Minimax Game-Theoretic Approach to Multiscale H-infinity Optimal Filtering

TL;DR

This paper introduces a minimax game-theoretic method for multiscale H-infinity filtering in hierarchical cyber-physical systems, improving robustness and signal quality over traditional Kalman filters.

Contribution

It develops a multiscale state-space model and formulates a multi-stage zero-sum game to design robust filters tailored for hierarchical data structures.

Findings

Enhanced SNR compared to Kalman filter

Effective multiscale data fusion in hierarchical systems

Robustness against noise in complex sensing environments

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).