A study of the effects of state transition matrix approximations

The effects of using an approximate state transition matrix in orbit estimation are investigated. The approximate state transition matrix results when higher order geopotential terms in the equations of motion are ignored in the formation of the variational equations. Two methods of orbit estimation are considered: the differential correction procedure (DC) and the extended Kalman filter (EKF). The system used for the study is the Research & Development version of the Goddard Trajectory Determination System. The effects of the approximation are analyzed on a number of orbits. These orbits of various inclinations and semimajor axes. Other parameters studied include geopotential models and DC arc length.