The problem of estimating parameters of a linear model in the presence of extraneous estimates of a parameter subset is considered. Two approaches are considered; one augments the linear model with the extra information and the second reduces the dimension and estimates only the remaining parameters. It is shown that the two approaches yield identical estimates of the unspecified parameter subset. In situations where one is interested only in the estimation of the unspecified parameter subset, computational advantages of the reduced model over the augmented model are pointed out. Application of such estimation to aircraft tracking in meteorological experiments is given.