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

TL;DR

This paper introduces a game-theoretic method for robustly fusing correlated estimates with unknown cross-correlations, improving decentralized state estimation over traditional approaches like Covariance Intersection.

Contribution

It develops a minimax formulation and numerical approach for optimal fusion under unknown correlations, extending to linear measurement models and decentralized estimation.

Findings

Proposed estimator outperforms Covariance Intersection in simulations.

Numerical examples demonstrate improved accuracy in decentralized state estimation.

Method effectively accounts for unknown cross-correlations, reducing conservativeness.

Abstract

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