Attitude estimation is an important problem for aircraft navigation and control which is commonly approached using nonlinear state estimation to fuse information from Global Positioning System (GPS) and inertial sensors. The Extended Kalman Filter (EKF) is a useful estimator for nonlinear systems; however the stability characteristics have not rigorously been proven with realistic assumptions. The stability analysis methods of previous authors were first implemented in order to obtain a baseline calculation of the requirements on the system's initial error and noise disturbances. Since these requirements were determined to be too strict for realistic application, modifications were applied to the stability analysis in order to relax these assumptions and prove the stability with more realistic assumptions. Experimental flight data is utilized to reinforce and demonstrate the theoretically derived results. Significant improvements in the initial error and noise bounds were achieved. The newly derived methods can also be applied to any other EKF application.