Optimal linear estimation and data fusion

Optimal mean square linear estimators are determined for general uncorrelated noise. We allow the noise variance matrix in the observation process to be singular. This requires properties of generalized inverses which are developed in Section II. The proofs appear to be new. When there are two observation sequences the optimal method of recursively fusing the two is determined. We derive a new formula for the covariance of the two estimates which then provides exact dynamics for a fused estimate.