Non linear sigma point kalman filter applied to orbit determination using GPS measurements

Abstract

The purpose of this paper is to present a development of a non linear Kalman filter, based on the sigma point unscented transformation, aiming at real time satellite orbit determination using actual GPS measurements. If the dynamic system and the observation model are linear, the conventional Kalman filter may be used as an estimation algorithm. However, not rarely, the dynamic systems and the measurements equations are of non linear nature. For solving such problems, convenient extensions of the Kalman filter have been sought. The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for non linear systems. However, this task is difficult to implement, difficult to tune, and only reliable for systems that are nearly linear on the time scale of the filter working updates. Therefore, there is a strong need for the search of a method that is probably more accurate than linearization, but does not incur either the implementation or additional computational costs. To overcome this limitation, the unscented transformation was developed as a method to propagate mean and covariance information through non linear transformations. In this work, the differential equations describing the orbital motion and the GPS measurements equations will be placed in a suitable form. They will be adapted for the unscented filter, using the sigma point Kalman filter.