Analysis of Partial Knowledge of Correlations in an Estimation Fusion Problem

A recently proposed algorithm of fusion under partially known correlations of estimation errors has been proved to outperform the classic Covariance Intersection algorithm, which was proposed for the case of no knowledge of correlation. This paper shows that the assumptions of the recently proposed algorithm are rather strict with respect to the classic one. Namely, the mean square error (MSE) matrices of the two state estimates cannot be upper-bounded arbitrarily. A relaxation of the assumption that the matrices have to be known exactly is discussed, as well as an iterative fusion of multiple estimates, and several examples dealing with dependent errors are provided.