Signal Processing for Distributed Kernel-based Estimation

With an increased utilization of large sensor networks in applications such as environmental monitoring, hazard detection and health care, the methodology of a data processing within the network has been identified as a promising concept. While common approaches rely on centralized processing, in-network processing exploits the interconnections among the nodes to obtain a cooperative result. By that, the network is equipped with estimation capabilities and an increased robustness against node failures within the network. Corresponding algorithms have been widely developed in the literature. However, the majority of these consider linear functions only whereas usually physical phenomena such as the spatial distribution of temperature, humidity, altitude or radioactivity are described by nonlinear functions. Hence, existing in-network processing algorithms will perform poorly when applied to the spatial reconstruction of such physical quantities. To suggest solutions to this issue this thesis aims at deriving algorithms that enable a distributed estimation and regression of nonlinear functions.

Within this thesis two core algorithms are proposed that achieve the aforementioned objective by a combination of concepts from kernel methods, set theoretic adaptive filtering and in-network processing. Simulative analyses of the proposed schemes for synthetic data as well as real altitude data show their capability for a distributed reconstruction of nonlinear functions. To enable a comprehensive study of the presented material this thesis provides insights to recent advances in kernel-based estimation, kernel adaptive filtering algorithms and distributed consensus-based schemes.