A Game-Theoretic Approach to Robust Fusion and Kalman Filtering Under Unknown Correlations

This work addresses the problem of fusing two random vectors with unknown\ncross-correlations. We present a formulation and a numerical method for\ncomputing the optimal estimate in the minimax sense. We extend our formulation\nto linear measurement models that depend on two random vectors with unknown\ncross-correlations. As an application we consider the problem of decentralized\nstate estimation for a group of agents. The proposed estimator takes\ncross-correlations into account while being less conservative than the widely\nused Covariance Intersection. We demonstrate the superiority of the proposed\nmethod compared to Covariance Intersection with numerical examples and\nsimulations within the specific application of decentralized state estimation\nusing relative position measurements.\n