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By measuring forces and moments that constrain a body of known inertial characteristics to move with a vehicle it is possible to determine acceleration in a set of specified axes and hence change in velocity and position. The principles of this method of navigation, known as inertial navigation, are outlined, and it is shown that the many possibilities of a practical realization can all be expressed in terms of a single block schematic of a computer which corrects for the expected variations in the specific force of gravity as a function of position and time. The magnitude of the problem of designing suitable gyroscopes and accelerometers is discussed, and the effect is calculated of certain errors in the components. Means for combining inertial navigation with radio navigation aids are outlined, and it is shown that these give an effective memory over periods in which the radio aid may be inoperative, a heavy filtering of the radio-aid output without introducing lag and loss of information, and interpolation between outputs of a low-data-rate system. The performance requirements for gyroscopes and accelerometers to obtain this can be much less stringent than for pure inertial navigation.