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Deflections of the vertical introduce errors into terrestrial inertial navigation systems. In many situations, these errors prove to be intolerable. However, if vertical deflection data are available prior to a mission, this information can in principle be used to reduce the navigation system errors. It is assumed that measurements of vertical deflections plus noise are available at equally spaced points on a square grid. The accuracy to which the Schuler loop errors can be controlled, given this set of measurements, is bounded by the accuracy to which the uncontrolled Schuler loop errors can be estimated given the same set of measurements. Thus lower bounds on the accuracy of the compensated system may be established by obtaining the optimal error covariances of the equivalent estimation problem. It is shown that the estimation problem can be modeled as a linear smoothing problem if the vehicle travels at a constant heading and at a constant velocity. The appropriate error covariances are found using the known techniques of optimal linear estimation theory, Kalman filtering and smoothing, both at and between the grid points.