Distributed Robust Kalman Filters Under Model Uncertainty and Multiplicative Disturbance

This article considers the problem of distributed robust state estimation for sensor networks in the presence of model uncertainty and multiplicative noise. More precisely, we assume that the modeling uncertainty, i.e., the actual state space model belongs to an ambiguity set or a set of convex polytopic uncertain parameters. Several robust Kalman filters are proposed based on projection theorem, variance-constrained optimization, and robust mean square error estimation with different types of ambiguity sets. Stability analysis and simulation example verify the presented distributed robust filters.