State interpolation for on-board navigation systems

Common concepts for autonomous on-board navigation systems rely on the numerical integration of a spacecraft trajectory between subsequent measurements of a navigation sensor such as GPS. In combination with a Kalman filter, a predicted state vector becomes available at discrete, but not necessarily equidistant time steps. When used for real-time attitude control or gee-coding of image data, the on-board navigation system has to provide continuous dense output at: equidistant time steps, which usually conflicts with the natural stepsize of the relevant integration methods and the non-equidistant measurement times. To cope with this problem, the integrator has to be supplemented by an interpolation scheme of compatible order and accuracy. After presenting a representative formulation of an on-board navigation system and deriving related timing and accuracy requirements, suitable Runge-Kutta methods and associated interpolants are selected and evaluated. Promising results are obtained for the classical RK4 method in combination with Richardson extrapolation and 5th-order Hermite interpolation. The 5th-order Fehlberg method with interpolation due to Enright and, for drag-free scenarios, the 5th-order Runge-Kutta-Nystrom method with 5th-order Hermite interpolation provide a good performance in terms of position interpolation. However, as both methods exhibit significant: errors for the velocity interpolation, they are not recommended for use with the outlined navigation filter. (C) 2001 Editions scientifiques et medicales Elsevier SAS.