The basic principle of GPS positioning is to determine the position of the point to be measured by using the method of space distance resection based on the instantaneous position of the high-spee
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The basic principle of GPS positioning is to determine the position of the point to be measured by using the method of space distance resection based on the instantaneous position of the high-speed moving satellite as the known starting data. Assuming that the GPS receiver is placed at the point to be measured on the ground at time t, the time △ t when the GPS signal arrives at the receiver can be measured. In addition to the satellite ephemeris and other data received by the receiver, the following four equations can be determined:
In the above four equations, the coordinates x, y, z and Vto of the point to be measured are unknown parameters, where di=c △ ti (i=1,2,3,4).
Di (i=1, 2, 3, 4) is the distance from satellite 1, satellite 2, satellite 3, and satellite 4 to the receiver.
△ ti (i=1, 2, 3, 4) is the time that the signal of satellite 1, satellite 2, satellite 3, and satellite 4 arrives at the receiver.
C is the propagation speed of GPS signal (i.e. the speed of light).
The meanings of each parameter in the four equations are as follows:
x. Y, z are the space rectangular coordinates of the coordinates of the point to be measured.
Xi, yi, zi (i=1, 2, 3, 4) are respectively the space rectangular coordinates of satellite 1, satellite 2, satellite 3, and satellite 4 at time t,
It can be obtained from satellite navigation messages.
Vti (i=1, 2, 3, 4) is the clock difference of satellite clocks of satellite 1, satellite 2, satellite 3, and satellite 4 respectively, which is provided by satellite ephemeris.
Vto is the clock error of the receiver.
The coordinates x, y, z of the point to be measured and the clock difference Vto of the receiver can be calculated from the above four equations.
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