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This analysis is directed toward finding the rms position error of a Doppler navigation system when the input to the system is composed of random velocity errors. Statistical techniques of time-stationary random processes are used to represent the input velocity. Results show that system errors expressed as a per cent of distance traveled are shown to decrease with increasing distance traveled. There is a need for specifying the effective noise bandwidth of a system when determining system accuracy by means of random analysis. The smaller the effective noise bandwidth of the input velocity errors, the larger the rms position error.