We know the satellite stays in the right orbit. The correct trajectory is compiled into an ephemeris, injected into the satellite, and sent to the magnetic gps tracker via the satellite. By receiving the ephemeris of each satellite correctly, the exact position of the satellite can be ascertained.
The GPS system has very sophisticated atomic clocks on each satellite, which are regularly calibrated by monitoring stations. Satellites send navigational information, but also precise time information. The magnetic gps tracker receives this information and synchronizes it with its own clock to obtain an accurate time. Therefore, in addition to accurate positioning, magnetic gps tracker can also produce accurate time information.
Since the position of the satellite can be accurately known, in GPS observation, we can get the distance from the satellite to the receiver, using the distance formula in three-dimensional coordinates, using three satellites, three equations can be formed to solve the position of the observation point (X, Y, Z). Considering the error between the clock of the satellite and the clock of the receiver, there are actually four unknowns, X, Y, Z and the clock difference, so it is necessary to introduce a fourth satellite to form four equations for solving, so as to obtain the longitude, latitude and elevation of the observation point.
It can be seen from the principle of GPS that the magnetic gps tracker does not transmit signals; it only receives satellite launch data for calculation and then solves the positioning problem. However, if in urban high-rise areas, often faced with a small number of star search, in the actual use of the process, generally three stars can be preliminatively positioned, as shown in the following figure. From this, the lateral coordinates, longitudinal coordinates and height can be determined.
But in urban tall areas, where there are tall buildings around, the magnetic gps tracker is weak, so the direct capture may only be a star or two overhead. If the orientation of the magnetic gps tracker is adjusted, it can often receive three or even four stars, and part of the received signal is often the reflected signal emitted by the satellite.
As shown in the figure below, Star 3 is blocked by a tall building, and the red line is the direct line when there is no block, when it is blocked by a tall building, the GPS signal cannot be received. At this time, the signal reflected by Star 3 after passing through the tall building appears in the magnetic gps tracker.
According to the calculation formula, the receiver determines its position according to the distance of stars 1, 2 and 3. We assume that if there is no no. 3 star, the result of the operation: the position reflected by stars 1 and 2 can only be located on one arc, as shown by the orange line in the figure.
The reflected signal received from Star 3 forms an error distance length in the magnetic gps tracker, the length of the blue line in the figure. If we take this length as the radius (shown by the green line) and star 3 as the center of the circle, we can draw a sphere, and this sphere (shown by the yellow line) intersects the orange line, which is the position of the receiver (the red star position), of course, this position is wrong.
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