The Extended Kalman Filter (EKF) is a widely used estimator for nonlinear systems. The stability characteristics of the EKF have been examined, but have not been rigorously proven for realistic assumptions on the initial error and noise disturbances. The existing stability analysis methods 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. Significant improvements in the initial error and noise bounds were achieved. Using a case study of low-cost attitude estimation, experimental flight data was utilized to reinforce and demonstrate the theoretically derived results. While the stability characteristics were examined in the context of a specific problem, the derived methods can be applied to any EKF application.