Spacecraft attitude estimation using the Global Positioning System - Methodology and results for RADCAL

Abstract

Methodology and results for the Global Positioning System based attitude determination of a gravity gradient stabilized satellite are presented. Algorithms for on-orbit antenna baseline estimation, attitude initialization, point solution, and Kalman filtering are described. These algorithms are demonstrated using flight data collected on board the U.S. Air Force RADCAL Satellite. The precision of the final attitude estimates is assessed to be at the level of 0.4 deg for pitch and roll and 0.7 deg for yaw. B b C e H I /1./2./3 lA,JA,kA k L v x x z ft Ar 8q S(p <$(•) v 0 Nomenclature = body frame = baseline vector = transformation matrix from orbit local to body frame = line of sight unit vector : measurement gradient matrix : identity matrix ; principal moments of inertia : basis vectors for coordinate frame A • integer cycle = orbit local frame = four-element attitude quaternion from orbit local to body frame = cross product matrix associated with the vector v; 0 v 3 -v 2Ṽ x = 0 0: state vector : measurement residual vector : line bias range difference : measured phase difference = three-element correction quaternion = phase difference residual : estimation error of a given quantity = phase difference measurement error = spacecraft orbital rate : inertial angular velocity of the body in body coordinates : local angular velocity of the body = vector quantity expressed in coordinate frame A • estimate of a quantity = quaternion composition operation; see Ref. 1

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“…The use of GPS for space applications was extended to spacecraft attitude determination by using carrier phase difference measurements between two antennas [1], [2]. However, the substantial problem is an integer ambiguity in the received carrier phase measurements.…”

A simple recursive method for stationary receiver position estimation using GPS difference measurements

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Control of Flexible Structures Using GPS: Methods and Experimental Results

“…9. The pulse tends to positively rotate the center section q 5 increasing and negatively rotate the end section q 8 decreasing. Both open and closed-loop system responses are compared to show the performance of the active vibration control.…”

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