Implicit Extended Kalman Filter for Optical Terrain Relative Navigation Using Delayed Measurements

The exploration of celestial bodies such as the Moon, Mars, or even smaller ones such as comets and asteroids, is the next frontier of space exploration. One of the most interesting and attractive purposes from the scientific point of view in this field, is the capability for a spacecraft to land on such bodies. Monocular cameras are widely adopted to perform this task due to their low cost and system complexity. Nevertheless, image-based algorithms for motion estimation range across different scales of complexities and computational loads. In this paper, a method to perform relative (or local) terrain navigation using frame-to-frame features correspondences and altimeter measurements is presented. The proposed image-based approach relies on the implementation of the implicit extended Kalman filter, which works using nonlinear dynamic models and corrections from measurements that are implicit functions of the state variables. In particular, here, the epipolar constraint, which is a geometric relationship between the feature point position vectors and the camera translation vector, is employed as the implicit measurement fused with altimeter updates. In realistic applications, the image processing routines require a certain amount of time to be executed. For this reason, the presented navigation system entails a fast cycle using altimeter measurements and a slow cycle with image-based updates. Moreover, the intrinsic delay of the feature matching execution is taken into account using a modified extrapolation method.