Inertial navigation system errors and dynamics

Includes bibliographical references (pages 253)The first half of this paper is concerned with the detection of a class of system errors generally known as heading sensitivity. It has been the author's goal to develop system level troubleshooting techniques to isolate the contributions of the known causes of these errors. The errors studied include twice spin translational, radial mass unbalance, and servo offset. Using the methods of the discrete Fourier series, heading sensitivity errors can be expressed as a finite sum of complex exponentials. Not only does this represent an improvement over the present straight line interpolation method but the magnitudes of the complex coefficients are related to the contributions of the different error sources. The second half of this paper addresses the modelability of nutation in our systems. A chapter is devoted to a study of three distinct open loop transfer functions used to assess closed loop stability of a two axes servo system. It is demonstrated that the present method of analysis employs a single axis model whpse accuracy breaks down at nutation frequencies (~650Hz). The present day open loop transfer function (o.l.t.f) measurement is found to yield absolute stability information only. Its relative stability margin at nutation is shown to be in error by 28.5 degrees. The complex o.l.t.f. appears to be the only appropriate frequency domain analysis technique. This technique is explained and a method for measuring the complex o.l.t.f is proposed. Using the complex analysis technique it is shown that nutation is impossible in platforms whose resonant frequencies are at or near 650 Hz. This is in direct contradiction to very strong and conclusive empirical findings. More data is requred to more firmly establish this contradiction. The weakest link in the analysis is in the gyro transfer function. When the gyro model is modified to include the effect of gyro case to shaft resonance at ~550 Hz it is found that all systems would nutate. The model needs to be modified further to include the effects of gyro mass unbalance. It is hoped that by controlling the sense of mass unbalance one could gain control over 180 degrees worth of phase shift. Although the nutation problem has been solved electrically and at considerable expense it needs to be understood. Furthermore the gyro transfer function needs to be modified to more closely reflect reality at nutation frequencies