On GPS based attitude determination

The TerraSAR-X/PAMIR experiment is a spaceborne/airborne hybrid bistatic synthetic aperture radar (SAR) experiment using the German earth-observation satellite TerraSAR-X as transmitter and the Fraunhofer-FHR's airborne radar system PAMIR as receiver. Due to the independent operation of the transmitter and receiver, accurate position, attitude and velocity parameters of the airborne platform serve as necessary parameters for the synchronization procedure and the subsequent generation of radar images. All these parameters can be obtained by using Global Positioning System (GPS) system. This thesis highlights the attitude determination technique using GPS multi-antenna system augmented by a constant angular rate model.
Differential positioning technique with carrier phase data is usually applied for accurate positioning. Cycle-slip detection and repair are prerequisites for processing the carrier phase data. By analyzing and refining the traditional dual-frequency approaches, a novel algorithm is elaborated for cycle-slip detection, determination and validation in triple-frequency GPS.
The differential positioning technique can be expanded onto the multiple GPS antennas for attitude determination. Regarding to this technique, a software package is developed and presented to process the GPS raw data in a post-processing. In order to improve the accuracy limited by the short antenna space on the airplane fuselage, the GPS multi-antenna system can be incorporated with a constant angular rate model through Kalman filters for less-maneuvering airplanes. By comparing different nonlinear Kalman filters in terms of the estimation accuracy and the computational burden, the extended Kalman filter is identified as a proper choice for this application. However, approximating the real dynamics by a constant angular rate model might lead to mismodeling errors. An adaptive interacting multiple-model approach is proposed to reduce the model transition errors as well as to tune the process noise online for an improved accuracy.
The precision of position, attitude and velocity parameters obtained from GPS is calculated first in order to analyze the error propagation from GPS measurements to the parameters for radar motion compensation. Based on a geometric representation of the radar Antenna Phase Center (APC) in the along/cross-track frame, a series of error analysis is carried out to derive the potential errors on the Doppler centroid frequency and the positioning error of the APC.