ratio of the variance of the proposed estimator to that of the centralized estimator approaches one in the long run. Last, we study the belief consensus problem in the networks. Instead of estimating a scalar or a vector, we are interested in the beliefs of nodes, which are represented as probability densities. The Chi-square information is used as the criterion to determine the optimal values of the weighting coefficients in the fusion of densities. We also prove that the optimization problem of minimizing the Chi-square information with respect to the weighting coefficients is convex, and therefore can be solved efficiently by existing methods. |
