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In an estimation problem the statistics of various random processes involved may not be known exactly. Using linear state space modeling techniques, this lack of information can often be represented by allowing certain system model parameters to assume any of a finite set of possible known values with corresponding a priori known probabilities. In this short paper a recursive minimum variance estimator, restricted to be a linear function of the observation data sequence, is obtained for an estimation problem which can be described by a linear discrete time system model with uncertain parameters; all initial information relative to these uncertain parameters is utilized by the estimator. The estimation error covariance matrix, in a recursive form, is also obtained. An example is given to illustrate the usefulness of this estimator.