Distributed estimation in large-scale networks : theories and applications

Abstract

Parameter estimation plays a key role in many signal processing applications. Traditional parameter estimation relies on centralized method which requires gathering of all information dispersed over the network in a central processing unit. As the scale of network increases, centralized estimation is not preferred since it requires not only the knowledge of network topology but also heavy communications from peripheral nodes to central processing unit. Besides, computation at the control center cannot scale indefinitely with the network size. Therefore, distributed estimation which involves only local computation at each node and limited information exchanges between immediate neighbouring nodes is needed. In this thesis, for local observations in the form of a pairwise linear model corrupted by Gaussian noise, belief propagation (BP) algorithm is investigated to perform distributed estimation. It involves only iterative updating of the estimates with local message exchange between immediate neighboring nodes. Since convergence has always been the biggest concern when using BP, we establish the convergence properties of asynchronous vector form Gaussian BP under the pairwise model. It is shown analytically that under mild condition, the asynchronous BP algorithm converges to the optimal estimates with estimation mean square error (MSE) at each node approaching the centralized Bayesian Cram´er-Rao bound (BCRB) regardless of the network topology. The proposed framework encompasses both classes of synchronous and asynchronous algorithms for distributed estimation and is robust to random link failures.

Two challenging parameter estimation problems in large-scale networks, i.e., network-wide distributed carrier frequency offsets (CFOs) estimation, and global clock synchronization in sensor network, are studied based on BP. The proposed algorithms do not require any centralized information processing nor knowledge of the global network topology and are scalable with the network size. Simulation results further verify the established theoretical analyses: the proposed algorithms always converge to the optimal estimates regardless of network topology. Simulations also demonstrate the MSE at each node approaches the corresponding centralized CRB within a few iterations of message exchange.

Furthermore, distributed estimation is studied for the linear model with unknown coefficients. Such problem itself is challenging even for centralized estimation as the nonlinear property of the observation model. One problem following this model is the power state estimation with unknown sampling phase error. In this thesis, distributed estimation scheme is proposed based on variational inference with parallel update schedule and limited message exchange between neighboring areas, and the convergence is guaranteed. Simulation results show that after convergence the proposed algorithm performs very close to that of the ideal case which assumes perfect synchronization, and centralized information processing.