GPS
Before GPS (the Global Positioning System), we relied on paper maps to find our ways to new locations. If we got lost, we would stop at a telephone booth – there were no cell phones yet – and call someone for directions.
That all changed when GPS became available on mobile phones. Today we jump in our cars, punch in the address of our destination, and let GPS guide us. We can even specify route preferences to avoid things like high-speed expressways, toll roads, and traffic jams.
The origins of GPS can be traced back to World War II. Its inventor, Dr. Ivan Getting, was originally a radar researcher at the MIT Radiation Lab. He was also familiar with Loran, a new navigation technology being developed in an adjacent wartime lab. Inspired by these experiences, Getting came up with the idea of using transmitters on satellites to determine location. If you’re interested in more details about his story, see:
Of course, satellites hadn’t been invented yet. The science fiction writer Arthur C. Clarke had started talking about the idea of using orbiting objects for communications in 1945. But It was not until 1957 that the Soviets demonstrated the ability to put an object in orbit around the earth. That satellite was called Sputnik, and it launched the space age.
The US followed suit with satellite technology. By 1973, many of the capabilities incorporated in earlier US satellites were incorporated into the NAVSTAR – Global Positioning System. A unique new feature included on each satellite was an onboard, space-ruggedized atomic clock. An atomic clock is a very accurate clock which keeps time based on the oscillation of atomic particles. The addition of the clock meant that NAVSTAR could transmit not only location information but also an accurate time signal. This basic architecture and the satellites were modernized over the decades into what we know as the GPS constellation today.
Modern GPS is composed of three segments: the space segment, the control segment, and the user segment. You are already familiar with the user segment because your smart phone is part of it. Your phone contains an antenna which can receive GPS signals. It may also be capable of receiving signals from other Global Navigation Satellite Systems (GNSS), like the European Galileo system, the Russian GLONASS system and the Chinese Beidou system.
User segment devices rely on the space segment of GPS. It’s composed of a constellation of 31 medium earth orbit (MEO) satellites that fly at an altitude of 20,200 km (12,550 miles). Coverage of the entire world requires 24 of the satellites to be simultaneously functioning. These 24 satellites are organized in 6 orbital planes, with 4 satellite slots per plane. If you are having a hard time visualizing this, go look at the pictures of the orbits at https://www.gps.gov/. The GPS constellation is designed so that every user device can always see four satellites. The signals from these four satellites allow the user device to determine its location.
The control segment consists of the global command and control network that manages the space segment. It has locations scattered around the world so it can keep an eye on the entire constellation. Its job is to monitor the health and status of the constellation, analyze its performance, and send commands and information to the satellites.
So how does GPS work? A satellite sends a GPS signal containing time and location information. Your cell phone receives it and, using its own clock, estimates the time t’ it took for the signal to arrive. With this, it can calculate its distance r’ from the satellite. This defines a spherical surface of radius r’ on which your cell phone can be located. The spherical surface determined by a second satellite’s signal intersects with the first spherical surface in a circle of possible location points. The spherical surface defined by a third satellite intersects with this circle in two possible location points. Oftentimes, one of the points can be logically eliminated so location is uniquely determined.
But GPS is designed to use four satellite signals to get a fix on location, not three. Why? We should only need to solve our system of equations for three variables – latitude, longitude, and altitude – right? Wrong. We also need to determine the correct time, just like we talked about with Loran last week. In that case, the navigator needed an extra signal because his clock wasn’t synchronized with the clocks of the Loran transmitters.
Now your cell phone is the navigator. Its non-atomic clock is not synchronized with the satellites’ very accurate atomic clocks. So the distance your cell phone calculates to each satellite is inaccurate and actually looks like a spherical shell of thickness x’. The intersection of two of these shells looks like a washer with a thickness y’. The intersection of three of these spheres looks like two line segments. Your cell phone needs the fourth satellite, and its spherical shell of some thickness, to intersect with these two line segments to disambiguate your location. The geometry is a little complicated, but you get the idea.
So now we understand a bit about GPS. But why does this subject of time keep coming up?
Time has always been important. Way back in 1675, King Charles II established a Royal Observatory – for astronomy, time and navigation – to support English explorers’ efforts to travel to new lands and open up new markets. By 1818, this observatory had been transferred to the Admiralty because it was seen as an essential element for a successful navy. Come back next week, and we’ll devote our blog to a discussion about time and timekeeping in America down to our modern era.