State and Covariance Matrix Propagation for Continuous-Discrete Extended Kalman Filter Using Modified Chebyshev Picard Iteration Method

In this paper, we propose a new method for the extended Kalman Filter state estimation for nonlinear systems with no closed-form solutions, given noisy state measurements are available with known uncertainties. The system is defined by a couple of sets of equations called the “moment equations.” In the CD-EKF discrete, noisy state estimations are available at known time stamps. Propagation of the state estimation requires the integration of the moment equations that can diverge if the underlying system is stiff. We are employing the MCPI method at this stage, thus significantly improving the propagation accuracy compared to traditional methods. The proposed CD-EKF is applied to two problems (1) the famous Duffing Oscillator, a known stiff system, (2) to the Xu-Wang equations of relative orbital propagation, which define the relative motion of two satellites under the J2 perturbation of Earth.