Evaluation of Precise Point Positioning method with different combinations of Dual-frequencies of Galileo and BeiDou using PPPteh software

Due to advances in global navigation satellite systems, it has been possible for satellites to send different frequencies. For this reason, different combinations of these frequencies can be considered to form ionospheric codes and phase observations. In this study, the aim is to evaluate the Precise Point Positioning method using a combination of different frequencies. For this purpose, the PPPteh software provided by the authors, written under MatLab is used. PPPteh has the ability to process observations from four GPS, GLONASS, BeiDou and Galileo satellite systems to perform precise point positioning. In this software, there are all possible combinations for making Dual-frequency ionosphere-free observations for all different frequencies. There are three modes for combining different frequencies for the GPS positioning system, ten modes for the Galileo system, and three modes for building the BeiDou satellite system to make ionospheric-free observations. To evaluate the precise point positioning method, four steps have been considered in terms of position accuracy and convergence time: 1) First, use the observations of two frequencies  related to GPS and determine the position, 2) Combine the two systems satellite GPS and Galileo and select the best combination model, 3) Combining the two systems GPS and BeiDou and selecting the best combination and 4) Finally, after the previous three steps, the combination position will be determined using the three systems by the best frequency model and the results will be compared with each other. Based on the results provided for the Galileo and BeiDou navigation satellite systems, two combinations  and were selected as the best combinations for use in determining the precise point positioning, respectively. Following the precise point positioning, the addition of observations on BeiDou satellites has reduced convergence time and, in most cases, increased the three-dimensional accuracy of the coordinate components. Using a combination of the signals has a better quality than the other two combinations. The same process was followed for observations of Galileo satellites, according to which the use of observations related to Galileo satellites when combined with GPS observations has increased accuracy and reduced convergence time. The use of  signal signals is of better combination than the other three combinations. Finally, by combining all three systems and considering the selected frequency model in the first stage, it was concluded that the combination of three satellite navigation satellite systems GPS, Galileo and BeiDou significantly improved both in reducing convergence time and increasing the three-dimensional accuracy of the coordinates provided. Also, the error provided (the difference in the estimated coordinates with the final coordinates of the station from the IGS file), when using the Galileo and BeiDou systems in combination with the GPS, is noticeably different both in convergence and in the accuracy of the coordinates. Combining all three systems together increases accuracy and reduces convergence time. But in dual-combination with GPS, the use of Galileo satellite observations gives us higher accuracy as well as less convergence time. Therefore, choosing the right signals to form ionosphere-free observations in determining the exact absolute position as well as combining different observations with the correct weight for each signal in combination with GPS, can meet the user's needs in terms of accuracy and convergence.