Two navigation technologies, three centuries apart

This blue plaque remembering John Harrison is ...

Image via Wikipedia

(Disclaimer: Although I am employed by Telenav, Inc., a company specializing in GPS applications, there is nothing proprietary included in this article – it is all information readily available from sources such as Wikipedia).

Navigation has changed quite significantly over the years. For quite some time, mariners have been able to calculate their latitude – their distance north or south of the Equator – with reasonable precision; just measure the angle of the sun above the horizon when highest in the sky, adjust for the tilt of the earth and the progress of the seasons, and, with a considerable bit of geometry (quite literally) out comes the result. It takes quite some effort to compute by hand, but such an essential requirement at sea deserves that much attention.

Establishing longitude, however, is a considerably more challenging proposition. In theory, it's quite simple, provided you can accurately tell the time. The notion of time zones is familiar; with every degree of longitude one travels east or west (about sixty nautical miles at the equator), the times of sunrises and sunsets shift by four minutes. In other words, if an accurate clock was set in Greenwich and taken on board a ship, observing the sun at noon and checking the time difference gives the longitude. The problem, though, is to find an accurate timepiece, particularly one that would operate satisfactorily on a ship with wide ranges of temperature, humidity, rough seas, and so on. Measuring longitude precisely was so important to navigation that the British Parliament passed an act in 1714 establishing a prize, worth millions in modern terms, for anyone who could suitably make progress in this field. John Harrison was a man who dedicated his entire life to this problem, making succession after succession of better and better chronometers; quite a tall order for the times. The terms and conditions of the prize required an accuracy better than sixty miles for an Atlantic crossing before any money would be paid; as mentioned above, that requires the clock stays within four minutes of true over the entire trip.

Nowadays, with atomic clocks and GPS, it seems the problems of three hundred years ago are far behind us, but in fact, even GPS depends on something very similar to the longitude problem. While most people have some ideas exactly how GPS works, there may be some surprising details. Basically, GPS satellites transmit time signals. A receiver can read the time signal, compute exactly where the satellite should be at that time based on its known orbit, calculate the time the message took to arrive and hence the distance to the satellite, and, with a bit of triangulation from multiple satellites, work out exactly where on the Earth the receiver is. At least, that's the theory – but, with a little thought, you'll realize that can't possibly work.

Radio waves travel at the speed of light, three hundred million meters per second. Even if time measurements for GPS were accurate to a millionth of a second, that's three hundred meters – hardly the sort of accuracy everyone expects from their navigation devices. And the quartz crystals in our mobile devices – yes, those very same quartz crystals that were vaunted for their accuracy when they were included in digital watches – are nowhere near as accurate as that. (The important thing about quartz crystals is not their accuracy – it's that they're ridiculously cheap). If the clocks in the mobile devices drift, it would be very difficult to compute a position on Earth; in fact, the position calculated would be thousands of miles off and maybe not on the planet at all. So how can GPS achieve the results with the accuracy we're used to? Is there another John Harrison who found a way to measure the time more accurately?

Almost. Instead, the problem is solved in a slightly different way. Instead of using GPS to locate our position in three dimensions (which would in theory take three satellites), we have to also locate ourselves in a fourth dimension, time, which takes four satellites. In essence, while our devices will incorporate an error in any time observations, that time error should be pretty much the same for all of the GPS satellites that are being observed. The time error produces what is known as a dilution of precision. The more satellites that can be seen, the more precise the calculable result. Although it might seem that your GPS device or navigation program can position you precisely, it requires a considerable number of measurements from ever-moving satellites to get that precision, not to mention a fair amount of mathematics. Something worth thinking about, when you find yourself literally holding what was once a secret Department of Defense technology in the palm of your hand.

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About darlingman1970

Born in the UK and a graduate in mathematics from Cambridge University, Chris Nash has followed a career in software engineering which he continued after moving the United States in 1996 and now brings him to California in 2010. However, Chris does not want to be considered as merely a code monkey, and has always been interested in writing; in areas as diverse as factual technical manuals all the way through to fiction. An avid reader, Chris is a fan particularly of mystery novels and enjoys above all the works of Agatha Christie and David Hewson. Chris has recently gone through some significant life changes which, at the moment, he is considering as the basis for a forthcoming novel and as food for thought on his blog. He manages to couple his loves of writing and technology and is particularly interested in how internet innovations have an impact on the writing and promotional process. Chris is a firm supporter of Creative Commons and other 'open' initiatives and believes strongly that such distribution mechanisms are the "right" way to handle intellectual property in an evolving digital world. Chris is a keen Nintendo DS and Wii player in his spare time, and is currently happily attached, living in the Central Coast area of California. Find him on Twitter as @darlingman1970. Don't ask him how old he is.
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