An analytic method of orbit determination in near-circular orbit using horizon sensor data

The problem of the estimation of the state parameters of a spacecraft in near-circular orbit around the oblate earth is presented. The measurement equations are valid for the spheroidal earth, and the dynamical equations account for the first-order effect of the J2 perturbation. An analytic, autonomous orbit determination subsystem is thereby created where position and velocity parameters respective to a rotating reference frame are updated on a regular basis. For the simplified case of the spherical earth where the measurements are linearized and the dynamics reduced to its simplest form, standard deviations for the position and velocity parameters are obtained in closed form as explicit functions of time.