Generalized Millman's formula and its application for estimation problems

We derive an optimal combination of arbitrary number correlated estimates. In particular, for two estimates this combination represents the well-known Millman and Bar-Shalom–Campo formulae for uncorrelated and correlated estimation errors, respectively. This new result is applied to the various estimation problems as least-squares estimation, Kalman filtering, and adaptive filtering. The new approximate reduced-order estimators with parallel structure are presented. A practical implementation issue to consider these estimators is also addressed. Examples demonstrate the accuracy and efficiency of application of the generalized Millman's formula.