Robust Signal Processing in Distributed Sensor Networks

Statistical robustness and collaborative inference in a distributed sensor network are two challenging requirements posed on many modern signal processing applications. This dissertation aims at solving these tasks jointly by providing generic algorithms that are applicable to a wide variety of real-world problems. The first part of the thesis is concerned with sequential detection---a branch of detection theory that is focused on decision-making based on as few measurements as possible. After reviewing some fundamental concepts of statistical hypothesis testing, a general formulation of the Consensus+Innovations Sequential Probability Ratio Test for sequential binary hypothesis testing in distributed networks is derived. In a next step, multiple robust versions of the algorithm based on two different robustification paradigms are developed. The functionality of the proposed detectors is verified in simulations, and their performance is examined under different network conditions and outlier concentrations. Subsequently, the concept is extended to multiple hypotheses by fusing it with the Matrix Sequential Probability Ratio Test, and robust versions of the resulting algorithm are developed. The performance of the proposed algorithms is verified and evaluated in simulations. Finally, the Dempster-Shafer Theory of Evidence is applied to distributed sequential hypothesis testing for the first time in the literature. After introducing a novel way of performing the Basic Probability Assignment, an evidence-based sequential detector for application in distributed sensor networks is developed and its performance is verified in simulations. The second part of the thesis deals with multi-target tracking in distributed sensor networks. The problem of data association is discussed and the considered state-space and measurement models are introduced. Next, the concept of random finite sets as well as Probability Hypothesis Density filtering are reviewed. Subsequently, a novel distributed Particle Filter implementation of the Probability Hypothesis Density Filter is developed, which is based on a two-step communication scheme. A robust as well as a centralized version of the algorithm are derived. Furthermore, the computational complexity and communication load of the distributed as well as the centralized trackers are analyzed. Finally, simulations are performed to compare the proposed algorithms with an existing distributed tracker. To this end, a distributed version of the Posterior Cramér-Rao Lower Bound is developed, which serves as a performance bound. The results show that the proposed algorithms perform well under different environmental conditions and outperform the competition