Comparison of EKF and UKF for Robotic Missions to Mars

The batched Kalman lter works well for a wide variety of orbit determination scenarios but requires linearized
approximations to the underlying dynamical system. Furthermore, implementation depends on the
computation of partial derivatives for all measurements and parameters used in the lter, a non-trivial task
even when analytical derivations are possible. To address these limitations, many extensions and modi -
cations to the linear Kalman lter have been proposed over the years since Kalman's initial publication.
Our investigation examines two popular variants of the Kalman lter, namely the Extended Kalman Filter
(EKF) and Unscented Kalman Filter (UKF), within the context of spacecraft missions to Mars. The EKF
relies on the same mathematical basis as the classic version of the lter, however it sequentially updates
the linearization as the ltering process is conducted. In contrast, the UKF is built upon the unscented
transform which samples the nearby solution space and numerically propagates perturbed trajectories as
part of the update / estimation process. We assess the performance of the ltering algorithms under a
variety of mission scenarios with the goal of establishing decision criteria for which implementation to use
under di ering circumstances.