Alignment of Inertial Navigators in Low-Speed Vehicles

This paper is addressed to some aspects of low-speed inertial system alignment. Particular attention is paid to practical problems encountered which limit the accuracy of alignment. The system under study has been taken to be of the three-gimbal north-vertical configuration (#-axis vertical, #-axis north, and y-axis east), including appropriate damping and gyrocompassing means. The earth is assumed spherical. Errors in indication of the vertical and azimuth due to both component random errors and vehicle motion are treated. It is noted that, in the analysis of system response due to vehicle motions, sinusoidal test excitations although analytically convenient are not generally a valid description of the true base motions of the vehicle. In fact, it is demonstrated that such sinusoidal testing leads to overly optimistic expectation of system errors. Vehicle motions instead are described in terms of an acceleration spectral density that is peaked at some nonzero angular frequency and that contains no energy at zero frequency. This represents an attempt to account for vehicle motion more realistically. It is graphically demonstrated that, since the inertial system behaves as a low-pass filter to the hypothesized acceleration random process, longer system settling times lead to lower rms navigation errors.