Robustness, Resilience, and Scalability of State Estimation Algorithms

State estimation is a type of an inverse problem in which some amount of observed data needs to be processed using computer algorithms (which are designed using analytical techniques) to infer or reconstruct the underlying model that produced the data. Due to the ubiquity of data and interconnected control systems in the present day, many engineering domains have become replete with inverse problems that can be formulated as state estimation problems. The interconnectedness of these control systems imparts the associated state estimation problems with distinctive structural properties that must be taken into consideration. For instance, the observed data could be high-dimensional and have a dependency structure that is best described by a graph. Furthermore, the control systems of today interface with each other and with the internet, bringing in new possibilities for large-scale collaborative sensor fusion, while also (potentially) introducing new sources of disturbances, faults, and cyberattacks.

The main thesis of this document is to investigate the unique challenges related to the issues of robustness, resilience (to faults and cyberattacks), and scalability of state estimation algorithms. These correspond to research questions such as, "Does the state estimation algorithm retain its performance when the measurements are perturbed by unknown disturbances or adversarial inputs?" and "Does the algorithm have any bottlenecks that restrict the size/dimension of the problems that it could be applied to?". Most of these research questions are motivated by a singular domain of application: autonomous navigation of unmanned aerial vehicles (UAVs). Nevertheless, the mathematical methods and research philosophy employed herein are quite general, making the results of this document applicable to a variety of engineering tasks, including anomaly detection in time-series data, autonomous remote sensing, traffic monitoring, coordinated motion of dynamical systems, and fault-diagnosis of wireless sensor networks (WSNs), among others.