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The application of nonlinear Kalman filtering techniques to the continuous updating of an inertial navigation system using individual radar terrain-clearance measurements has been investigated. During this investigation, three different approaches for handling the highly nonlinear terrain measurement function were developed and their performance was established. These were 1) a simple first-order extended Kalman filter using local derivatives of the terrain surface, 2) a modified stochastic linearization technique which adaptively fits a least squares plane to the terrain surface and treats the associated fit error as an additional noise source, 3) a parallel Kalman filter technique utilizing a bank of reduced-order filters that was especially important in applications with large initial position uncertainties. Theoretical and simulation results are presented.