Robust Inference in Wireless Sensor Networks

This dissertation presents a systematic approach to obtain robust statistical inference schemes in unreliable networks. Statistical inference offers mechanisms for deducing the statistical properties of unknown parameters from the data. In Wireless Sensor Networks (WSNs), sensor outputs are transmitted across a wireless communication network to the fusion center (FC) for final decision-making. The sensor data are not always reliable. Some factors may cause anomaly in network operations, such as malfunction, corruption, or compromised due to some unknown source of contamination or adversarial attacks. Two standard component failure models are adopted in this study to describe the system vulnerability: the probabilistic and static models. In probabilistic models, we consider a widely known ε−contamination model, where each node has ε probability of malfunctioning or being compromised. In contrast, the static model assumes there is up to a certain number of malfunctioning nodes. It is assumed that the decision center/network operator is aware of the presence of anomaly nodes and can adjust the operation rule to counter the impact of the anomaly. The anomaly node is assumed to know that the network operator is taking some defensive actions to improve its performance. Considering both the decision center (network operator) and compromised (anomalous) nodes and their possible actions, the problem is formulated as a two-player zero-sum game. Under this setting, we attempt to discover the worst possible failure models and best possible operating strategies. First, the effect of sensor unreliability on detection performance is investigated, and robust detection schemes are proposed. The aim is to design robust detectors when some observation nodes malfunction. The detection problem is relatively well known under the probabilistic model in simple binary hypotheses testing with known saddle-point solutions. The detection problem is investigated under the mini-max framework for the static settings as no such saddle point solutions are shown to exist under these settings. In the robust estimation, results in estimation theory are presented to measure system robustness and performance. The estimation theory covers probabilistic and static component failure models. Besides the standard approaches of robust estimation under the frequentist settings where the interesting parameters are fixed but unknown, the estimation problem under the Bayes settings is considered where the prior probability distribution is known. After first establishing the general framework, comprehensive results on the particular case of a single node network are presented under the probabilistic settings. Based on the insights from the single node network, we investigate the robust estimation problem for the general network for both failure models. A few robust localization methods are presented as an extension of robust estimation theory at the end.