Introduction:

Our ancestors had to go to pretty extreme measures to keep from getting lost. They erected monumental landmarks, laboriously drafted detailed maps and learned to read the stars in the night sky.

Things are much, much easier today. For less than $100, you can get a pocket-sized gadget that will tell you exactly where you are on Earth at any moment. As long as you have a GPS receiver and a clear view of the sky, you'll never be lost again.

The Global Positioning System (GPS) is actually a constellation of 27 Earth-orbiting satellites (24 in operation and three extras in case one fails). The U.S. military developed and implemented this satellite network as a military navigation system, but soon opened it up to everybody else.

Each of these 3,000- to 4,000-pound solar-powered satellites circles the globe at about 12,000 miles (19,300 km), making two complete rotations every day. The orbits are arranged so that at any time, anywhere on Earth, there are at least four satellites "visible" in the sky.

A GPS receiver's job is to locate four or more of these satellites, figure out the distance to each, and use this information to deduce its own location. This operation is based on a simple mathematical principle called trilateration. To understand it, will start from 2D Trilateration and then move to 3D Trilateration.

2-D Trilateration

Imagine that you are lost somewhere in Gujarat. You ask someone and figure out that you are 60 km away from Vadodara. But that cannot locate your position by itself as you can be anywhere on the radius of 60 km from Vadodara. Than you figured out that you are 45 km away from Nadiad. That might help you to locate your position. As you can see in the picture, you have two possible locations where you can be. Now to get the exact location out of two, you need a third reference. For the third reference, you figured out that you are 200 km away from Surat, you can eliminate one of the possibilities and figure out the exact location.

3-D Trilateration

Fundamentally, three-dimensional trilateration isn't much different from two-dimensional trilateration, but it's a little trickier to visualize. Imagine the radii from the previous examples going off in all directions. So instead of a series of circles, you get a series of spheres.

If you know you are 10 miles from satellite A in the sky, you could be anywhere on the surface of a huge, imaginary sphere with a 10-mile radius. If you also know you are 15 miles from satellite B, you can overlap the first sphere with another, larger sphere. The spheres intersect in a perfect circle. If you know the distance to a third satellite, you get a third sphere, which intersects with this circle at two points.

The Earth itself can act as a fourth sphere -- only one of the two possible points will actually be on the surface of the planet, so you can eliminate the one in space. Receivers generally look to four or more satellites, however, to improve accuracy and provide precise altitude information.

In order to make this simple calculation, then, the GPS receiver has to know two things: * The location of at least three satellites above you * The distance between you and each of those satellites

The GPS receiver figures both of these things out by analyzing high frequency, low-power radio signals from the GPS satellites. Better units have multiple receivers, so they can pick up signals from several satellites simultaneously.

Radio waves are electromagnetic energy, which means they travel at the speed of light (about 186,000 miles per second, 300,000 km per second in a vacuum). The receiver and satellite has to work together to figure out how far the signal has traveled.

GPS Calculations

GPS receiver calculates the distance to GPS satellites by timing a signal's journey from satellite to receiver.

At a particular time (let's say midnight), the satellite begins transmitting a long, digital pattern called a…