Grant: Discovery Grants Program - Individual

Statistical signal processing deals with extracting signals from noisy measurements. In this project, motivated by energy, communication and computational constraints, we address the deeper issue of how to dynamically schedule and optimize signal processing resources to extract signals from noisy measurements. Such sensor scheduling/management problems involve the interplay of ideas in Bayesian signal processing, stochastic optimization, stochastic control and game theory. Our research involves four inter-related parts. In Part 1, we conduct fundamental research on the structural properties of sensor management problems formulated as constrained Markov decision processes, partially obeserved Markov decision processes and stochastic games. In Part 2, we exploit the structure in Part 1 to derive sophisticated simulation-based optimization algorithms for sensor management. In Part 3, we exploit the fundamental results in Part 1 and Part 2 to design and analyse efficient algorithms for networked sensors in surveillance and radar resource management. In Part 4, we use the fundamental results in Part 2 to devise efficient multiparticle Brownian dynamics and Molecular dynamics simulation of ion permeation in biological membrane ion channels. The key idea underpinning our research is the study of stochastic scheduling and games for dynamical systems. This unifying theme motivates our fundamental theory and applications. The outcomes of this project are twofold: (i) Novel theoretical developments and analysis in the structure of sensor scheduling policies (ii) Computationally efficient numerical algorithms and associated convergence analysis in sensor scheduling and large-scale interacting particle simulation. These algorithms will serve as useful computational tools for radar resource management, sensor networks and computational biophysics. To achieve our objectives we will use powerful analysis tools such as supermodularity, weak convergence, analysis of differential inclusions, and game theoretic ideas such as global games and correlated equilibria. Many of these fundamental tools are motivated by recent advances in the economics literature.