The research in distributed algorithms is linked with the developments of statistical inference
in wireless sensor networks (WSNs) applications. Typically, distributed approaches process
the collected signals from networked sensor nodes. That is to say, the sensors receive local
observations and transmit information between each other. Each sensor is capable of combining
the collected information with its own observations to improve performance. In this thesis, we
propose novel distributed methods for the inference applications using wireless sensor networks.
In particular, the efficient algorithms which are not computationally intensive are investigated.
Moreover, we present a number of novel algorithms for processing asynchronous network events
and robust state estimation.
In the first part of the thesis, a distributed adaptive algorithm based on the component-wise
EM method for decentralized sensor networks is investigated. The distributed component-wise
Expectation-Maximization (EM) algorithm has been designed for application in a Gaussian
density estimation. The proposed algorithm operates a component-wise EM procedure for local
parameter estimation and exploit an incremental strategy for network updating, which can provide
an improved convergence rate. Numerical simulation results have illustrated the advantages of
the proposed distributed component-wise EM algorithm for both well-separated and overlapped
mixture densities. The distributed component-wise EM algorithm can outperform other EM-based
distributed algorithms in estimating overlapping Gaussian mixtures.
In the second part of the thesis, a diffusion based EM gradient algorithm for density estimation
in asynchronous wireless sensor networks has been proposed. Specifically, based on the
asynchronous adapt-then-combine diffusion strategy, a distributed EM gradient algorithm that
can deal with asynchronous network events has been considered. The Bernoulli model has been
exploited to approximate the asynchronous behaviour of the network. Compared with existing
distributed EM based estimation methods using a consensus strategy, the proposed algorithm
can provide more accurate estimates in the presence of asynchronous networks uncertainties,
such as random link failures, random data arrival times, and turning on or off sensor nodes
for energy conservation. Simulation experiments have been demonstrated that the proposed
algorithm significantly outperforms the consensus based strategies in terms of Mean-Square-
Deviation (MSD) performance in an asynchronous network setting.
Finally, the challenge of distributed state estimation in power systems which requires low
complexity and high stability in the presence of bad data for a large scale network is addressed.
A gossip based quasi-Newton algorithm has been proposed for solving the power system state
estimation problem. In particular, we have applied the quasi-Newton method for distributed
state estimation under the gossip protocol. The proposed algorithm exploits the Broyden-
Fletcher-Goldfarb-Shanno (BFGS) formula to approximate the Hessian matrix, thus avoiding the
computation of inverse Hessian matrices for each control area. The simulation results for IEEE
14 bus system and a large scale 4200 bus system have shown that the distributed quasi-Newton
scheme outperforms existing algorithms in terms of Mean-Square-Error (MSE) performance with
bad data
