In this paper, a high order filter is presented for estimation of nonlinear dynamic systems. The proposed filter computes higher order moment update equations in a Jacobian free manner and a computationally attractive manner. Compared to the conventional filters such as the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), the proposed filter captures desired order of statistical moments by making use of the higher order state transition matrices developed in our previous works, providing more accurate estimates through sparse measurements. The connection between the conventional high order method, the higher order state transition matrices and the proposed filter is discussed. Orbit estimation problem is considered to demonstrate the numerical efficiency and accuracy of the proposed filter.