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This paper is concerned with the navigation of a manned space vehicle during its powered deboost phase of flight prior to landing on the moon. An inertial measurement unit (IMU), which operates continuously, is provided on board the vehicle along with an altimeter and a doppler radar. The basic problem of interest is to determine the best way to navigate the vehicle with these instruments, considering factors such as equipment operating ranges, data rates, random and bias measurement errors, terrain anomalies, and computational complexity. The navigation systems presented are based on the least-squares estimation techniques developed by Kalman and Battin. Up-to-date estimates of the vehicle's state are obtained by comparing altimeter or doppler-radar measurements with IMU-derived estimates of the same physical quantity. The key to the estimation process is the determination of the best weighting to use on these measurement differences in the updating procedure. Several different sets of weighting factors for use in the deboost phase are developed in the paper, using minimization of mean-squared estimation errors as the basic performance criterion. Bias errors in the IMU measurements, uncertainties in the knowledge of the orientation of the radar antennas relative to the IMU, and anomalies of the lunar terrain are assumed to be the predominant navigation-system error sources. The major differences between the weighting factors result from the particular model employed for the navigation sensors, the model used for the lunar terrain, and the methods used to account for measurement bias errors in the weighting-factor computations.