Fully distributed wireless sensor networks (WSNs) without fusion center have advantages such as scalability in network size and energy efficiency in communications. Each sensor shares its data only with neighbors and then achieves global consensus quantities by in-network processing. This dissertation considers robust distributed parameter estimation methods, seeking global consensus on parameters of adaptive learning algorithms and statistical quantities.

Diffusion adaptation strategy with nonlinear transmission is proposed. The nonlinearity was motivated by the necessity for bounded transmit power, as sensors need to iteratively communicate each other energy-efficiently. Despite the nonlinearity, it is shown that the algorithm performs close to the linear case with the added advantage of power savings. This dissertation also discusses convergence properties of the algorithm in the mean and the mean-square sense.

Often, average is used to measure central tendency of sensed data over a network. When there are outliers in the data, however, average can be highly biased. Alternative choices of robust metrics against outliers are median, mode, and trimmed mean. Quantiles generalize the median, and they also can be used for trimmed mean. Consensus-based distributed quantile estimation algorithm is proposed and applied for finding trimmed-mean, median, maximum or minimum values, and identification of outliers through simulation. It is shown that the estimated quantities are asymptotically unbiased and converges toward the sample quantile in the mean-square sense. Step-size sequences with proper decay rates are also discussed for convergence analysis.

Another measure of central tendency is a mode which represents the most probable value and also be robust to outliers and other contaminations in data. The proposed distributed mode estimation algorithm achieves a global mode by recursively shifting conditional mean of the measurement data until it converges to stationary points of estimated density function. It is also possible to estimate the mode by utilizing grid vector as well as kernel density estimator. The densities are estimated at each grid point, while the points are updated until they converge to a global mode.