Distributed, Non-linear Signal Processing for Large Scale Engineering Applications

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The research program lies at the intersection of three domains within Electrical and Computer Engineering, namely, signal processing, control theory, and optimization. The overarching theme that brings these three areas together is to develop smart, efficient, and robust, distributed signal processing algorithms for multi-agent systems. While signal processing for linear applications has a rich theoretical framework, non-linear, distributed signal processing lacks a universal set of tools for analysis and design. The objective of the program is to unify the study of a broad class of non-linear signal processing algorithms that emerge from statistical estimation principles for high-dimensional and distributed dynamical systems, where underlying signals arise from non-Gaussian processes. Recently implemented variants of the Kalman filter, random finite set methods, sequential Monte Carlo approaches, and particle flow methods have shown promise though for scenarios where the state space has a relatively low dimension. As the dimensions grow, the curse of state-space dimensionality and the associated high computational cost lead to a rapid deterioration in their performance. The research program will develop practical implementations of generic Monte Carlo methods for large-scale, non-linear, distributed applications and demonstrate their efficacy on real-life engineering problems. We will focus on the following inter-connected research problems in the context of geographically-distributed agent networks as representatives of large-scale, non-linear signal processing systems: (a) Diffusive fusion for large dimensional Monte Carlo approaches; (b) Event based distributed signal processing and control; (c) Weighted graph signal processing for large data sets; and (d) Derivation of the convergence properties and performance bounds of the algorithms we propose. These signal processing algorithms will be applied to practical engineering applications, including multi-target surveillance (for jointly estimating the number of targets and their states), distributed camera networks (for tracking moving objects), and electric smart grids (for estimating the operating status of smart grids in real-time). Within the signal processing community, this research will result in the development of a universal set of tools and design principles for analyzing large data sets and processing mission critical systems in a computationally efficient manner while respecting the non-linear physics of the underlying processes. Over the length of the research grant, the societal impact is achieved through HQP training of six PhD and six Masters students (in addition to fifteen undergraduate students who will build prototypes as capstone projects) in the area of non-linear signal processing, developing a range of technical skills needed to design the next generation technologies.