New Approach to Achieving Stand Alone GPS Attitude Determination using Dual Short Baselines for Small-Satellite

This paper proposes a new approach to GPS (Global Positioning System) attitude determination for small satellite application in LEO (low Earth orbit). Prior knowledge of attitude and integer resolution is not required. The methodology of the new approach includes integer ambiguity search, initial estimation of attitude and line bias, attitude initialisation, path difference estimation and fine attitude determination. The observable is the carrier phase difference measurement between two GPS antennas. A dual short baseline (typical baseline length up to 30 cm) is assumed in this research. The key point to initialising attitude is to estimated the attitude of individual baseline vectors with respect to the reference frame. Elimination of integer ambiguity is a simple task. Two set of vectors are required to determine an initial attitude. Once attitude is initialised, an estimation algorithm based on the extended Kalman filter starts to determine the attitude. The integer ambiguities and cycle slips can be resolved properly. The filter now is converged and, fine attitude is estimated. The robustness of the filtering estimator is tested with simulated anomalous conditions. Nomenclature A : transformation attitude matrix b : baseline vector s : line-of-sight unit vector to GPS satellite λ : L1 carrier wavelength η : integer ambiguity k : integer ambiguity including effects of error β : line bias w : measurement noise φ : real phase difference (to + ) r : actual modulo path difference (/2 to + /2) r m ( ) : measured modulo path difference r : actual path difference r m ( ) : path difference including error φ : roll angle θ : pitch angle ψ : yaw angle sup T : transpose of matrix sub B : body-fixed frame sub R : reference frame hat ^ : estimate Introduction Spacecraft attitude determination is generally based on the use of traditional attitude sensors such as Sun sensors, Earth sensors, star sensors, inertial sensors, and magnetometers. However, since GPS has been successfully used for spacecraft navigation, a new approach using GPS attitude determination has been rapidly developing for space applications. In 1993, GPS attitude determination was demonstrated for the first time on the RADCAL satellite. Using an onboard GPS receiver and multiple GPS antennas, GPS attitude sensing can be achieved through carrier phase difference measurements between two antennas. The measured scalar phase difference is used as an observable for the attitude algorithm for determining spacecraft orientation. However, there are several problems involved in the system implementation. Firstly, as a GPS receiver can measure only a fraction of carrier phase cycle (to + in radian or in equivalent /2 to + /2 in range), the number of full