Analytical and numerical study of differential error equations for autonomous strapdown INS functioning in normal geographic frame

Abstract

This paper presents the results of analytical and numerical study of nonhomogeneous full (nonlinear) and linear (linearized) differential error equations for autonomous strapdown INS, functioning in the normal geographic frame, which were derived earlier by the authors of this paper. These equations form the tenth-order system of nonstationary differential equations for object's altitude, latitude and longitude errors, northerly, vertical and easterly components of object's relative velocity error, and the errors for Rodrigues-Hamilton (Euler) parameters, which describe the orientation of an object in the normal geographic frame. Analytical estimates of strapdown INS errors are derived. For the three particular cases of object's motion, the analytical solutions are derived for the linear nonhomogeneous differential error equations for strapdown INS, and the following formulas are obtained: exact explicit formulas, which express the roots of the sixth-order characteristic equations, which characterize the intrinsic dynamics of strapdown INS and its instability for those particular cases of object's motion, through the parameters of object's unperturbed motion; the formulas for the amplitudes, frequencies, initial phases of harmonic components of the laws of variation of the errors of object's altitude, latitude, longitude, relative velocity projections; the formulas for the exponents of exponential components of these errors, which characterize their decrease or increase over time (these formulas characterize intrinsic dynamics of the INS).