Main Errors in GPS Positioning and Their Elimination Algorithm

　　The main errors in GPS positioning include: star clock error, relativity error, earth rotation error, ionosphere and troposphere error. 1) Star clock error Star clock error is caused by the error between the satellite clock and GPS standard time. GPS measurement is based on precise time measurement. The star clock error time can reach 1 ms, and the distance deviation caused can reach 300 km, which must be eliminated. Generally, binomial is used to express the star clock error. (3) In GPS ephemeris, binomial coefficients are sent to achieve the purpose of correction. After this correction, the error between the clock and GPS standard time can be controlled within 20ns. 2) Relativity error According to the theory of relativity, after the clock with frequency on the ground is installed on the satellite running at speed, the clock frequency will change, and the change amount 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 GPS ephemeris to eliminate the relativistic error, which can be controlled within 70ns. 3) The GPS positioning of the earth rotation error adopts a protocol earth coordinate system fixed to the earth, which rotates along the z axis 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 at a certain position in the protocol coordinate system at the moment of signal transmission, when the ground receiver receives the satellite signal, due to the rotation of the earth, the satellite is no longer at the instant of signal transmission (coordinate value). In other words, in order to solve the position of the receiver in the protocol coordinate system at the time of receiving satellite signals, the coordinate system at that 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 that time must be converted to the position in the reference coordinate system. If the earth rotation angle speed is we, and the signal propagation delay from the instant of the transmitted signal to the instant of the received signal is △ t, then in this time process, the longitude of the ascending intersection point is adjusted to, and the three-dimensional coordinate is adjusted to (4) The positioning error caused by the earth rotation is at the meter level, which must be considered to be eliminated during precision positioning. 4) Ionosphere and troposphere error Ionosphere refers to the atmosphere above the earth at a height of 50-1000km from the ground. The gas molecules in the ionosphere are strongly ionized due to various radiation from the sun and other celestial bodies, 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 150 meters in the horizontal direction. At present, it is impossible to describe the size and change rule of electron density with a strict mathematical model. Therefore, the ionospheric correction model or dual frequency observation is used to eliminate the ionospheric error. Troposphere refers to the bottom layer of the atmosphere within 40km from the ground up, accounting for 99% of the total air quality. Its atmospheric density is larger than the ionosphere, and its atmospheric state is more complex. The troposphere contacts the ground and receives radiant heat from the ground. The temperature decreases with the rise of height. Tropospheric refraction includes two parts: one is the path delay caused by the slow propagation speed of electromagnetic wave or light speed in the atmosphere, which is the main part; Second, when GPS satellite signals pass through the troposphere, the propagation path will also be bent, which will lead to deviation in the measured distance. 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. In GPS ephemeris, ionospheric and tropospheric errors are eliminated by setting ionospheric and tropospheric models and model parameters. The experimental data show that the ionospheric error and tropospheric error can be improved by 75% and 95% respectively.

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