How GPS Works
I couldn’t live without GPS. It accompanies me on late night walks, driving through unfamiliar territory, and in tracking my lost AirPods for the third time in a day.
Global Positioning System (GPS) is, without a doubt, one of the most useful inventions of the late 20th century. It has enabled cars, planes, ships, and people to navigate themselves with never before seen ease and accuracy.
Introduction
GPS is a satellite-based navigation system originally developed by the US Department of Defense as a military tool. Today, it has been made available to the public and is used in everything from smart watches to tracking products in the global supply chain. GPS relies fundamentally on the principle of trilateration, where a receiver determines its position by measuring the distance from at least three satellites.
What sparked my curiosity for this topic was a bike ride I took with my friend. We had biked to a beautiful lookout and wanted to save the coordinates so we could find it again. When we both pulled up our GPS, our phones output slightly different coordinates, despite us standing side by side. This made me curious as to why standing in the same location might result in multiple sets of coordinates.
This article will explain not only how locations are determined, but also the impact various conditions may have on generating accurate location data.
What Is GPS?
The US government maintains a set of 31 satellites orbiting Earth at an altitude of approximately 20,200 km. These satellites constantly broadcast radio signals to receivers on Earth, including a timestamp indicating when the signal left and their location at the time of transmission.
How far away each satellite is from the receiver can be computed using the speed of light and the difference in time between the receiver’s clock and the satellites’ clock. This is done using the general formula:
D = (t2-t1)c
where D represents the distance from the satellite to the receiver, t2 represents the time on the receiver’s clock at the moment of reception, t1 represents the time transmitted by the satellite clock, and c represents the speed at which the signal travels (speed of light).
These distances are treated as the radii of spheres, centered on the satellite. Hence, the intersection of the satellites’ radii gives the receiver’s position. This is computed as a system of equations.
where x, y, and z are the rectangular coordinates of the receiver, A, B, and C are the coordinates of the satellites, d is the difference in time between the receiver and the satellite’s clocks (error), and t is the signal travel time from the satellite to the receiver.
If, for example, there was a delay in receiving satellite 1’s transmission in the image above, the distance would be falsely calculated to be greater. Accordingly, the red sphere would increase in radius, resulting in a different or multiple intersections with the other spheres and a confused hiker who seems to be in multiple places at once.
Error Factors
In the real world, each satellite faces its own unique set of conditions which create errors specific to that satellite in the exact moment the signal was transmitted. Given that these satellites are in constant motion, each time they send a signal their transmission will face a different assortment of potential error factors.
Atmosphere
Atmospheric conditions have the greatest impact on reading accuracy.
Although a GPS signal spends most of its journey in the obstruction-free vacuum of space, as it nears Earth it must eventually travel through the atmosphere.
Earth’s atmosphere is composed of the ionosphere, which for our purposes ionizes gases, therefore slowing down the propagation of our signal. How much it’s slowed down depends on the time of day and overall solar activity, since this will effect how many free electrons are generated from gas ionization. Errors due to the ionosphere are more prevalent at high latitudes and during solar flares.
Secondly, the atmosphere contains the troposphere, where the index of refraction increases as a result of the dense concentration of gases and water vapor (such as in clouds). This further slows down broadcasted radio signals and is variable depending on the movement of water vapor. Troposphere errors are more impactful in areas with high humidity, such as near coastlines, and during adverse weather conditions, such as heavy rain or snow.
The further and more diagonal through the atmosphere the signal has to travel will increase the effect of atmospheric conditions on travel time. Radio signals can move a lot quicker through space’s vacuum than through a bunch of gas molecules!
Since the atmosphere is constantly changing, ionosphere and troposphere modeling and real-time data from meteorological sources are what engineers use to ensure the most accurate calculations.
Multipath
Another very common receiver-related error is multipath, which happens when the transmitted signal is reflected off of buildings, mountains, or other objects before reaching the receiver.
This can cause the signal to arrive at the receiver at slightly different times, since the path it traveled in may not have been the most direct. This creates a timing error. Advanced signal processing techniques such as filtering, correlation, and phase tracking, are often employed by receivers to correct for multipath.
Clock Error
Another source of discrepancy is a receiver clock error. While the satellites carry atomic clocks, the clocks in your average receiver are not nearly as accurate. When the times on the satellite clock and the receiver clock do not align, the distance calculated between the two will be incorrect. Given that satellites have highly precise and frequently corrected atomic clocks, time errors are usually due to the receiver clock, which may be anything from a watch to a phone. This was touched on earlier, by increasing the radius of the red satellite 1.
Conclusion
Throughout the years, mathematicians and physicists have developed incredibly intricate methods of maintaining GPS integrity, yet errors still (and will likely always) remain. Luckily, for most people’s personal usage, the GPS systems available are more than accurate enough.
And for me and my friend, the imperfect GPS reading we got at our lookout is just an excuse for another adventure 🚵🏼♀️
Recommended Further Reading
If you’re interested in learning more about how GPS works, here are some of my favorite articles on the topic:
Thanks for reading!
