Estimation Fusion Based on Simplified Model for Cross-Covariance of Local Estimation Errors

Abstract

Cross-correlation generally exists between local estimation errors in distributed estimation fusion but is hard to know exactly. In some cases, the cross-correlation is partially known (e.g., only correlation level is known approximately or known within an interval). Utilizing correlation information benefits estimation. To use it, one way is to model the correlation by a generalized Pearson's correlation coefficient times the matrix product of local MSE matrices. The correlation coefficient is used to measure linear relation between two random vectors, and is assumed to be random (e.g., uniformly distributed) over the provided interval. Based on the way the cross-covariance matrix is modeled, the assumption about correlation coefficient and by applying best linear unbiased estimation (BLUE) fusion, an estimation fusion algorithm, called expected BLUE fuser (EBF), is presented. Compared with similar algorithms, its comparable or better performance demonstrates its effectiveness. Considering the fusion results under various given correlation intervals, we observe that strong correlation benefits fusion performance, and point out that EBF gets good fusion results when the given correlation interval cover the true correlation coefficient tightly.