A direct quadrature based nonlinear filtering with extended Kalman filter update for orbit determination

An optimal estimation of the states of a nonlinear continuous system with discrete measurements can be achieved through the solution of the Fokker-Planck equation, along with the Bayes´ formula. However, solving the Fokker-Planck equation is restrictive in most cases. Recently a nonlinear filtering algorithm using a direct quadrature method of moments and the extended Kalman filter update mechanism was proposed, in which the associated Fokker-Planck equation was solved efficiently and accurately via discrete quadrature and the measurement update was done through the extended Kalman filter update mechanism. In this paper this hybrid filter based on the DQMOM and the EKF update is applied to the orbit determination problem with appropriate modification to mitigate the filter smugness. Unlike the extended Kalman filter, the hybrid filter based on the DQMOM and the EKF update does not require the burdensome evaluation of the Jacobian matrix and Gaussian assumption for system noise, and can still provide more accurate estimation of the state than those of the extended Kalman filter especially when measurements are sparse. Simulation results indicate that the advantages of the hybrid filter based on the DQMOM and the EKF update make it a promising alternative to the extended Kalman filter for orbit estimation problems.