Precise GPS orbit determination and prediction using H ∞ neural network

Abstract In this paper, I present a method to determine and predict precisely the GPS satellite orbit by using a neural network. The neural network used in this paper is based on the BP (backpropagation) learning algorithm. The BP algorithm is particularly attractive because it is H ∞ optimal. It is a robust algorithm in the sense that small disturbances and modeling errors lead to small estimation errors (For a non‐robust algorithm, such as the classical maximum likelihood and least square methods, it is possible that small disturbances and modeling errors may result in large estimation errors). This is certainly the case for the estimation of the GPS satellite orbit because the satellite orbital model usually contains small disturbances and perturbations that are difficult to model. Currently, the simulation result shows that we can use the well‐trained network to predict about six days’ data and the orbital will can be within a meter. The result is compared with the classical polynomial interpolation method. It is believed that, if we extend the training time, the prediction period can be much longer.