Optimal Linear Estimation Fusion—Part III: Cross-Correlation of Local Estimation Errors

The knowledge of the cross correlation of the errors of local estimates is needed in many techniques for distributed fusion. In fact, this cross covariance is a key quantity for the best linear unbiased estimation (BLUE), also known as linear minimum mean-square error (LMMSE) estimation, and optimal weighted least squares (WLS) fusion rules presented in Part I [8]. This paper presents exact, explicit, and easily computable formulas for their computation for all cases with linear observations. Formulas for cases of nonlinear observations are also given. The formulas presented are valid for all linear unbiased estimators, regardless of whether they are optimal (in any sense) or not. Simulation verification is provided.