GPS - Global Positioning System - How It Works

Nearly everyone thinks they are an expert as to how GPS works, but virtually no one is. It is immensely complicated, and it entirely is based on the Laws of Physics.

The curvature of the Earth's surface limits the line-of-sight distance available in any location. Various radio systems, including Triangulation have been in use for many decades, but they did not provide the extreme precision that the US Military wanted regarding possible battlefield logistics. So in the early 1980s, the concept of the GPS system was created.

In a crude sense, it is based on the known speed of light, and the fact that modern computers can calculate where an earth-orbiting satellite is at any instant. If both a satellite and an unknown earth location point can agree on the exact time, then a mathematical sphere can be drawn around each satellite. If this is done four different times, in calculating the distance between four DIFFERENT earth-orbiting satellites and an unknown location on the surface of the earth, a LOT of calculation can determine the one unique intersection point of the four spheres to the different satellites (each having a radius of the distance value), then you will know the location of the unknown location, usually converted into Latitude, Longitude and Altitude.

This sounds great, and it sounds easy to do, but EVERY step of the process has massive complications! Each satellite has a computer clock inside it, but those clocks are sensitive to alternately being heated by the Sun and cooled by the shadow of the Earth, twice every 90 minutes. Since it turns out that you need to have time accurate to ONE ONE-BILLIONTH of a second, if you hope to get good accuracy, constant changes in those satellite clock times is a problem, and each satellite clock must be constantly adjusted for their time, every few seconds.

Each of these satellites is also orbiting the Earth at around 17,000 miles per hour, so constant calculation of exactly where each of them are is also necessary (in massive computers on the ground) and this precise updated satellite position information must be sent up to each of the satellites. Note again that if you hope for good final accuracy, you MUST know the exact location of each satellite, every few seconds.

The Earth is NOT round (it is Oblate) and it is not smooth (there are mountains and ocean floors all over). An APPROXIMATE satellite orbit is pretty easy to calculate, but all these thousands of gravitational attractions on each satellite must also be calculated, again, every few seconds.

So now the satellites each know WHERE they are and WHEN they are!

But the calculations needed cannot be done at the satellite! A GPS device must receive a radio signal from each satellite, which passes along the time and location (x, y, and z) information to the GPS device. This information has to come FROM each of the satellites. So the FIRST thing that a GPS device must do is use its antenna to FIND four GPS satellites in the sky from that location at that time, and then it has to receive the needed time and satellite location information. Early GPS devices often took several minutes to FIND four satellites which were above the horizon, before starting to do the hard stuff!

Note that the satellite time and location information was only true for a tiny fraction of a second, as the satellite shot on by as it proceeded along in its orbit. So GPS satellites each send a 'unique pulse train' within the signal that the GPS device receives from that satellite. This pulse train is impressive complex, being a carefully chosen sequence of dots and dashes and spaces, where over 200,000 sequential characters are sent.

All GPS devices were made with that exact same pulse sequence inside them.

The GPS radio receiver constantly listens to the pulse train that is being received from that specific satellite, and it holds a sequence of the most recent 200,000 pulses in its computer memory. The GPS device then also has electronic circuits called Comparators, which compares each of those 200,000 pulses being received against the 200,000 pulses in the sequence it was born with in its computer memory. In general, the multiple comparisons results in tens of thousands of matches but also tens of thousands of not-matches, which means that the GPS device has not yet received the unique signal it is waiting for from that satellite. So, a billionth of a second later, the incoming pulse train has changed, being shifted one spot up in the Comparator's memory, and it again does all those Comparisons, and again, there is an unnotable mix of pulse matches and pulse non-matches.

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This continues. There are enormous numbers of failures in the Comparator's effort. However, if the correct satellite had sent out the pulse train, and it exactly matches the exact sequence of pulses that the GPS device is looking for, there is ONE instant when magic happens! At this ONE Comparison, ALL 200,000 pulses exactly match the known pattern in the GPS device's RAM memory.

The way that the electronics tracks all of this is to COUNT how many exact matches there are in the Comparator's efforts each time. In general, random matches might give a SUM of maybe 10,000 matches (out of 200,000 possible). And so, a different electronic circuit keeps track of these SUMS. In general, this is a graph which looks like random noise, relatively level but not significant. However, at that ONE instant when the pulse trains exactly match, the SUM for that Comparison is 200,000, and there is an extremely obvious spike in the data. This event was called an EPIC.

Why is this important? Because it informs the GPS device of the EXACT INSTANT when it RECEIVED the signal that the satellite had sent!

We now have identified the EXACT moment that the satellite had SENT the pulse train (which had been calculated on the ground and adjusted timing info was sent up to the satellite) and also the exact moment that the pulse train was RECEIVED. IF we could assume that the speed of light was constant, we could now subtract the time difference and multiply by the speed of light and then get the exact distance which had existed between that satellite and the unknown location of the GPS device.

But there are lots of new problems! The GPS device now REQUIRES an anazingly precise clock at its end, but where the satellite clocks keep getting constant corrections from the ground, your GPS device does not have so obvious a source of precise timing info. Your GPS device is constantly finding satellites just to check its timing accuracy, and then adjusting its own timing accuracy, but it is never really precise! If your GPS device heats or cools or otherwise affects timing by even just one part in ten billion, over a ten second interval, your results have become limited in precision!

In addition, we know the speed of light in empty space, but it is slower as light passes through our atmosphere, or through storm clouds or other affectors. You might actually have achieved the desired accuracy regarding the timing interval between when the signal was sent from the satellite and when it was received by your GPS device, but if it then multiples by an inaccurate value for the speed of light, the the radius of that mathematical sphere would be different, which changes the results you get.

Because of these various effects described here, GPS devices generally only have a repeatable position accuracy of around ± 100 feet. It is just physically impossible to achieve better accuracy than that from the basic GPS devices. IF you had been out in the wilderness, the ±100 foot accuracy of GPS would not have been a serious problem. But when trying to find a Pizza place, a half-block uncertainty regarding accuracy would be an inconvenience. There IS a way to 'tweak' the system by including some non-GPS technology. Say that there was a KNOWN object near your location in a city. Your device could do TWO calculations regarding locations, your actual unknown location and also the known landmark location. Rather tha just depending on actual GPS, it turns out that it is far easier and FAR more accurate to calculate your DIFFERENTIAL distance from the landmark! Since the precise Latitude and Longitude of the landmark is known, your device now knows YOUR location, to rather impressive precision!

It is actually NOT due to GPS' abilities, except indirectly. But you are then able to find the Pizza place! The GPS technology gets a little more credit than it deserves!

There is another subject. For a GPS device to first FIND four different satellites, and then LISTEN to each for the expected long pulse train, and then wait more until an EPIC is found for each, the remaining calculations are pretty fast, but the entire procedure is rather time consuming! Early GPS devices generally took around two minutes before they could do all the procedures to give you the location results. Modern GPS still have those same problems but antennas are much better and electronics is much faster, so the process takes less time today. In addition, your GPS device MIGHT be turned on and searching for satellites BEFORE you even realize it is trying! So it might accomplish some of the time-consuming processes before you think you even start! So, your impression might be that it is much faster than I am describing. There are also many other 'tricky details' that can be put into a GPS device electronics, such as a memory of WHERE your previous locations were. The odds are that they were not in Australia or Norway, that your various GPS locations are likely to be within the same region. If the computer knows that, it can make some assumptions which can speed up the calculations!


This presentation was learned and composed in 1984, while I was designing my entirely different PSST system, and then first placed on the Internet in March 2013.

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago