GPS is a satellite-based navigation system that is able to determine the exact position of objects on the Earth, sky, or space. By increasing the velocity of a moving object, the accuracy of positioning decreases; meanwhile, the calculation of the exact position in the movement by high velocities like airplane movement or very high velocities like satellite movement is so important. In this paper, seven methods for solving navigation equations in very high velocities using least squares method and its combination with the variance estimation methods for weighting observations based on their qualities are studied. Simulations on different data with different velocities from 100 m/s to 7000 m/s show that proposed method can improve the accuracy of positioning more than 50%.

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It is well known that in high-speed movements, the positioning accuracy of global positioning system (GPS) receivers decreases drastically. The models presented so far to describe high-speed motion do not represent the state of the system precisely, so positioning accuracy with the methods based on these models is not appropriate. Here, a comprehensive method is proposed to solve the accuracy issue of the single-frequency GPS receiver at high-speed motions without increasing the computational complexity. Suitable modelling of the GPS receivers at high-speed motion, using the sequential extended Kalman filter, correct determination of the process noise covariance matrix and accurately estimating the variance of the observations are the basics of the proposed approach. Simulations with different data and motion scenarios (at speeds from 100 to 7300 m/s) show that the proposed method, while not increasing the computational cost, improves the accuracy of positioning more than 70% when compared to the conventional methods.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.