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The basic principle of GPS positioning is to use the instantaneous position of high-speed moving satellites as known starting data, and use the method of spatial distance resection to determine the position of the test point.
Assuming that a GPS receiver is placed at the ground test point at time t, the time △ t of the GPS signal reaching the receiver can be determined. In addition, the satellite ephemeris and other data received by the receiver can determine the following four equations:
The meanings of each parameter in the four equations are as follows:
x. Y and z are the spatial Cartesian coordinates of the coordinates of the point to be measured.
Vto is the clock deviation of the receiver.
C is the propagation speed of GPS signals, that is, the speed of light.
Di (i=1, 2, 3, 4) is the distance between satellite 1, satellite 2, satellite 3, and satellite 4 to the receiver.
△ ti (i=1, 2, 3, 4) is the time it takes for signals from satellites 1, 2, 3, and 4 to reach the receiver.
Di=c △ ti (i=1, 2, 3, 4)
Xi, yi, zi (i=1, 2, 3, 4) are the spatial Cartesian coordinates of satellite 1, satellite 2, satellite 3, and satellite 4 at time t, obtained from satellite navigation messages.
Vti (i=1, 2, 3, 4) is the clock deviation of satellite clocks for satellites 1, 2, 3, and 4, provided by the satellite ephemeris.
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