In this era of smartphones most of us will be familiar with GPS (Global Positioning System).It helps us in position tracking and navigation. But did you ever wonder how GPS works?. GPS was built by the US military and has been fully operational since 1995. Now countries like Russia(GLONASS), China, India(IRNSSnot fully operational) and European union possess their own positioning and navigation systems. GPS uses a lot of complex technologies, but basic concept is simple.
There are three parts for GPS system: A 24 to 32 solarpowered satellites orbiting the earth in orbits at an altitude of approximately 20000 kilometers(24 satellites are operational at a time), a control station and a GPS receivers such as the one in a car or a GPS enabled smartphone.
The Basic principle behind GPS: trilateration
GPS system uses a mathematical principle called trilateration to locate position. The orbits of satellites are designed so that there are always 46 satellites in view, from most places on the earth. At least signals from three satellites are needed to carry out trilateration process.
2D illustration of trilateration
Let us assume you are lost some where in Australia. One of your friend in Adelaide told you,you are 650 kms away from him, which means you could be any where on the circle with radius 650 kms and centre Adelaide.

Fig1 
Like that Another friend from Sydney told you, you are 700 kms away from him. Now you know you are on either point p1 or p2 (marked in below figure).

Fig2 
If a third friend told you ,you are 1400 kms from Brisbane ,you can locate your position with respect to three cities. Your position will be intersection point of three circles.(Fig3)

Fig3 
This method of locating position is called trilateration. This same concept works in 3 dimension. But , instead of circles you should think in terms of spheres.
Trilateration in 3D space
Assume 3 satellites are visible to your GPS receiver. Name them A,B and C. If you know your distance from A , you could be anywhere on the surface of a huge sphere of that radius.

Fig1 
If you know your distance from satellite B you can overlap 1st sphere with 2nd and they intersect in a perfect circle. Now you know you are somewhere on circle.

Fig2 
So If you know distance to a third satellite C you got a third sphere which intersects with this circle at to points. And earth acting as fourth sphere ,you can eliminate point in space because you are on earth.

Fig3 
If only 3 satellites are available, the GPS receiver can get an approximate position by making the assumption that you are at mean sea level. If you really are at mean sea level, the position will be reasonably accurate. In other words, it requires only 3 satellite to determine latitude and longitude with reasonable accuracy. But calculate altitude you require a fourth satellite. A modern GPS receiver will typically track all of the available satellites simultaneously, but only a selection of them will be used to calculate your position
How GPS receiver determines distance from satellites.
The GPS receiver gets a signal from each GPS satellite. The satellites transmit the exact time the signals are sent. By subtracting the time the signal was transmitted from the time it was received, the GPS can tell how far it is from each satellite. The GPS receiver also knows the exact position in the sky of the satellites, at the moment they sent their signals. So given the travel time of the GPS signals from three satellites and their exact position in the sky, the GPS receiver can determine your position in three dimensions  latitude, longitude and altitude. Distance is calculated by the formula
ts= time signal from satellite
Conventional GPS and AGPS
Conventional GPS :To determine the location of the GPS satellites two types of data are required by the GPS receiver; the almanac and the ephemeris. This data is continuously transmitted by the GPS satellites and your GPS receiver collects and stores this data. The almanac contains information about the status of the satellites and approximate orbital information. The GPS receiver uses the almanac to calculate which satellites are currently visible. Ephemeris gives very precise information about the orbit of each satellite. Your GPS receiver can use the ephemeris data to calculate the location of a satellite precisely.
AGPS(assisted GPS):GPS receiver in our cell phones are example of a AGPS. The AGPS device will use a data connection (internet connection on a cellphone) to contact an assistance server. The server can supply almanac and ephemeris data so the GPS doesn't have to wait to receive them from the satellites. This improves first locking speed considerably.
Atomic clocks
Atomic clocks are high precision clocks used in scientific applications. Since GPS satellites transmits time signal to the receivers it is important to keep precise timing equipment on board . Every single GPS satellite is home to a family of atomic clocks (typically four) that derive their time from cesium or rubidium atoms. In these clocks the energy difference between two specific atomic states is measured. When an atom changes from the highenergy state to the lower energy state, the energy difference is emitted in the form of light. The frequency, or ticking rate, of this light is what we count and how we define time. This energy difference is always the same. These clocks are so precise that it won’t lose a second for 15 billion years.
Though GPS satellites have atomic clocks that keep very precise time, it's not feasible to equip a GPS receiver with an atomic clock. However, if the GPS receiver uses the signal from a fourth satellite it can solve an equation that lets it determine the exact time, without needing an atomic clock.
Real working of GPS system is much more complex.Hope this article gave you an idea about basic navigation system,GPS satellite and their working principle.