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The purpose of this paper is to present an applications-oriented discussion of the Kalman filter theory. The subject has received extensive treatment in the fields of orbit estimation and deterministic control system theory. This paper will emphasize the extraction of information from an additive-noise environment, i.e., the classical observation problem and its relation to the estimation theory. This subject is chosen in order to make the discussion concrete, and because of the general lack of application of the newer Kalman theory to this important area. Engineering application of the filter theory is discussed by working through a filter design that involves both compensation and estimation.