A new method called the approximate second-order extended Kalman filter (AS-EKF) has been developed to improve accuracy and reduce computing time in nonlinear filtering systems. Unlike the traditional extended Kalman filter (EKF) which linearizes all nonlinear models, the AS-EKF estimates the expectation value to the second-order of accuracy. This new approach is shown to be more accurate than the EKF and requires less computing time than the unscented Kalman filter (UKF). It can be used in nonlinear filtering applications where both accuracy and computing time are important.