Main Errors and Elimination Algorithms in GPS Positioning

　　The main errors in GPS positioning are: star clock error, relativistic error, earth rotation error, ionosphere and troposphere error. 1) Star clock error The star clock error is formed by the error between the on-board clock and the GPS standard time. GPS measurement is based on precise time measurement. The star clock error time can reach 1ms, and the resulting distance deviation can reach 300Km. It must be be eliminated. The star clock error is generally represented by a binomial equation. (3) The purpose of correction is achieved by sending the binomial coefficients in the GPS ephemeris. After this correction, the error between the star clock and the GPS standard time can be controlled within 20ns. 2) Relativistic error According to the theory of relativity, after the clock with frequency on the ground is installed on the satellite running at the speed of , the clock frequency will change, and the amount of change is:

　　That is, the clock on the satellite is slower than that on the ground. To correct this error, the method of coefficient improvement can be used. This coefficient is broadcast in the GPS ephemeris to eliminate the relativistic error, and the relativistic error can be controlled within 70ns. 3) Earth rotation error GPS positioning adopts the agreement earth coordinate system that is fixed with the earth, and rotates around the z-axis together with the earth. The position (coordinate value) of the satellite relative to the protocol earth system is relative to the epoch. If the satellite is in a certain position in the protocol coordinate system at a certain moment of transmitting the signal, when the ground receiver receives the satellite signal, due to the rotation of the earth, the satellite is no longer at the position (coordinate value) at the moment of transmission. That is to say, in order to solve the position in the protocol coordinate system when the receiver receives the satellite signal, the coordinate system at this time must be used as the reference coordinate system for solving. The time used to solve the satellite position is the time when the satellite transmits the signal. In this way, the satellite position solved at this moment must be transformed into the position in the reference coordinate system. Let the angular velocity of the earth's rotation be we, and the signal propagation delay from the instant of the transmitted signal to the instant of the received signal is △t, then the longitude of the ascending node is adjusted to be in this time process, then the three-dimensional coordinate is adjusted to be (4) The positioning error caused by the earth's rotation is in meters level, which must be considered to be eliminated during precise positioning. 4) Ionospheric and tropospheric errors The ionosphere refers to the atmosphere above the earth at a height between 50 and 1000 km above the ground. The gas molecules in the ionosphere are strongly ionized due to the radiation of various rays from celestial bodies such as the sun, forming a large number of free electrons and positive ions. The ionospheric error mainly consists of ionospheric refraction error and ionospheric delay error. The error caused by it can reach about 50 meters in the vertical direction and about 150 meters in the horizontal direction. At present, a strict mathematical model cannot be used to describe the magnitude and variation of electron density. Therefore, to eliminate ionospheric errors, use ionospheric correction models or dual-frequency observations to correct them. The troposphere refers to the bottom layer of the atmosphere within a range of about 40km from the ground, accounting for 99% of the entire atmospheric mass. Its atmosphere is denser and more complex than the ionosphere. The troposphere is in contact with the ground, and the radiant heat energy is obtained from the ground, and the temperature decreases with the increase of altitude. Tropospheric refraction includes two parts: one is the path delay caused by the slowing of the propagation speed of electromagnetic waves or the speed of light in the atmosphere, which accounts for the main part; the other is that when the GPS satellite signal passes through the troposphere, the propagation path is also bent, which makes the measurement The distance is biased. It can reach 2.5 meters in the vertical direction and 20 meters in the horizontal direction. Tropospheric errors are also corrected by empirical models. The ionospheric and tropospheric errors are eliminated in the GPS ephemeris by giving the ionospheric tropospheric model and model parameters. The experimental data show that the effectiveness of using the model to improve the ionospheric error is 75%, and the effectiveness of the tropospheric error is 95%.

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Main Errors and Elimination Algorithms in GPS Positioning