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 constraint to restrict the set of possible cross-covariance matrices first. Then this constraint, named allowance degree of cross-covariance, is used to derive a fusion method. Based on the allowance degree, we present an optimal robust fusion method in the minimax sense via semi-definite programming and also a suboptimal fusion. We analyze the properties of the proposed fusion methods and describe the relationship between the suboptimal fusion and some existing fusion methods. Numerical examples are given to illustrate their performance compared with the traditional covariance intersection method.