High Dimensional Separable Representations for Statistical Estimation and Controlled Sensing
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This thesis makes contributions to a fundamental set of high dimensional problems in the following areas: (1) performance bounds for high dimensional estimation of structured Kronecker product covariance matrices, (2) optimal query design for a centralized collaborative controlled sensing system used for target localization, and (3) global convergence theory for decentralized controlled sensing systems. Separable approximations are effective dimensionality reduction techniques for high dimensional problems. In multiple modality and spatio-temporal signal processing, separable models for the underlying covariance are exploited for improved estimation accuracy and reduced computational complexity. In query-based controlled sensing, estimation performance is greatly optimized at the expense of query design. Multi-agent controlled sensing systems for target localization consist of a set of agents that collaborate to estimate the location of an unknown target. In the centralized setting, for a large number of agents and/or high-dimensional targets, separable representations of the fusion center’s query policies are exploited to maintain tractability. For large-scale sensor networks, decentralized estimation methods are of primary interest, under which agents obtain new noisy information as a function of their current belief and exchange local beliefs with their neighbors. Here, separable representations of the temporally evolving information state are exploited to improve robustness and scalability. The results improve upon the current state-of-the-art.