Dynamic Models of Satellite Relative Motion and their effects on Kalman Filter

Abstract

Abstract In this paper we will study the effects of an increasingly complex Kalman filter state transition matrix on the accuracy of the estimation of a non-linear relative navigation system. The propagation model will be constant in all the cases. The measurements are generated using Xu-Wang model and then noise is added. Whereas the process non-linear vector function/propagation matrix of the Kalman filter will be modified. In the first scenario the Clohessy-Wiltshire equations are considered as the basic propagation model of the Kalman Filter. In the second scenario the eccentricity of the chief satellite’s orbit is included in the model of the Kalman Filter. In the 3rd case we are using the model presented by Xu-Wang which incorporates the oblateness of Earth into the Tschauner-Hempel model. The divergence of the Kalman Filter is studied and provides a guideline to design engineers.