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A direct derivation of the optimal minimal-order leastsquares estimator (OMOLSE) is presented using the recently developed general two-stage Kalman filter (GTSKF). Using this new result, the reduced-order estimators of O'Reilly and Fairman are readily shown to be equivalent. A practical implementation issue to consider these two estimators is also addressed. Index Terms-Least-squares estimator, minimal-order estimator, reduced-order estimator, two-stage Kalman filter.doi:10.1109/9.964689 fatcat:qiu3uystpbfk5av46zthhas5ie