An Improved Kalman Filter for Satellite Orbit Predictions

The nonlinear problem of tracking and predicting where a satellite will be over some time can be difficult with the recognition of modeling error and ground site radar tracking errors. For this reason it is important to have an accurate modeling program with the fidelity to correct for any errors in orbital motion and predict the most accurate positioning at some future time. The Extended Kalman Filter is one such program that can accurately determine position over time given estimate ranges for sources of error. However, the Extended Kalman Filter contains many linear approximations that allow its prediction and correction methods to work. This paper will discuss the effects of replacing the linearizing approaches made in the orbital model part of the program with numerical small-step approaches. The overall errors during prediction will be compared for an analysis of the corrective ability of the filter. Additionally a final prediction at a later date and another location will serve as an indicator to the usefulness of the prediction capabilities over time. In exploring these effects, it will be shown that the linearizing approximations made in the development are a good approximation to the numerical results. The effects of modeling error, perturbation effects included, and the degree of approximation all play a significant role in accuracies of prediction. The effects of removing linearizations are small in comparison to the effects of perturbations and modeling error. The results of the numerical approximations contain a great robustness and as such help simplify the modeling process. The modeling process is discussed with reference to ADA program code. With these results it can be seen that there are several methods of using the Extended Kalman Filter for orbital prediction which maintain a high degree of accuracy and can be very useful when applied to real-world satellite prediction.