Sampling and Quantization Errors in a Digitally Mechanized Inertial Navigator

This paper investigates the effects of sampling and quantization in a digitally mechanized inertial navigator. A constant altitude, meridian plane, pure Schuler tuned inertial navigator model on a nonrotating earth is used for analysis. Insofar as sampling and quantization effects are concerned, nothing significant is lost by this restriction since the cross-coupling effects are small, and the earth rotation vector components on the platform axes are slowly varying. On the other hand, the analysis is greatly simplified by these restrictions. Time and frequency domain analysis of the sampled-data system is presented and the effects of quantization present at the digital computer input and output are evaluated. It is concluded that root-mean-square position errors can be held to a few thousand feet for a two hour mission, using a sampling rate of the order of one second and a gyro impulse torquer quantization level of about one arc second.