%0 Journal Article
%T Accurate Solution of Navigation Equations in GPS Receivers for Very High Velocities Using Pseudorange Measurements
%A N. Rahemi
%A M. R. Mosavi
%A A. A. Abedi
%A S. Mirzakuchaki
%J Advances in Aerospace Engineering
%D 2014
%R 10.1155/2014/435891
%X 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%. 1. Introduction Global positioning system (GPS) does the positioning with the help of a group of satellites that each travels in its orbit around the Earth [1]. These satellites by sending L1 and L2 signals with frequency of 1575.42£¿MHz and 1227.6£¿MHz, respectively, identify their time and place toward the Earth. A GPS receiver by receiving these signals from at least four satellites organizes the navigation equations and by solving them shows the position of the user [1¨C4]. At present the only way of positioning a kinematic receiver in real time with high accuracy is by differential mode that is a relative positioning of two receivers [5, 6]. To achieve a higher accuracy, many researches have been done on differential GPS [7¨C10]. In some other research efforts too, it has been tried to combine GPS with other navigation systems to attain a higher accuracy [11¨C13]. But none of these methods are suitable for positioning at velocities of up to 7,000£¿m/s. Calculation of the exact position in the movement by high velocities like airplane movement or very high velocities like satellite movement using GPS receivers is very important. Jumping at outputs data of GPS receivers¡¯ situation and sudden acceleration at very high velocities leads to making too much error in determining the position of receiver. Some methods like least squares (LS) method that has been presented for solving navigation equations up to now generally have low precision and much error [14]. So we are looking for a method which can solve the navigation equations at very high velocities and significantly decrease positioning errors. The LS is a standard approach to the approximate solution of overdetermined systems, that is, sets of equations in which there are more equations than unknowns. According to this method, the
%U http://www.hindawi.com/journals/aae/2014/435891/