A statistical analysis of gravity-induced errors in airborne inertial navigation

Abstract

This paper describes a simple yet powerful statistical technique for calculating Inertial Navigation System (INS) errors due to errors in the Navigation Gravity Model (NGM). Position and velocity e rror variances are obtained by multiplying the Power Spectral Density (PSD) of horizontal gravity disturbance error by the timedependent frequency response function of the INS and integrating over f requency. Two-dimensional disturbance error spectra a re projected onto the flight path to obtain t he along-track and crosstrack PSDs. These PSDs have dramatically different shapes with t he cross-track component having much greater variance at t he low frequencies (especially when a detailed NGM is used). The response of a lightly damped INS is sharply peaked at the Schuler f requency so that at aircraft speeds nearly a1 1 the error is initially induced in the cross-track channel and only enters the along-track channel through Coriolis coupling. The results obtained f rom this simple analytical method are in excellent agreement with more compl icated error analyses based on