The following is a step-by-step explanation of the "principle of satellite positioning," which cannot be avoided when talking about GEONET Stations.
You may use a tripod to hold the camera in steady position. The ceiling microphone in a concert hall is suspended by three wires. Distances from the three points determine a single point in 3D space.
The principle of satellite positioning is the same. The receiver's position is determined by knowing the distances from three satellites and it's positions. I could say the receiver is suspended by three wires from satellites fixed to the celestial sphere. Although two solutions exist geometrically, your choice is clear, the one closer to the center of the earth. Because of the gravity in the case of the suspended microphone, and it should be near the earth's surface in the case of GPS.
In addition, the same principle applies to earthquake epicenter estimation. But in meteorite trajectory estimation, the principle is different because that is a matter of angle, not distance.
In the begining of GPS's texts, it is explained to require a minimum of four satellites. This is a consequence of the fact that radio waves are used as a measuring instrument.The speed of radio waves , "c" the speed of light, is incredibly fast, about 300 million meters per second. To obtain a reasonable accuracy of distance, the clock accuracy has to be on the order of 1/300 million of a second.
The atomic clocks on GNSS satellites have that level of accuracy and are, of course, extremely large, expensive, and difficult to handle.
The "fourth satellite" appears as a solution, when you don't have such a clock in the receiver.
Knowing the position means finding the value of the coordinates x, y and z. Two equations are needed for two unknowns, and three equations are needed three. As you know , this is first taught in math class of junior high school.
We treat the time appears on the clock of the receiver " t ", as the unknown. Now there are four unknowns: x, y, z, and t. To find values of these four unkowns, we need four equations. By receiving signals from four satellites with known positions, we are able to formulate the necessary four equations, which can then be solved to find the values of four unknowns.
To explain these, I wrote articles below.
- 宝探しで理解する衛星測位（1）2次元（平面）の測位
- 宝探しで理解する衛星測位（2）3次元（空間）の測位
- 宝探しで理解する衛星測位（3）衛星3機での測位
- 宝探しで理解する衛星測位（4）距離に誤差がある場合の測位
In the fourth article, I thought it was a very good idea to express the distance error X common to all satellites (equivalant to receiver's clock error) in terms of the entity of "sliding a ring at the end of bundled ropes," but it was only well received by a small portion of the readers (tears).
Anyway, the number and orbits of the first GNSS, the U.S. GPS, were determined based on the design requirement that "at least four satellites should be visible from everywhere on the earth. "
This is the core of the system and the reason it is called the Global Positioning System.
With a receiver equipped with the good-performing atomic clock, positioning would be possible with only three satellites, as the principle shows.
In the future that atomic clocks become commodity, cell phone towers, WiFi access points, and even coffee makers or refrigerators will start sending out signals, and we will be able to determine our exact location without directly relying on satellites. It may happen, or may not.