Study On The Optimized Method Of Interpolating Precise Orbit And Clock Error In Precise Point Positioning Of GNSS

In recent years, Precise Point Positioning has become research hotspot in GNSS. It uses the file of satellite precise ephemeris and precise clock bias, utilizing only one dual satellite receiver, and use the pseudorange and carrier phase observations value for calculating, which can realize the high-accuracy positioning in static or dynamic mode anywhere all over the world.It is extremely important to study the error reduction method of this technique, because it can't eliminate the error by the differential method in Precise Point Positioning. And the satellite ephemeris error and satellite clock error is the main factor affecting the positioning accuracy. Performing Precise Point Positioning of Centimeter level accuracy is required to the high-precision precise ephemeris. The sampling interval of the precise satellite ephemeris provided for users by the major data analysis center is generally large, but in the practical positioning application, the sampling interval of user's receiver is relatively small. In order to get fast and accurate position of the satellite, it is necessary that using interpolation methods encrypts the satellite ephemeris. At present, the commonly used interpolation methods include linear interpolation, Lagrange interpolation, Newton interpolation, least squares curve fitting and Chebyshev polynomial fitting. Therefore in practical application, selecting which kind of satellite ephemeris interpolation method is one of the key problems to be solved currently. Aimed at such problem, the precise ephemeris interpolation methods were studied and discussed in this article, and the improved method is put forward to solve the problems existing in interpolation process of the commonly used interpolation method. And with a large number of examples to verify its accuracy and applicability at last.At first, this article introduces the principle of precise point positioning, the basic equation of observation value and the source of errors as well as the methods to correct them in positioning process. Then it describes in detail the principle and mathematical model of five commonly used interpolation methods(including linear interpolation, Lagrange interpolation, Newton interpolation, least squares curve fitting, Chebyshev polynomial fitting), and analysis the characteristics and applicability of this five interpolation methods. And programming the interpolation algorithm of linear interpolation, Lagrange interpolation, least squares curve fitting in MATLAB. This paper applied a set of Beidou satellite data and GPS satellite data as the experimental data and adopt three methods to encrypt Beidou satellite orbit and clock errors and GPS satellite orbit and clock errors. Contrast the interpolation accuracy of three methods with the encrypted data result. Then it proposes a interpolation method to weakened "Runge phenomenon" in the Lagrange interpolation algorithm, and verify this method can achieve the desired results with a group of Beidou data. Finally, using this method to complete the interpolation of GPS satellite orbit, this paper combines with the encrypted precise clock error data using linear interpolation method to encrypt, and completes the precise point positioning solver in RTKLIB2.4.2. Get the standard deviation on N, E, U three directions. Analysis the accuracy of calculation and draw the conclusion that improved Lagrange polynomial can improve the accuracy of Precise Point Positioning.