Global Position Reporting
Linux, amateur radio and the APRS protocol are only part of the system we have discussed so far. The GPS is truly what makes the system practical. Although the details of the GPS are extremely complex, the basic idea is relatively simple. Triangulation is used to pinpoint a receiver.
For example, assume you and your friend both have accurate synchronized clocks. At some unknown distance from you, she yells, “It is now 6:00 and 0.000 seconds.” When you hear her, your clock shows the time as 6:00 and 0.333 seconds. You can now compute your distance from her as 100 meters by multiplying the speed of sound (300 meters per second) by the elapsed time (0.333 seconds). With this single test point, you are able to compute your distance from the source. Specifically, you are located in any direction 100 meters from your friend. This scenario is shown in Figure 4A by the multiple dots located on the circumference of the circle.
With a second friend, we can further clarify our position. In Figure 4B, a friend at point Y, also with an accurate clock, takes another measurement. Again you make the computation and find the distance from this friend. You now have your position narrowed to two points shown by the two dots where the circles intersect. Using a third friend at point Z and another measurement, you are able to pinpoint your exact location.
The GPS works on a similar principle; however, the speed of light replaces the speed of sound in the experiment, and your friends are replaced by satellites. In the above explanation we have conveniently assumed that the world is flat to provide a clearer understanding of the concept. When the concept is extended to three dimensions, a single measurement does not produce a circle as shown in Figure 4A, but a sphere. A second measurement does not limit our position to two unique locations as shown in Figure 4B, but a circle that is the intersection of two spheres. Last, a third measurement does not yield a unique location as shown in 4C, but two points which are the intersection of three spheres. Thus, with three measurements, we have two possible locations. The good news is that one of the points can be eliminated since it corresponds to a position above the Earth's atmosphere. So unless you are an astronaut, your unique location on earth has been found with only three measurements.
We made a second convenient assumption, specifically that all parties in the experiment had accurate clocks. Although the GPS satellites have accurate atomic clocks, the receiver on the ground does not have such a luxury, nor would it be practical. Fortunately, by adding a fourth satellite, the person on the ground does not require an atomic clock. This is a simple algebraic problem in four unknowns: latitude, longitude, altitude and time. With four satellites we can solve for all four unknowns and provide an accurate and unique position for the listener on Earth. The experienced GPS user may argue that he has obtained accurate positions with only three satellites. This is true; it is done by letting the GPS receiver assume the altitude is 0 (sea level). Therefore, if we are willing to give up knowing our altitude, which is valid in many applications, the GPS can indeed provide an accurate position using only three satellites, since we have three unknowns and three equations.
The above explanation is in many ways an oversimplification. In real life, numerous variables affect the accuracy of the system. For example, radio frequency transmissions are affected by objects such as buildings and trees. These structures cause reflections, referred to as multi-path. Signals from the satellites are reflected off nearby structures, causing delays which ultimately affect the accuracy of the measurement. Radio frequencies are also affected by rain, sleet, snow, humidity and even the temperature of the air, since the speed of the transmission is affected as well as the attenuation of the signal. All of these variables result in loss of accuracy. However, these inaccuracies are small compared with the deliberate error called Selective Availability (SA).
To understand SA, we must understand that GPS applications fall into two service categories: the Standard Positioning Service (SPS) for civilians, and the Precise Positioning Service (PPS) for military and authorized personnel. PPS GPS receivers remove the adverse affects of SA and are therefore far more accurate. SPS GPS receivers provide less accuracy than the GPS is capable of, and each is generally limited to an accuracy of 100 meters. However, there are ways of overcoming the limitations of SPS receivers by using Differential GPS (DGPS). For those interested in DGPS, the web is an excellent source of further information.
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