Robust Linear Estimation Fusion with Allowable Unknown Cross-Covariance

This paper deals with distributed estimation fusion under unknown cross-covariance between errors of local estimates. We propose a formulation to restrict the set of possible cross-covariance matrices. The constraint in the formulation, named allowance of cross-covariance, provides a flexible way to utilize some prior information on cross-correlation in fusion methods. Then based on the allowance, an optimal robust fusion method is proposed in the minimax sense via semi-definite programming, and suboptimal fusion methods are also discussed to reduce the computational load. We analyze the properties of the proposed fusion methods and describe the relationships between our proposed fusion and some existing fusion methods. Numerical examples are given to illustrate their performance.