In this paper we compare the performance of the extended Kalman filter (EKF) with that of a proposed filter called modified extended Kalman filter (MEKF), in terms of the actual state and the estimated state as a function of time and the integral-squared error as a function of noise intensity both for dynamics and measurement noise. All the simulation results indicate that the performance of the MEKF is better than EKF. For illustration, numerical examples are presented using both EKF and MEKF.