why is the requirement of a fourth satellite for calculation of posn in a GPS receiver?

Answer 1

Sorry to inform all of you that the answers up to here did miss the real point.
The first answer is completely wrong Your GPS receiver does NOT send a signal to the GPS satellites.

Then the real true answers why four satellites for position determination are used, is as follows:

To determine the exact position of the GPS receiver's location in latitude, longitude and altitude you need 3 exactly known distances from 3 satellites being in reasonable geometry to give good determination.

Now to measure those exact distances you have to measure the time it takes the signal to travel from the satellites to your receiver. The GPS satellites have high-precision atomic clocks on board that are synchronized in all satellites. Now the core of the reason for the fourth satellite: Your GPS receiver does not have a built-in high-precision atomic clock - and it can not be synchronized with the GPS satellites clocks when you switch on your receiver. Now after determining a rough non-precise position with three satellites and the built in non-precision quartz clock of your receiver the synchronization process starts and a fourth satellite is used to "over-determine" the 3D position according the non- synchronized quartz time. This results in an algorithm that determines the exact GPS system precision timing.
Now with the help of the fourth satellite the 3D position PLUS time is determined.
From now on you may loose the fourth satellite for quite some time (two or three minutes) without bad loss of position accuracy, because the once synchronized time is carried over by the temperature and drift-compensated quartz clock until a fourth satellite signal is available again to precision-synchronize the GPS receiver's time.

I hope this helps.

Answer 2

Patrick T's answer is partially right, but has a couple key errors in it. The GPS that you carry with you or have in your car is a GPS _Receiver_. It doesn't transmit anything (and thus can be used on an airplane, incidentally). By virtue of being passive, can be much smaller, use much less battery, and the same 24 satellites can service an infinite number of receivers because they do the same amount of work serving one as a thousand.

What those satellites do is, as Patrick T described, is broadcast the time very precisely. Your GPS receiver compares the time from several satellites of known position, and the difference tells the lag from when each time was broadcast. Since all radio waves travel at the same speed through the atmosphere, that time lag is proportional to the distance to the satellite. As he said, that distance can be thought as a sphere of radius [distance] around that one satellite. Do that with two sats, and the spheres should intersect at one small, elliptical plane [Think two bubbles sharing a common wall, or reduce it to two dimensions and think of two circles crossing at only two points], three sats and they should intersect at exactly one -- your position.

The problems come in the "should." There is error in GPS calculations. Atmospheric distortion, poor signal quality or obstructions of the signal, wobble, or signals bouncing off buildings and getting to your position indirectly are some of the many ways that error creeps in. The fourth satellite, and as many others as are available, help remove that error. They provide extra spheres to the intersection to make the tiny bubble of space where the spheres come together smaller, and more accurate. Also, if one satellite or sat's signal's atmospheric path is bad, the fourth and fifth sat's can help cancel out those problems.

Mostly, Patrick T. got that part right. The fourth satellite, however, doesn't give you your altitude. Four are required to give altitude, and that dimension (as opposed to North or East) does benefit the most from extra satellites. That has nothing to do with one satellite providing the altitude data, but the fact that each extra sat increases accuracy, and it takes at least four to provide enough accuracy to calculate Altitude, but it is calculated using all satellites' signals at once.

Hope that helps

Answer 3

The GPS reciever computes the distance of the receiver from each satellite.

With one satellite, the locus of distance is a sphere, and the receiver could be anywhere on that sphere.

With two satellites, the locus is the intersection of two spheres, which is always a circle. The reciever could be anywhere on that circle.

With three satellites, the locus is the intersection of that circle with a third sphere, which is exactly two points. The reciever is at one of those two points.

With the fourth satellite, the ambiguity between those two points is resolved, and the solution is complete.

Often GPS units will give you a pretty good answer with only three satellites by using the surface of the earth as the fourth sphere of location. They can do this only by guessing that your altitude is zero.

Answer 4

The long answer? Well...ok, but it will take some time, but it will be complete.

First, let's make sure we know what's going on when we use GPS. First, the device in your car sends up a signal to one of 4 satellites. This signal carries a time stamp, so when the satellite gets it, it will know exactly how long it took for the signal to reach it. Now, the signal is a form of light, just like gamma rays, radio waves, and visible light rays. Light travels at a FINITE speed (this is an important point!). Light travels at 186,000 miles per second.

Let's put it together: if you know the speed and the time, the satellite can calculate the distance your gps is. This 'radius' of however many miles, creates a big circle, with the satellite in the middle. So, with one satellite your car (or whatever) is somewhere on this very large circle. But the GPS sends this signal to a different satellite at a different distance away. This creates another radius which will cross the original circle at two points (it helps if you draw a picture).

Finally, a third satellite is used, and this time the circle will go thru one of the two intersection points previously drawn. There! Now you have your exact location...almost.

The 4th and final satellite intersects where the previous three do, but this time gives you a height. So, the 4th satellite is responsible for your ALTITUDE.

I hope that helps!

Answer 5

Strictly speaking, you don't need 4 satellites visible. But the more datum points you have to work with, the better the measurement of your position. Most modern GPS recivers are designed to track from 4 to 7 satellites.

Doug

Answer 6

Hey i am here for the first time. I came across this question and I find the replies truly helpful. I'm hoping to offer something back to the community and help others too.

Answer 7

This is a very interesting topic