Gaussian belief propagation (BP) has been widely used for distributed estimation in large-scale networks such as the smart grid, communication networks, and social networks, where local meansurements/observations are scattered over a wide geographical area. However, the convergence of Gaussian BP is still an open issue. In this paper, we consider the convergence of Gaussian BP, focusing in particular on the convergence of the information matrix. We show analytically that the exchanged message information matrix converges for arbitrary positive semidefinite initial value, and its distance to the unique positive definite limit matrix decreases exponentially fast.

This paper presents a distributed hybrid power state estimator, with measurements from both the traditional supervisory control and data acquisition (SCADA) system and the newly invented phasor measurement units (PMUs). The proposed distributed algorithm, which jointly estimates the power states and PMU phase errors, only involves local computations and limited information exchange between neighboring areas, thus alleviating the heavy communication burden compared to the centralized approach. Simulation results show that the performance of the proposed algorithm is very close to that of centralized optimal hybrid state estimates without sampling phase error.

In this paper, we propose a fully distributed algorithm for joint clock skew and offset estimation in wireless sensor networks. With the proposed algorithm, each node can estimate its clock skew and offset by communicating only with its neighbors. Such algorithm does not require any centralized information processing or coordination. Simulation results show that estimation mean-square-error at each node converge to the centralized Cramér-Rao bound with only a few number of message exchanges.

In this paper, we propose a fully distributed algorithm for joint clock skew and offset estimation in wireless sensor networks based on belief propagation. In the proposed algorithm, each node can estimate its clock skew and offset in a completely distributed and asynchronous way: some nodes may update their estimates more frequently than others using outdated message from neighboring nodes. In addition, the proposed algorithm is robust to random packet loss. Such algorithm does not require any centralized information processing or coordination, and is scalable with network size. The proposed algorithm represents a unified framework that encompasses both classes of synchronous and asynchronous algorithms for network-wide clock synchronization. It is shown analytically that the proposed asynchronous algorithm converges to the optimal estimates with estimation mean-square-error at each node approaching the centralized Cramer-Rao bound under any network topology. Simulation results further show that {the convergence speed is faster than that corresponding to a synchronous algorithm.

In this letter, we investigate the problem of CFO estimation in OFDM systems when the timing offset and channel length are not exactly known. Instead of explicitly estimating the timing offset and channel length, we employ a multi-model approach, where the timing offset and channel length can take multiple values with certain probabilities. The effect of multimodel is directly incorporated into the CFO estimator. Results show that the proposed estimator outperforms the estimator selecting only the most probable model and the method taking the maximal model.