Estimation fusion algorithms in the presence of partially known cross-correlation of local estimation errors

• The concept of correlation coefficient is introduced to represent the level of cross-correlation.
• The rationality and effectiveness of the concept of correlation coefficient are verified.
• A min–max estimation fusion model is proposed by minimizing the maximal Mahalanobis distance between two fused estimates.
• A closed form of estimation fusion is derived by assuming that the correlation coefficient follows a prior distribution.

This paper addresses estimation fusion when the cross-correlation of local estimation errors is partially known. The statistical dependence of local estimation errors is first discussed, and then the concept of correlation coefficient is introduced to model the cross-correlation approximately. Two algorithms are proposed. One is based on min–max technique, which minimizes the maximal Mahalanobis distance between two fused estimates. The other one uses the prior distribution of the correlation coefficient and obtains a closed form of estimation fusion with the help of a series of matrix manipulations. Compared with some available algorithms in literature, simulation results demonstrate the effectiveness of the proposed approaches.