Gravity-induced errors in airborne inertial navigation

Abstract

This paper describes a simple yet powerful statistical technique for calculating the effects of errors in a detailed navigation gravity model on an inertial navigation system (INS) traveling a great circle flight path. Error variances in the horizontal position and velocity of an aircraft are computed from the time-dependent frequency response of the inertial navigation system and the power spectral densities of errors in the along- and cross-track gravity disturbance components derived from the navigation gravity model. The power spectra are obtained by first computing the spectrum of the vertical gravity disturbance errors using available degree spectrum models and results of mean gravity value estimation error analyses, then using fundamental equations of gravitational potential theory to relate this vertical disturbance error spectrum to the desired along- and cross-track disturbance error spectra. These spectra have dramatically different shapes with the cross-track component having much greater power at low frequencies. Since the response of a lightly damped INS is sharply peaked at low frequencies, nearly all of the navigation error is initially induced in the cross-track direction and accumulates in the along-track direction primarily through Coriolis coupling.