Dynamic real-time estimation of states and parameters of nonlinear models can be done using an extended Kalman Filter (EKF), which is one of the most popular state estimators for nonlinear uncertain dynamic systems. It is considered here in its continuous discrete (CD) form, which enhances its performances if a robust and computationally efficient numerical integration method is used. The purpose of this paper is to present new efficient integration methods suited to the implementation of the CDEKF and to compare them to classical integration methods like the Dormand-Prince (DP) and Euler methods. They are then applied to a Linear Frequency-Modulated Signal (LFMS) model and to the charge/discharge of a supercapacitor. The numerical results show that for nonlinear dynamic systems or for a low sampling frequency, the proposed implementation of the EKF provides better accuracy and convergence on the tested models.