Use of nonlinearities for increased observability in relative orbit estimation

In this paper, the effects of incorporating nonlinearities in sequential relative orbit estimation are studied for a chief spacecraft in a circular orbit, assuming either range or line-of-sight measurement of the deputy from the chief. The relative motion models used in an extended Kalman filter can be categorized into four cases: first order (HCW equation), second order, third order and full nonlinear. Observability is studied analytically using Lie derivatives and numerically with the observability index and condition number obtained from employing an extended Kalman filter. The results highlight the improving benefits of using higher order nonlinear models.