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Optimum linear filter and control theory is applied to the practical problem of supplementing an inertial navigation system with discrete reference information. The information takes the form of position obtained from Loran C or Decca, for example, and occasional azimuth fixes obtained from star sightings. In particular, optimum use of this information is discussed for the Ship's Inertial Navigation System (SINS) installations intended for missile carrying submarines and warships. A model representative of the SINS dynamics is formulated appropriate for application of optimum filter and control theory. Interpretation of the optimum control dictated in part by the augmented SINS model is discussed. Simulation studies that show the relative transient behavior and the stabilizing effect of the closed-loop filter and control processes are also presented.