GPS: An Overview-How does GPS trilateration work?
In this era of smartphones, most of us are familiar with GPS (Global Positioning System). It helps us with position tracking and navigation. But have you ever wondered how GPS works? GPS was built by the US military and has been fully operational since 1995. Now, countries like Russia (GLONASS), China, India (IRNSS – not fully operational), and the European Union possess their own positioning and navigation systems. While GPS uses a lot of complex technologies, the basic concept is simple.a technique called trilateration.
There are three parts to the GPS system:
- A constellation of 24 to 32 solar-powered satellites orbiting the Earth at an altitude of approximately 20,000 kilometers (24 satellites are operational at a time).
- A control station.
- GPS receivers, such as those in cars or GPS-enabled smartphones.
The Basic Principle Behind GPS: Trilateration
GPS uses a mathematical principle called trilateration to locate positions. The orbits of satellites are designed so that there are always 4-6 satellites in view from most places on Earth. At least signals from three satellites are needed to carry out the trilateration process.
2D Illustration of Trilateration
Imagine you are lost somewhere in Australia. One of your friends in Adelaide tells you that you are 650 km away from them, which means you could be anywhere on a circle with a radius of 650 km centered on Adelaide.
Another friend from Sydney tells you that you are 700 km away from them. Now you know you are at either point P1 or P2 (marked in the figure below).
If a third friend tells you that you are 1400 km from Brisbane, you can locate your position with respect to the three cities. Your position will be the intersection point of the three circles.
This method of locating a position is called trilateration. The same concept works in three dimensions, but instead of circles, you should think in terms of spheres.
Trilateration in 3D Space
Assume three 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.
If you know your distance from satellite B, you can overlap the first sphere with the second, and they intersect in a perfect circle. Now you know you are somewhere on that circle.
If you know the distance to a third satellite C, you get a third sphere that intersects with this circle at two points. With Earth acting as a fourth sphere, you can eliminate one point in space because you are on Earth.
If only three satellites are available, the GPS receiver can get an approximate position by assuming 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 three satellites to determine latitude and longitude with reasonable accuracy. However, to 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 a 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 positions in the sky, the GPS receiver can determine your position in three dimensions – latitude, longitude, and altitude. Distance is calculated by the formula.
(D = (tr – ts)C), where:
- (tr) = time at receiver
- (ts) = time signal from satellite
- (C) = speed of light
Distance=Time*Speed
Conventional GPS and A-GPS
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.
The 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.
A-GPS (Assisted GPS)
GPS receivers in our cell phones are examples of A-GPS. The A-GPS 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 the first locking speed considerably.
Atomic Clocks
Atomic clocks are high-precision clocks used in scientific applications. Since GPS satellites transmit time signals to the receivers, it is important to keep precise timing equipment onboard. 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 high-energy 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 they 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.
In summary, GPS technology relies on a sophisticated combination of satellite data, assistance servers, and exceptionally accurate atomic clocks to provide precise location and timingnformation using trilateration principle. While satellites harness the power of atomic clocks to maintain unfaltering time signals, receivers on the ground employ mathematical solutions and supplemental data sources to overcome practical limitations. The seamless integration of these elements—orbital data, timing accuracy, and assisted connections—enables GPS to be a dependable tool in our everyday lives, guiding everything from smartphones to scientific explorations with remarkable precision.
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