High Precision Satellite Orbit Simulation: A Test Bench for Automatic Differentiation in MATLAB.




A detailed understanding of the earth's gravitational field is crucial for a precise prediction of a satellite flight trajectory. The model of the CHAMP gravitational potential based on recent high accuracy measurements is taken as a starting point for a mechanically generated implementation of its gradient. For a more detailed mathematical model, the Jacobian of the right-hand side of the motion equation is also mechanically computed. This is achieved by automatic differentiation with the recent software tool ADiMat (Bischof et al., SCAM2002, pp. 65-72, IEEE Comp. Soc., 2002). Since an analytic form of the gradient and the Jacobian are available, the situation serves as a suitable test case for ADiMat implementing automatic differentiation in MATLAB.