State interpolation for on-board navigation systems

Common concepts for autonomous on-board navigation systems rely on the nume rical integration of a spacecraft trajectory between subsequent measurement s 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-co ding of image data, the on-board navigation system has to provide continuou s dense output at: equidistant time steps, which usually conflicts with the natural stepsize of the relevant integration methods and the non-equidista nt measurement times. To cope with this problem, the integrator has to be s upplemented by an interpolation scheme of compatible order and accuracy. After presenting a representative formulation of an on-board navigation sys tem and deriving related timing and accuracy requirements, suitable Runge-K utta methods and associated interpolants are selected and evaluated. Promis ing results are obtained for the classical RK4 method in combination with R ichardson extrapolation and 5th-order Hermite interpolation. The 5th-order Fehlberg method with interpolation due to Enright and, for drag-free scenar ios, the 5th-order Runge-Kutta-Nystrom method with 5th-order Hermite interp olation provide a good performance in terms of position interpolation. Howe ver, as both methods exhibit significant: errors for the velocity interpola tion, they are not recommended for use with the outlined navigation filter. (C) 2001 Editions scientifiques et medicales Elsevier SAS.