Vertical scaling optimization algorithm for a fractal interpolation model of time offsets prediction in navigation systems

Abstract

System time offsets between Global Navigation Satellite Systems is a key issue in multi-system positioning. A high-precision time offsets prediction model is required in actual navigation applications. In this study, the fractal characteristics of time offsets in American and Russian navigation systems are directly confirmed through fractal dimension calculations. Then, the influence of the vertical scaling factor on the prediction accuracy of the fractal interpolation prediction model is confirmed. It is found that perturbation on the estimated vertical scaling factor causes a minimal attractor bias, which is positively correlated with the prediction error. After proving the existence of the estimated vertical scaling factor of the minimal attractor biases, an optimization method of the fractal interpolation prediction model is proposed, and the related algorithms are given. The numerical results show that the time offsets prediction errors using the new model are less than 1 ns for the American navigation system and close to 2 ns for the Russian navigation system. The prediction accuracy of this model has an improvement of at least 60% over the commonly used quadratic and grey models, and an improvement of more than 13% over the standard fractal interpolation prediction model.