Why does GPS need 24 satellites to form a satellite constellation, and why does it need 4 satellites to locate accurately?

The space part of GPS consists of 24 working GPS satellites, which together form a constellation of GPS satellites, of which 2 1 is a navigation satellite and 3 are active backup satellites. These 24 satellites are distributed in six orbits around the earth with an inclination of 55. The operating period of the satellite is about 12 sidereal time. Every GPS working satellite will send out navigation and positioning signals. GPS users use these signals to work.

At any time, there are no less than 6 satellites at the zenith of any area, usually 6-9, and satellites can be seen.

The basic principle of GPS positioning is that according to the instantaneous position of high-speed moving satellite as the known initial data, the position of the point to be measured is determined by the method of space distance intersection. As shown in the figure, assuming that a GPS receiver is installed 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, and other data such as satellite ephemeris received by the receiver can be added to determine the following four equations:

The coordinates x, y, z and Vto of the point to be measured in the above four equations are unknown parameters, where di=c△ti (i= 1, 2,3,4).

Di (i= 1, 2, 3, 4) are the distances from satellite 1, satellite 2, satellite 3 and satellite 4 to the receiver respectively.

△ti (i= 1, 2, 3, 4) is the time when the signals of satellite 1, satellite 2, satellite 3 and satellite 4 arrive at the receiver respectively.

C is the propagation speed of GPS signal (that is, the speed of light).

The meaning of each parameter in the four equations is as follows:

X, y and z are the spatial rectangular coordinates of the coordinates of the points to be measured.

, yi, zi (i= 1, 2, 3, 4) are the spatial rectangular coordinates of satellite 1, satellite 2, satellite 3 and satellite 4 at time t, respectively, which can be obtained from satellite navigation messages.

Vt i (i= 1, 2, 3, 4) are the clock differences of satellite clocks of satellite 1, satellite 2, satellite 3 and satellite 4 respectively, which are provided by satellite ephemeris.

Vto is the clock error of the receiver.

The coordinates x, y and z of the point to be measured and the clock error Vto of the receiver can be calculated from the above four equations.