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A philosophy for the synthesis of a very accurate inertial navigation system is developed here. First, the requirements for a spherical earth navigator are determined, and the basis for a navigator error analysis is developed through the use of mathematical error models. Four types of redundant information are then considered in sequence: external speed information, redundant system gyro, external discrete position source, and additional inertial navigators. The complete inertial navigation system arrived at utilizes all of this redundant information. The presentation is tutorial, emphasizing system accuracy considerations. Reliability as a result of redundant navigators is discussed briefly.