Title: Minimax Game-Theoretic Approach to Multiscale H-infinity Optimal Filtering,
Abstract: Sensing in complex systems requires large-scale information exchange and
on-the-go communications over heterogeneous networks and integrated processing
platforms. Many networked cyber-physical systems exhibit hierarchical
infrastructures of information flows, which naturally leads to a multi-level
tree-like information structure in which each level corresponds to a particular
scale of representation. This work focuses on the multiscale fusion of data
collected at multiple levels of the system. We propose a multiscale state-space
model to represent multi-resolution data over the hierarchical information
system and formulate a multi-stage dynamic zero-sum game to design a
multi-scale $H_{\infty}$ robust filter. We present numerical experiments for
one and two-dimensional signals and provide a comparative analysis of the
minimax filter with the standard Kalman filter to show the improvement in
signal-to-noise ratio (SNR).