all the sensors in the network achieve global agreement using only local transmissions. In this dissertation, several consensus and consensus-based algorithms in WSNs are studied.

Firstly, a distributed consensus algorithm for estimating the maximum and minimum value of the initial measurements in a sensor network in the presence of communication noise is proposed. In the proposed algorithm, a soft-max approximation together with a non-linear average consensus algorithm is used. A design parameter controls the trade-off between the soft-max error and convergence speed. An analysis of this trade-off gives guidelines towards how to choose the design parameter for the max estimate. It is also shown that if some prior knowledge of the initial measurements is available, the consensus process can be accelerated.

Secondly, a distributed system size estimation algorithm is proposed. The proposed algorithm is based on distributed average consensus and L2 norm estimation. Different sources of error are explicitly discussed, and the distribution of the final estimate is derived. The CRBs for system size estimator with average and max consensus strategies are also considered, and different consensus based system size estimation approaches are compared.

Then, a consensus-based network center and radius estimation algorithm is described. The center localization problem is formulated as a convex optimization problem with a summation form by using soft-max approximation with exponential functions. Distributed optimization methods such as stochastic gradient descent and diffusion adaptation are used to estimate the center. Then, max consensus is used to compute the radius of the network area.

Finally, two average consensus based distributed estimation algorithms are introduced: distributed degree distribution estimation algorithm and algorithm for tracking the dynamics of the desired parameter. Simulation results for all proposed algorithms are provided.]]>