How GPS works?


GPS- Global Positioning System

GPS became the integral part of our life. We can see few useful applications as examples. GPS is a really interesting technology uses a system of 24 satellites. Continuously orbiting the earth and requires at least four satellites to track your location.

It uses an atomic clock and time error of mobile phone also a matter of great concern. Moreover Albert Einstein theory of reality is important role in GPS technology.

Let’s assume friend wants to find out your location you have mobile phone which has a integrated GPS receiver. In GPS interesting mathematical technique called Transliteration is used to locate someone’s position. Let’s understand transliteration in 2D-way at least two satellites are required to find out the position in 2D transliteration using engineering techniques satellite measure the distance between you and satellites.

How GPS works? How GPS works?

Now the first satellite knows your distance of R1. You somewhere in the circle (red) second satellite know the distance of R2. You should be in the yellow circle this means your actual location is satisfied both these circles. In short you should be in intersection points.

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How GPS works?

Now there is a small issue two intersection points. This is your final position. As this consider earth surface as third circle and eliminate the improbable solution. In third dimensional world you can also use same approach. Here it requires three satellites. In 3D world we were somewhere in a world with use on second satellite your position Nero downs the circle.

How GPS works?

Now intersection of two spheres forms a circle. Now with the help of third satellite you will be Nero down your location just two points.

How GPS works?

Here intersection of circle and sphere gives two points by using earth as fourth phase we find the correct   points with special coordinates.

Let’s us see how distance between you and satellite is measured.

All satellites are kept to the very atomic clock. The satellite sends a radio signal to the earth. This radio signal contain the exact time the signal was sent and position of the satellite.

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How GPS works?

Assume the receiver has very accurate clock. The receiver on the earth receives the signal. A typically smart phone GPS receiver is shown in diagram.

How GPS works?

Since radio waves travels a speed of light your receiver receives the signal after certain time duration by finding the difference between the sent time and received time multiply by the speed of the light. We will find out the distance between you and satellite.

Distance = (t2-t1)*C

How GPS works?

Since the satellite already sends to your coordinates you can easily build sphere around the satellites center point and find out your position explained before. One thing in time measurement should be very accurate even in error of microsecond error in the range of kilometer. Since the speed of light is very huge.

Here comes the main issue your receiver has not having very accurate clock. Your mobile phones and laptops were having crystal clocks that are not accurate as atomic clocks. Having an atomic clock in smartphone is simply impractical. You can see how inaccurate your smart phone is compared to atomic clock by checking the time setting.

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We called the difference between the actual the actual time and the time measured by a mobile phone as time offset. This time offset will cause huge error in GPS calculations.

How GPS works?

Here we overcome this issue the good news is the time offset of your smart phone with offset the three satellites is same. Since satellite keeps the same time

How GPS works?

The time offset of your dives becomes new or known. This means about three special coordinates have to solve the time offset value of the receiver. We need the extra satellite to solve the fourth unknown. That’s why we need four satellite to measure your location.

If you check your GPS constellation it will be clear that at least four satellites can see your location at any point on time.

Even all these technologies GPS will not give your right location.

Here it comes the Einstein’s theory of relativity time is not absolute it depends on many other factors.

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According to theory of special relativity fast moving clock slow down atomic clock moves under a speed of 14000km/hr will slow down by 7ms/day every day to do this.

At attitude of 20000 kms about the earth the satellite experience one quarter of earth’s gravity. Generally relativity theory clock will takes slightly faster. In this case around 45 microsecond/day this means the 38 microsecond/day offset is created every day in the atomic clock. To compensate for this theory of relativity is integrated in the computer chips at just the rate of atomic clocks without this application of theory of relativity GPS produced an error of 10 km/day.

GPS is the navigation system developed by US department of defence. This completely free for the public

Does GPS require any internet connection?

GPS does not require an internet or cell phone signal. However with their help the GPS start-up can be speeded up satellite information can be downloaded internet.

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